@article {717951,
	title = {: Semi-supervised learning for materials discovery},
	year = {Submitted},
	abstract = {We present an artificial intelligence implementation of semi-supervisedlearning that is designed to accelerate materials discovery. The framework is composedof an autoencoder neural network architecture, which learns a low-dimensional latentrepresentation of the input materials descriptors, and a multilayer feed-forward neuralnetwork trained to map the latent representation to material properties, such as theformation energy and magnetic moment. The framework learns a representation thatis appropriate for predicting these properties. Furthermore, because unlabeled datacan be used to improve the representation learned by the autoencoder, this coupledstructure is ideally suited to tackle learning tasks that are challenging due to a sparsityof labeled data. As a concrete example, we study the performance of this approachwhen applied to the search for novel two-dimensional magnetic materials.},
	author = {Trevor David Rhone and Bethany Lusch and Marios Mattheakis and Dylan Sheils and Romakanta Bhattarai and Larson, Daniel T. and Yoshiharu Krockenberger and Efthimios Kaxiras}
}
@article {690760,
	title = {Physics-informed neural networks for quantum control},
	journal = {Phys. Rev. Lett. },
	volume = {132},
	year = {2024},
	pages = {010801 },
	abstract = {
	Quantum control is a ubiquitous research field that has enabled physicists to delve into the dynamics and features of quantum systems. In addition to steering the system, quantum control has delivered powerful applications for various atomic, optical, mechanical, and solid-state systems. In recent years, traditional control techniques based on optimization processes have been translated into efficient artificial intelligence algorithms. Here, we introduce a computational method for optimal quantum control problems via physics-informed neural networks (PINNs). We apply our methodology to open quantum systems by efficiently solving the state-to-state transfer problem with high probabilities, short-time evolution, and minimizing the power of the control. Furthermore, we illustrate the flexibility of PINNs to solve the same problem under changes in parameters and initial conditions, showing advantages in comparison with standard control techniques.

},
	url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.010801},
	author = {Ariel Norambuena and Marios Mattheakis and Francisco J. Gonzalez and Raul Coto}
}
@article {696772,
	title = {HubbardNet: Efficient Predictions of the Bose-Hubbard Model Spectrum with Deep Neural Networks},
	journal = {Phys. Rev. Research },
	volume = {5},
	year = {2023},
	pages = {043084},
	abstract = {
	We present a deep neural network (DNN) -based model (HubbardNet) to variationally find the ground-state and excited-state wave functions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with\&nbsp;M\&nbsp;sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion,\&nbsp;U, and the total number of particles,\&nbsp;N, from a single training. This approach bypasses the need to solve a new Hamiltonian for each different set of values (U,N) and generalizes well even for out-of-distribution (U,N). Using\&nbsp;HubbardNet, we identify the two ground-state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the Hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice Hamiltonians.

},
	url = {https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.043084},
	author = {Zhu, Ziyan and Marios Mattheakis and Weiwei Pan and Efthimios Kaxiras}
}
@article {698556,
	title = {Artificial intelligence guided studies of van der Waals magnets},
	journal = {Advanced Theory and Simulations},
	year = {2023},
	pages = {2300019},
	abstract = {A materials informatics framework to explore a large number of candidate van der Waals (vdW) materials is developed. In particular, in this study a large space of monolayer transition metal halides is investigated by combining high-throughput density functional theory calculations and artificial intelligence (AI) to accelerate the discovery of stable materials and the prediction of their magnetic properties. The formation energy is used as a proxy for chemical stability. Semi-supervised learning is harnessed to mitigate the challenges of sparsely labeled materials data in order to improve the performance of AI models. This approach creates avenues for the rapid discovery of chemically stable vdW magnets by leveraging the ability of AI to recognize patterns in data, to learn mathematical representations of materials from data and to predict materials properties. Using this approach, previously unexplored vdW magnetic materials with potential applications in data storage and spintronics are\&nbsp;identified.},
	url = {https://onlinelibrary.wiley.com/doi/10.1002/adts.202300019},
	author = {Trevor David Rhone and Romakanta Bhattarai and Haralambos Gavras and Bethany Lusch and Misha Salim and Marios Mattheakis and Larson, Daniel T. and Yoshiharu Krockenberger and Efthimios Kaxiras}
}
@article {680416,
	title = {Unsupervised Reservoir Computing for Solving Ordinary Differential Equations},
	journal = {International Journal on Artificial Intelligence Tools},
	volume = {32},
	number = {1},
	year = {2023},
	month = {2022},
	abstract = {
	There is a wave of interest in using physics-informed neural networks for solving differen-tial equations. Most of the existing methods are based on feed-forward networks, whilerecurrent neural networks solvers have not been extensively explored. We introduce areservoir computing (RC) architecture, an echo-state recurrent neural network capableof discovering approximate solutions that satisfy ordinary differential equations (ODEs).We suggest an approach to calculate time derivatives of recurrent neural network outputswithout using back-propagation. The internal weights of an RC are fixed, while only a lin-ear output layer is trained, yielding efficient training. However, RC performance stronglydepends on finding the optimal hyper-parameters, which is a computationally expensiveprocess. We use Bayesian optimization to discover optimal sets in a high-dimensionalhyper-parameter space efficiently and numerically show that one set is robust and canbe transferred to solve an ODE for different initial conditions and time ranges. A closed-form formula for the optimal output weights is derived to solve first-order linear equa-tions in a one-shot backpropagation-free learning process. We extend the RC approachby solving nonlinear systems of ODEs using a hybrid optimization method consisting ofgradient descent and Bayesian optimization. Evaluation of linear and nonlinear systemsof equations demonstrates the efficiency of the RC ODE solver.

},
	url = {https://www.worldscientific.com/doi/abs/10.1142/S0218213023500306},
	author = {Marios Mattheakis and Hayden Joy and Pavlos Protopapas}
}
@article {630946,
	title = {Hamiltonian neural networks for solving equations of motion},
	journal = {Phys. Rev. E},
	volume = {105},
	year = {2022},
	note = {
	The codes that reproduce the results can be found here:



	\&nbsp;



	https://github.com/mariosmat/hamiltonian_networks

or


	https://codeocean.com/capsule/2751575/tree



	\&nbsp;



	\&nbsp;



	\&nbsp;

},
	pages = {065305},
	abstract = {
	There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton{\textquoteright}s equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic H ́enon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network in order to achieve the same order of the numerical error in the predicted phase space trajectories.



	\&nbsp;

},
	url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.065305},
	author = {Marios Mattheakis and David Sondak and Akshunna S. Dogra and Pavlos Protopapas}
}
@conference {682945,
	title = {One-Shot Transfer Learning of Physics-Informed Neural Networks},
	booktitle = {ICML, workshop AI4Science},
	year = {2022},
	abstract = {Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed Neural Networks (PINNs) to tackle such problems as they provide numerous benefits over traditional numerical approaches. Despite their potential benefits for solving differential equations, transfer learning has been under explored. In this study, we present a general framework for transfer learning PINNs that results in one-shot inference for linear systems of both ordinary and partial differential equations. This means that highly accurate solutions to many unknown differential equations can be obtained instantaneously without retraining an entire network. We demonstrate the efficacy of the proposed deep learning approach by solving several real-world problems, such as first- and second-order linear ordinary equations, the Poisson equation, and the time-dependent Schrodinger complex-value partial differential equation.},
	url = {https://arxiv.org/abs/2110.11286},
	author = {Shaan Desai and Marios Mattheakis and Hayden Joy and Pavlos Protopapas and Stephen Roberts}
}
@article {680698,
	title = {Modeling the effect of the vaccination campaign on the Covid-19 pandemic},
	journal = {Chaos, Solitons and Fractals},
	volume = {154},
	year = {2022},
	month = {2021},
	pages = {111621},
	abstract = {
	Population-wide vaccination is critical for containing the SARS-CoV-2 (Covid-19) pandemic when combined with restrictive and prevention measures. In this study we introduce SAIVR, a mathematical model able to forecast the Covid-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains sev- eral parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neural network to solve the SAIVR differ- ential equations, a supervised framework then estimates the optimal conditions and parameters that best fit recent infectious curves of 27 countries. Instructed by these results, we performed an extensive study on the temporal evolution of the pandemic under varying values of roll-out daily rates, vaccine efficacy, and a broad range of societal vaccine hesitancy/denial levels. The concept of herd immunity is questioned by studying future scenarios which involve different vaccination efforts and more infectious Covid-19 variants.

},
	url = {https://www.sciencedirect.com/science/article/pii/S0960077921009759?via\%3Dihub},
	author = {Mattia Angelia and Georgios Neofotistos and Marios Mattheakis and Efthimios Kaxiras}
}
@conference {677817,
	title = {Encoding Involutory Invariance in Neural Networks},
	booktitle = {IJCNN at IEEE World Congress on Computational Intelligence},
	year = {2022},
	abstract = {
	In certain situations, Neural Networks (NN) are trained upon data that obey underlying physical symmetries. However, it is not guaranteed that NNs will obey the underlying\&nbsp;symmetry unless embedded in the network structure. In this work, we explore a special kind of symmetry where functions are invariant with respect to involutory linear/affine transformations up to parity\&nbsp;p\&nbsp;=\&nbsp;{\textpm}1. We develop mathe- matical theorems and propose NN architectures that ensure invariance and universal approximation properties. Numerical experiments indicate that the proposed mod- els outperform baseline networks while respecting the imposed symmetry. An adaption of our technique to convolutional NN classification tasks for datasets with inherent horizontal/vertical reflection symmetry has also been proposed.

},
	url = {https://arxiv.org/pdf/2106.12891.pdf},
	author = {Anwesh Bhattacharya and Marios Mattheakis and Pavlos Protopapas}
}
@conference {695800,
	title = {First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces},
	booktitle = {NeurIPS Workshop on Machine Learning and  Physical Sciences},
	year = {2022},
	month = {2022},
	publisher = {https://arxiv.org/pdf/2211.04607.pdf},
	organization = {https://arxiv.org/pdf/2211.04607.pdf},
	abstract = {
	Physics-informed neural networks have been widely applied to learn general para- metric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We apply our method to solve the hydrogen molecular ion. This is an\&nbsp;ab initio\&nbsp;deep learning method that solves the Schrödinger equation with the Coulomb potential yielding realistic wavefunctions that include a cusp at the ion positions. The neural solutions are continuous and differentiable functions of the interatomic distance and their derivatives are analytically calculated by applying automatic differentiation. Such a parametric and analytical form of the solutions is useful for further calculations such as the determination of force fields.

},
	url = {https://ml4physicalsciences.github.io/2022/files/NeurIPS_ML4PS_2022_71.pdf},
	author = {Marios Mattheakis and Gabriel R. Schleder and Larson, Daniel T. and Efthimios Kaxiras}
}
@conference {695801,
	title = {HubbardNet: Efficient Predictions of the Bose-Hubbard Model Spectrum with Deep Neural Networks},
	booktitle = {NeurIPS Workshop on Machine Learning and  Physical Sciences},
	year = {2022},
	month = {2022},
	abstract = {
	We present a deep neural network (DNN)-based model, the\&nbsp;HubbardNet, to vari- ationally solve for the ground state and excited state wavefunctions of the one- dimensional and two-dimensional Bose-Hubbard model on a square lattice. Using this model, we obtain the Bose-Hubbard energy spectrum as an analytic function of the Coulomb parameter,\&nbsp;U\&nbsp;, and the total number of particles,\&nbsp;N\&nbsp;, from a single training, bypassing the need to solve a new hamiltonian for each different input. We show that the DNN-parametrized solutions have excellent agreement with exact di- agonalization while outperforming exact diagonalization in terms of computational scaling, suggesting that our model is promising for efficient, accurate computation of exact phase diagrams of many-body lattice hamiltonians.

},
	url = {https://ml4physicalsciences.github.io/2022/files/NeurIPS_ML4PS_2022_87.pdf},
	author = {Zhu, Ziyan and Marios Mattheakis and Weiwei Pan and Efthimios Kaxiras}
}
@conference {687645,
	title = {Physics-Informed Neural Networks for Quantum Eigenvalue Problems},
	booktitle = {IJCNN at IEEE World Congress on Computational Intelligence},
	year = {2022},
	abstract = {Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained solutions are given in an analytical and differentiable form that identically satisfies the desired boundary conditions. The network optimization is data-free and depends solely on the predictions of the neural network. We introduce two physics-informed loss functions. The first, called ortho-loss, motivates the network to discover pair-wise orthogonal eigenfunctions. The second loss term, called norm-loss, requests the discovery of normalized eigenfunctions and is used to avoid trivial solutions. We find that embedding even or odd symmetries to the neural network architecture further improves the convergence for relevant problems. Lastly, a patience condition can be used to automatically recognize eigenfunction solutions. This proposed unsupervised learning method is used to solve the finite well, multiple finite wells, and hydrogen atom eigenvalue quantum problems.},
	url = {https://arxiv.org/abs/2203.00451},
	author = {Henry Jin and Marios Mattheakis and Pavlos Protopapas}
}
@article {691743,
	title = {RcTorch: a PyTorch Reservoir Computing Package with Automated Hyper-Parameter Optimization},
	journal = {arXiv paper},
	year = {2022},
	abstract = {
	Reservoir computer\&nbsp;(RC) are among the fastest to train of all neural networks, especially when they are compared to other recurrent neural networks. RC has this advantage while still handling sequential data exceptionally well. However, RC adoption has lagged other neural network models because of the model{\textquoteright}s sensitivity to its hyper-parameters (HPs). A modern unified software package that automatically tunes these parameters is missing from the literature. Manually tuning these numbers is very difficult, and the cost of traditional grid search methods grows exponentially with the number of HPs considered, discouraging the use of the RC and limiting the complexity of the RC models which can be devised. We address these problems by introducing\&nbsp;RcTorch, a\&nbsp;PyTorch\&nbsp;based RC neural network package with automated HP tuning. Herein, we demonstrate the utility of\&nbsp;RcTorchby using it to predict the complex dynamics of a driven pendulum being acted upon by varying forces. This work includes coding examples. Example Python Jupyter notebooks can be found on our GitHub repository\&nbsp;https://github.com/blindedjoy/RcTorch\&nbsp;and documentation can be found at\&nbsp;https://rctorch.readthedocs.io/.

},
	url = {https://arxiv.org/pdf/2207.05870.pdf},
	author = {Hayden Joy and Marios Mattheakis and Pavlos Protopapas}
}
@conference {695802,
	title = {Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows},
	booktitle = {NeurIPS Workshop on Machine Learning and  Physical Sciences},
	year = {2022},
	month = {2022},
	abstract = {Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning approach for PINNs and introduce a multi-head model to efficiently obtain accurate solutions to nonlinear systems of ordinary differential equations with random potentials. In particular, we apply the method to simulate stochastic branched flows, a universal phenomenon in random wave dynamics. Finally, we compare the results achieved by feed forward and GAN-based PINNs on two physically relevant transfer learning tasks and show that our methods provide significant computational speedups in comparison to standard PINNs trained from scratch.},
	url = {https://ml4physicalsciences.github.io/2022/files/NeurIPS_ML4PS_2022_181.pdf},
	author = {Raphael Pellegrin and Blake Bullwinkel and Marios Mattheakis and Pavlos Protopapas}
}
@article {678510,
	title = {Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems},
	journal = {Phys Rev. E},
	volume = {104},
	year = {2021},
	pages = {034312},
	abstract = {Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed \emph{port-Hamiltonian neural network} can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.},
	url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.034312},
	author = {Shaan Desai and Marios Mattheakis and David Sondak and Pavlos Protopapas and Stephen Roberts}
}
@article {678512,
	title = {Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systems},
	journal = {Phys. Rev. E},
	volume = {104},
	year = {2021},
	pages = {035310},
	abstract = {Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce Variational Integrator Graph Networks - a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single and many-body problems studied in recent literature. We empirically show that the improvements arise because high order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the Partitioned Runge-Kutta method.},
	url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.035310},
	author = {Shaan Desai and Marios Mattheakis and Stephen Roberts}
}
@manuascript {667984,
	title = {A New Artificial Neuron Proposal with Trainable Simultaneous Local and Global Activation Function},
	year = {2021},
	abstract = {The activation function plays a fundamental role in the artificial neural net-work learning process. However, there is no obvious choice or procedure todetermine the best activation function, which depends on the problem. Thisstudy proposes a new artificial neuron, named Global-Local Neuron, with atrainable activation function composed of two components, a global and alocal. The global component term used here is relative to a mathematicalfunction to describe a general feature present in all problem domains. Thelocal component is a function that can represent a localized behavior, like atransient or a perturbation. This new neuron can define the importance ofeach activation function component in the learning phase. Depending on theproblem, it results in a purely global, or purely local, or a mixed global and local activation function after the training phase. Here, the trigonometric sinefunction was employed for the global component and the hyperbolic tangentfor the local component. The proposed neuron was tested for problems wherethe target was a purely global function, or purely local function, or a com-position of two global and local functions. Two classes of test problems wereinvestigated, regression problems and differential equations solving. The experimental tests demonstrated the Global-Local Neuron network{\textquoteright}s superiorperformance, compared with simple neural networks with sine or hyperbolictangent activation function, and with a hybrid network that combines thesetwo simple neural networks.},
	author = {Tiago A. E. Ferreira and Marios Mattheakis and Pavlos Protopapas}
}
@conference {664610,
	title = {Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread},
	booktitle = {2020 NeurIPS Workshop on Machine Learning and the Physical Sciences},
	year = {2020},
	publisher = {NeurIPS},
	organization = {NeurIPS},
	abstract = {
	Studying the dynamics of COVID-19 is of paramount importance to understanding the efficiency of restrictive measures and develop strategies to defend against up- coming contagion waves. In this work, we study the spread of COVID-19 using a semi-supervised neural network and assuming a passive part of the population remains isolated from the virus dynamics. We start with an unsupervised neural network that learns solutions of differential equations for different modeling param- eters and initial conditions. A supervised method then solves the inverse problem by estimating the optimal conditions that generate functions to fit the data for those infected by, recovered from, and deceased due to COVID-19. This semi-supervised approach incorporates real data to determine the evolution of the spread, the passive population, and the basic reproduction number for different countries.

},
	url = {https://ml4physicalsciences.github.io/2020/files/NeurIPS_ML4PS_2020_29.pdf},
	author = {Alessandro Paticchio and Tommaso Scarlatti and Marios Mattheakis and Pavlos Protopapas and Marco Brambilla}
}
@conference {664609,
	title = {Unsupervised Neural Networks for Quantum Eigenvalue Problems},
	booktitle = {2020 NeurIPS Workshop on Machine Learning and the Physical Sciences},
	year = {2020},
	publisher = {NeurIPS},
	organization = {NeurIPS},
	abstract = {Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that identically satisfy the boundary conditions. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions. The network optimization is data-free and depends solely on the predictions. The unsupervised method is used to solve the quantum infinite well and quantum oscillator eigenvalue problems.},
	url = {https://ml4physicalsciences.github.io/2020/files/NeurIPS_ML4PS_2020_16.pdf},
	author = {Henry Jin and Marios Mattheakis and Pavlos Protopapas}
}
@magazinearticle {662331,
	title = {Riding Waves in Neuromorphic Computing},
	journal = {APS Physics},
	volume = {12},
	number = {132},
	year = {2020},
	pages = {1-3},
	abstract = {An artificial neural network incorporating nonlinear waves could help reduce energy consumption within a bioinspired (neuromorphic) computing device.},
	url = {https://physics.aps.org/articles/v13/132},
	author = {Marios Mattheakis}
}
@article {661034,
	title = {In-situ nanoscale imaging of moir{\'e} superlattices in twisted van der Waals heterostructures},
	journal = {Nature Communication},
	volume = {11},
	number = {4209},
	year = {2020},
	pages = {1-7},
	abstract = {Direct visualization of nanometer-scale properties of moir{\'e} superlattices in van der Waalsheterostructure devices is a critically needed diagnostic tool for study of the electronic and optical phenomena induced by the periodic variation of atomic structure in these complex systems. Conventional imaging methods are destructive and insensitive to the buried device geometries, preventing practical inspection. Here we report a versatile scanning probe\&nbsp; microscopy employing infrared light for imaging moir{\'e} superlattices of twisted bilayers graphene encapsulated by hexagonal boron nitride. We map the pattern using the scattering dynamics of phonon polaritons launched in hexagonal boron nitride capping layers via its interaction with the buried moir{\'e} superlattices. We explore the origin of the double-line features imaged and show the mechanism of the underlying effective phase change of the phonon polariton reflectance at domain walls. The nano-imaging tool developed provides a non-destructive analytical approach to elucidate the complex physics of moir{\'e} engineered heterostructures.},
	url = {https://www.nature.com/articles/s41467-020-18109-0},
	author = {Yue Luo and Rebecca Engelke and Marios Mattheakis and Tamagnone, Michele and Carr, Stephen and Kenji Watanabe and Takashi Taniguchi and Efthimios Kaxiras and Philip Kim and William L. Wilson}
}
@article {646667,
	title = {Electronic structure calculations of twisted multi-layer graphene superlattices},
	journal = {2D Materials},
	volume = {7},
	year = {2020},
	note = {
	Read about this work from social media articles at Harvard News \&amp; Events, PhysOrg , GrapheneCouncil , printedElectronics, nanowerk

},
	pages = {035028},
	abstract = {Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and studied, a systematic investigation of the properties of arbitrarily layered graphene assemblies is still lacking. We introduce theoretical concepts and methods for the processing of materials information, and as a case study, apply them to investigate the electronic structure of multi-layer graphene-based assemblies in a high-throughput fashion. We provide a critical discussion of patterns and trends in tight binding band structures and we identify specific layered assemblies using low-dispersion electronic bands as indicators of potentially interesting physics like strongly correlated behavior. A combination of data-driven models for visualization and prediction is used to intelligently explore the materials space. This work more generally aims to increase confidence in the combined use of physics-based and data-driven modeling for the systematic refinement of knowledge about 2D layered materials, with implications for the development of novel quantum devices.},
	url = {https://iopscience.iop.org/article/10.1088/2053-1583/ab8f62},
	author = {Tritsaris, G. A. and S. Carr and Z. Zhu and Xie, Y. and S. Torrisi and J. Tang and M.Mattheakis and D. Larson and E. Kaxiras}
}
@article {642675,
	title = {LAN -- A materials notation for 2D layered assemblies},
	journal = {J. Chem. Inf. Model. },
	year = {2020},
	note = {Read about this work from social media articles at Harvard News \&amp; Events, PhysOrg , GrapheneCouncil, printedElectronics, nanowerk},
	abstract = {Two-dimensional (2D) layered materials offer intriguing possibilities for novel physics and applications. Before any attempt at exploring the materials space in a systematic fashion, or combining insights from theory, computation and experiment, a formal description of information about an assembly of arbitrary composition is required. Here, we introduce a domain-generic notation that is used to describe the space of 2D layered materials from monolayers to twisted assemblies of arbitrary composition, existent or not-yet-fabricated. The notation corresponds to a theoretical materials concept of stepwise assembly of layered structures using a sequence of rotation, vertical stacking, and other operations on individual 2D layers. Its scope is demonstrated with a number of example structures using common single-layer materials as building blocks. This work overall aims to contribute to the systematic codification, capture and transfer of materials knowledge in the area of 2D layered materials.},
	url = {https://pubs.acs.org/doi/10.1021/acs.jcim.0c00630},
	author = {Tritsaris, Georgios A. and Xie, Yiqi and Alexander M. Rush and Carr, Stephen and Marios Mattheakis and Efthimios Kaxiras}
}
@article {648739,
	title = {NeuroDiffEq: A Python package for solving differential equations with neural networks},
	journal = {Journal of Open Source Software},
	volume = {5},
	number = {46},
	year = {2020},
	url = {https://joss.theoj.org/papers/10.21105/joss.01931},
	author = {Feiyu Chen and David Sondak and Pavlos Protopapas and Marios Mattheakis and Shuheng Liu and Devansh Agarwal and Marco Di Giovanni}
}
@article {638222,
	title = {Robust prediction of complex spatiotemporal states through machine learning with sparse sensing},
	journal = {Physics Letters A},
	volume = {384},
	year = {2020},
	month = {2020},
	pages = {126300},
	abstract = {Complex spatiotemporal states arise frequently in material as well as biological systems consisting of multiple interacting units. A specific, but rather ubiquitous and interesting example is that of {\textquotedblleft}chimeras{\textquotedblright}, existing in the edge between order and chaos. We use Machine Learning methods involving {\textquotedblleft}observers{\textquotedblright} to predict the evolution of a system of coupled lasers, comprising turbulent chimera states and of a less chaotic biological one, of modular neuronal networks containing states that are synchronized across the networks. We demonstrated the necessity of using {\textquotedblleft}observers{\textquotedblright} to improve the performance of Feed-Forward Networks in such complex systems. The robustness of the forecasting capabilities of the {\textquotedblleft}Observer Feed-Forward Networks{\textquotedblright} versus the distribution of the observers, including equidistant and random, and the motion of them, including stationary and moving was also investigated. We conclude that the method has broader applicability in dynamical system context when partial dynamical information about the system is available.},
	url = {https://www.sciencedirect.com/science/article/pii/S0375960120300992?utm_campaign=STMJ_75273_AUTH_SERV_PPUB\&utm_medium=email\&utm_dgroup=Email1Publishing\&utm_acid=-1907525791\&SIS_ID=-1\&dgcid=STMJ_75273_AUTH_SERV_PPUB\&CMX_ID=\&utm_in=DM670829\&utm_source=AC_30},
	author = {G. Barmparis and G. Neofotistos and M.Mattheakis and J. Hitzanidi and G. P. Tsironis and E. Kaxiras}
}
@article {609159,
	title = {Homogenization of plasmonic crystals: Seeking the epsilon-near-zero behavior},
	journal = {Proceedings of the Royal Society A},
	volume = {475},
	number = {2230},
	year = {2019},
	abstract = {By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell{\textquoteright}s equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host.\&nbsp; This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. By using a Drude model for the surface conductivity of the sheet, we construct a Lorentzian function that describes the effective dielectric permittivity tensor of the plasmonic crystal as a function of frequency.},
	url = {https://royalsocietypublishing.org/doi/10.1098/rspa.2019.0220},
	author = {M. Maier and M.Mattheakis and E. Kaxiras and M. Luskin and D. Margetis}
}
@conference {636171,
	title = {Graphene epsilon-near-zero plasmonic crystals},
	booktitle = {NANOCOM {\textquoteright}19 Proceedings of the Sixth Annual ACM International Conference on Nanoscale Computing and Communication},
	year = {2019},
	address = {Dublin, Ireland},
	abstract = {Plasmonic crystals are a class of optical metamaterials that consist of engineered structures at the sub-wavelength scale. They exhibit optical properties that are not found under normal circumstances in nature, such as negative-refractive-index and epsilon-near-zero (ENZ) behavior. Graphene-based plasmonic crystals present linear, elliptical, or hyperbolic dispersion relations that exhibit ENZ behavior, normal or negative-index diffraction. The optical properties can be dynamically tuned by controlling the operating frequency and the doping level of graphene. We propose a construction approach to expand the frequency range of the ENZ behavior. We demonstrate how the combination of a host material with an optical Lorentzian response in combination with a graphene\&nbsp; conductivity that follows a Drude model leads to an ENZ condition spanning a large\&nbsp; frequency range.},
	url = {https://dl.acm.org/citation.cfm?doid=3345312.3345496},
	author = {Marios Mattheakis and Matthias Maier and Wei Xi Boo and Efthimios Kaxiras}
}
@article {646816,
	title = {Physical Symmetries Embedded in Neural Networks},
	journal = {arXiv paper},
	number = {1904.08991},
	year = {2019},
	abstract = {Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations. Two fundamental challenges facing the development of neural networks in physics applications is their lack of interpretability and their physics-agnostic design. The focus of the present work is to embed physical constraints into the structure of the neural network to address the second fundamental challenge. By constraining tunable parameters (such as weights and biases) and adding special layers to the network, the desired constraints are guaranteed to be\&nbsp; satisfied without the need for explicit regularization terms. This is demonstrated on\&nbsp; supervised and unsupervised networks for two basic symmetries: even/odd symmetry of a function and energy conservation. In the supervised case, the network with embedded constraints is shown to perform well on regression problems while simultaneously obeying the desired constraints whereas a traditional network fits the data but violates the underlying\&nbsp; constraints. Finally, a new unsupervised neural network is proposed that guarantees energy conservation through an embedded symplectic structure. The symplectic neural network is used to solve a system of energy-conserving differential equations and out-performs an\&nbsp; unsupervised, non-symplectic neural network.},
	url = {https://arxiv.org/abs/1904.08991v1},
	author = {M.Mattheakis and Protopapas, P. and D. Sondak and M. Di Giovanni and E. Kaxiras}
}
@article {610525,
	title = {Machine learning with observers predicts complex spatiotemporal behavior},
	journal = {Front. Phys. - Quantum Computing },
	volume = {7},
	number = {24},
	year = {2019},
	pages = {1-9},
	abstract = {Chimeras and branching are two archetypical complex phenomena that appear in many physical systems; because of their different intrinsic dynamics, they delineate opposite non-trivial limits in the complexity of wave motion and present severe challenges in predicting chaotic and singular behavior in extended physical systems. We report on the long-term forecasting capability of Long Short-Term Memory (LSTM) and reservoir computing (RC) recurrent neural networks, when they are applied to the spatiotemporal evolution of turbulent chimeras in simulated arrays of coupled superconducting quantum interference devices (SQUIDs) or lasers, and branching in the electronic flow of two-dimensional graphene with random potential. We propose a new method in which we assign one LSTM network to each system node except for {\textquotedblleft}observer{\textquotedblright} nodes which provide continual {\textquotedblleft}ground truth{\textquotedblright} measurements as input; we refer to this method as {\textquotedblleft}Observer LSTM{\textquotedblright} (OLSTM). Wedemonstrate that even a small number of observers greatly improves the data-driven (model-free) long-term forecasting capability of the LSTM networks and provide the framework for a consistent comparison between the RC and LSTM methods. We find that RC requires smaller training datasets than OLSTMs, but the latter require fewer observers. Both methods are benchmarked against Feed-Forward neural networks (FNNs), also trained to make predictions with observers (OFNNs).},
	url = {https://www.frontiersin.org/articles/10.3389/fphy.2019.00024/full},
	author = {G. N. Neofotistos and M.Mattheakis and G. Barmparis and J. Hitzanidi and G. P. Tsironis and E. Kaxiras}
}
@article {618288,
	title = {Sensorless Node Architecture for Events Detection in Self-Powered Nanosensor Networks},
	journal = { Nano Communication Networks},
	volume = {19},
	year = {2018},
	pages = {1-9},
	abstract = {Due to size, computational and power limitations an integrated nanosensor device needs to be redesigned with a limited number of components. A sensorless event detection node can overcome these limitations where such node can be powered using energy harvested from various events. The harvested energy could also be a significant factor for events detection without using any sensors. This study presents a detailed description of a sensorless event detection node which consists of two components {\textemdash} an energy harvester and a pulse generator. We discuss the state of the art configurations for these two components. However, due to the low complexity of the nanoscale device, the pulse generator should be kept simple. We, therefore, theoretically investigate different approaches for the pulse generator to generate Surface Plasmon Polaritons (SPPs) which reasonably resemble femtoseconds long pulses in graphene. Based on our analysis, we find that SPPs can be excited using a near-field excitation method for the THz band which is simple and can produce Electromagnetic (EM) radiation with a wide range of high wavenumber. Hence, the coupling condition can be easily satisfied and consequently, the SPP wave can be excited. However, such method excites SPPs locally, which requires improvement in practice. Thus we numerically investigate how operating frequency, the doping amount of graphene and the properties of the evanescent source affect the plasmon resonance of SPPs. We also studied different evanescent sources such as electric dipole, and hexapole, and find that the former provides better SPP resonance. We also observe that through fine-tuning of the chemical potential, frequency and source phase angle, higher amplitude SPPs can be excited on graphene surface in the THz band. The proposed model can be a good candidate for a low-complexity realization of a THz pulse generator in self-powered sensorless events detection node.},
	url = {https://doi.org/10.1016/j.nancom.2018.10.005},
	author = {Najm Hassan and Marios Mattheakis and Ding, Ming}
}
@article {603571,
	title = {Emergence and dynamical properties of stochastic branching in the electronic flows of disordered Dirac solids},
	journal = {EPL},
	volume = {122},
	year = {2018},
	month = {2018},
	pages = {27003},
	abstract = {Graphene as well as more generally Dirac solids constitute two dimensional materials where the electronic flow is ultra relativistic. When a Dirac solid is deposited on a different substrate surface with roughness, a local random potential develops through an inhomogeneous charge impurity distribution. This external potential affects profoundly the charge flow and induces a chaotic pattern of current branches that develops through focusing and defocusing effects produced by the randomness of the surface. An additional bias voltage may be used to tune the branching pattern of the charge carrier currents. We employ analytical and numerical techniquesin order to investigate the onset and the statistical properties of carrier branches in Dirac solids. We find a specific scaling-type relationship that connects the physical scale for the occurrenceof branches with the characteristic medium properties, such as disorder and bias field. We usenumerics to test and verify the theoretical prediction as well as a perturbative approach that gives a clear indication of the regime of validity of the approach. This work is relevant to deviceapplications and may be tested experimentally.},
	url = {http://iopscience.iop.org/article/10.1209/0295-5075/122/27003/meta},
	author = {Marios Mattheakis and G. P. Tsironis and Efthimios Kaxiras}
}
@article {508006,
	title = {Quantum plasmons with optical-range frequencies in doped few-layer graphene},
	journal = {Phys. Rev. B},
	volume = {97},
	year = {2018},
	pages = {195435},
	abstract = {Although plasmon modes exist in doped graphene, the limited range of doping achieved by gating restricts the plasmon frequencies to a range that does not include the visible and infrared. Here we show, through the use of first-principles calculations, that the high levels of doping achieved by lithium intercalation in bilayer and trilayer graphene shift the plasmon frequencies into the visible range. To obtain physically meaningful results, we introduce a correction of the effect of plasmon interaction across the vacuum separating periodic images of the doped graphene layers, consisting of transparent boundary conditions in the direction perpendicular to the layers; this represents a significant improvement over the exact Coulomb cutoff technique employed in earlier works. The resulting plasmon modes are due to local field effects and the nonlocal response of the material to external electromagnetic fields, requiring a fully quantum mechanical treatment. We describe the features of these quantum plasmons, including the dispersion relation, losses, and field localization. Our findings point to a strategy for fine-tuning the plasmon frequencies in graphene and other two-dimensional materials.},
	url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.195435},
	author = {Shirodkar, Sharmila N. and Marios Mattheakis and Cazeaux, Paul and Prineha Narang and Marin Solja{\v c}i{\'c} and Efthimios Kaxiras}
}
@article {574931,
	title = {Universal behavior of dispersive Dirac cone in gradient-index plasmonic metamaterials},
	journal = {Phys. Rev. B},
	volume = {97},
	number = {3},
	year = {2018},
	pages = {035307},
	abstract = {We demonstrate analytically and numerically that the dispersive Dirac cone emulating an epsilon-near-zero (ENZ) behavior is a universal property within a family of plasmonic crystals consisting of two-dimensional (2D) metals. Our starting point is a periodic array of 2D metallic sheets embedded in an inhomogeneous and anisotropic dielectric host that allows for propagation of transverse-magnetic (TM) polarized waves. By invoking a systematic bifurcation argument for arbitrary dielectric profiles in one spatial dimension, we show how TM Bloch waves experience an effective dielectric function that averages out microscopic details of the host medium. The corresponding effective dispersion relation reduces to a Dirac cone when the conductivity of the metallic sheet and the period of the array satisfy a critical condition for ENZ behavior. Our analytical findings are in excellent agreement with numerical simulations.},
	url = {https://journals.aps.org/prb/accepted/58071Y18Ye81985155572d3708639adb90a646ab0},
	author = {Matthias Maier and Marios Mattheakis and Efthimios Kaxiras and Luskin, Mitchell and Dionisios Margetis}
}
@inbook {503796,
	title = {Graphene and Active Metamaterials: Theoretical Methods and Physical Properties},
	booktitle = {Nanoplasmonics - Fundamentals and Applications},
	year = {2017},
	publisher = {InTech},
	organization = {InTech},
	abstract = {
	The interaction of light with matter has triggered the interest of scientists for long time. The area of plasmonics emerges in this context through the interaction of light with valence electrons in metals. The random phase approximation in the long wavelength limit is used for analytical investigation of plasmons in three-dimensional metals, in a two-dimensional electron gas and finally in the most famous two-dimensional semi-metal, namely graphene. We show that plasmons in bulk metals as well as in a two-dimensional electron gas originate from classical laws, whereas, quantum effects appear as non-local corrections. On the other hand, graphene plasmons are purely quantum modes and, thus, they would not exist in a {\textquotedblleft}classical world{\textquotedblright}. Furthermore, under certain circumstances, light is able to couple with plasmons on metallic surfaces, forming a surface plasmon polariton, which is very important in nanoplasmonics due to its subwavelength nature. In addition, we outline two applications that complete our theoretical investigation. Firstly, we examine how the presence of gain (active) dielectrics affects surface plasmon polariton properties and we find that there is a gain value for which the metallic losses are completely eliminated resulting to lossless plasmon propagation. Secondly, we combine monolayers of graphene in a periodic order and construct a plasmonic metamaterial that provides tunable wave propagation properties, such as epsilon-near-zero behavior, normal and negative refraction.

},
	url = {https://www.intechopen.com/books/nanoplasmonics-fundamentals-and-applications/graphene-and-active-metamaterials-theoretical-methods-and-physical-properties},
	author = {M.Mattheakis and G. P. Tsironis and E. Kaxiras},
	editor = {Gregory Barbillon}
}
@conference {605839,
	title = {Amplification of surface plasmons in active nonlinear hyperbolic systems},
	booktitle = {47th European Microwave Conference (EuMC)},
	year = {2017},
	pages = {488-491},
	address = {Nuremberg, Germany},
	abstract = {In this paper, we study propagation of surface waves at a boundary of an amplifying isotropic medium and hyperbolic metamaterial. We demonstrate that the gain material can be used to counterbalance the losses in hyperbolic medium. We show that the gain-loss balance can be maintained even in the presence of nonlinear saturation leading to the surface wave amplification.},
	url = {http://ieeexplore.ieee.org/document/8230896/},
	author = {O. V. Shramkova and Marios Mattheakis and G. P. Tsironis}
}
@article {509181,
	title = {Manipulating polarized light with a planar slab of Black Phosphorus},
	journal = { Journal of Physics Communications},
	volume = {1},
	year = {2017},
	pages = {045003},
	abstract = {
	Wave polarization contains valuable information for electromagnetic signal processing; hence, the ability to manipulate it can be extremely useful in photonic devices. In this work, we propose designs solely comprised of one of the emerging and interesting two-dimensional media; Black Phosphorus. Due to substantial in-plane anisotropy, the simplest possible structure: a single slab of Black Phosphorus, can be very efficient and for manipulating the polarization state of electromagnetic waves. We propose Black Phosphorus films that filter the fields along one direction, or achieve large magnetic-free Faraday rotation, or convert linear polarization to circular; these slabs can be employed as\&nbsp; components in numerous mid-IR integrated devices.

},
	url = {http://iopscience.iop.org/article/10.1088/2399-6528/aa90c8/meta},
	author = {Constantinos A. Valagiannopoulos and Marios Mattheakis and Shirodkar, Sharmila N. and Efthimios Kaxiras}
}
@article {461001,
	title = {Epsilon-Near-Zero behavior from Plasmonic Dirac Point: theory and realization using two-dimensional materials},
	journal = {Physical Review B},
	volume = {94},
	number = {20},
	year = {2016},
	month = {2016},
	pages = {201404(R)},
	abstract = {The electromagnetic response of a two-dimensional metal embedded in a periodic array of a dielectric host can give rise to a plasmonic Dirac point that emulates Epsilon-Near-Zero (ENZ) behavior. This theoretical result is extremely sensitive to structural features like periodicity of the dielectric medium and thickness imperfections. We propose that such a device can actually be realized by using graphene as the 2D metal and materials like the layered semiconducting transition-metal dichalcogenides or hexagonal boron nitride as the dielectric host. We propose a systematic approach, in terms of design characteristics, for constructing metamaterials with linear, elliptical and hyperbolic dispersion relations which produce ENZ behavior, normal or negative diffraction.},
	url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.201404},
	author = {M.Mattheakis and C. A. Valagiannopoulos and E. Kaxiras}
}
@article {250631,
	title = {Extreme events in complex linear and nonlinear photonic media},
	journal = {Chaos, Solitons \& Fractals},
	volume = {84},
	year = {2016},
	month = {2016},
	pages = {73-80},
	abstract = {Ocean rogue waves (RW) are huge solitary waves that have for long triggered the interest of scientists. The RWs emerge in a complex environment and it is still under investigation if they are due to linear or nonlinear processes. Recent works have demonstrated that RWs appear in various other physical systems such as microwaves, nonlinear crystals, cold atoms, etc. In this work we investigate optical wave propagation in strongly scattering random lattices embedded in the bulk of transparent glasses. In the linear regime we observe the appearance of extreme waves, RW-type, that depend solely on the scattering properties of the medium. Interestingly, the addition of nonlinearity does not modify the RW statistics, while as the nonlinearities are increased multiple-filamentation and intensity clamping destroy the RW statistics. Numerical simulations agree nicely with the experimental findings and altogether prove that optical rogue waves are generated through the linear strong scattering in such complex environments.},
	url = {http://www.sciencedirect.com/science/article/pii/S0960077916000175},
	author = {M Mattheakis and I. J. Pitsios and G. P. Tsironis and S. Tzortzakis}
}
@article {313821,
	title = {Phase transition in PT symmetric active plasmonic systems},
	journal = {IEEE Journal of Selected Topics in Quantum Electronics},
	volume = {22},
	number = {5},
	year = {2016},
	month = {2016},
	pages = {1-7},
	abstract = {Surface plasmon polaritons (SPPs) are coherent electromagnetic surface waves trapped on an insulator-conductor interface. The SPPs decay exponentially along the propagation due to conductor losses, restricting the SPPs propagation length to few microns. Gain materials can be used to counterbalance the aforementioned losses. We provide an exact expression for the gain, in terms of the optical properties of the interface, for which the losses are eliminated. In addition, we show that systems characterized by lossless SPP propagation are related to PT symmetric systems. Furthermore, we derive an analytical critical value of the gain describing a phase transition between lossless and prohibited SPPs propagation. The regime of the aforementioned propagation can be directed by the optical properties of the system under scrutiny. Finally, we perform COMSOL simulations verifying the theoretical findings.},
	url = {http://ieeexplore.ieee.org/xpl/login.jsp?tp=\&arnumber=7298367\&url=http\%3A\%2F\%2Fieeexplore.ieee.org\%2Fstamp\%2Fstamp.jsp\%3Ftp\%3D\%26arnumber\%3D7298367},
	author = {M.Mattheakis and T. Oikonomou and Μ. Molina and G. P. Tsironis}
}
@inbook {250636,
	title = {Extreme waves and branching flows in optical media},
	booktitle = {Quodons in Mica: Nonlinear localized travelling excitations in crystals },
	volume = {221},
	year = {2015},
	pages = {425-454},
	publisher = {Springer},
	organization = {Springer},
	abstract = {We address light propagation properties in complex media consisting of random distributions of lenses that have specific focusing properties. We present both analytical and numerical techniques that can be used to study emergent properties of light organization in these media. As light propagates, it experiences multiple scattering leading to the formation of light bundles in the form of branches; these are random yet occur systematically in the medium, particularly in the weak scattering limit. On the other hand, in the strong scattering limit we find that coalescence of branches may lead to the formation of extreme waves of the {\textquotedblleft}rogue wave{\textquotedblright} type. These waves appear at specific locations and arise in the linear as well as in the nonlinear regimes. We present both the weak and strong scattering limit and show that these complex phenomena can be studied numerically and analytically through simple models.},
	url = {http://link.springer.com/chapter/10.1007/978-3-319-21045-2_18},
	author = {M Mattheakis and G. P. Tsironis}
}
@mastersthesis {251896,
	title = {Electromagnetic wave propagation in gradient index metamaterials, plasmonic systems and optical fiber networks},
	year = {2014},
	type = {PhD thesis},
	abstract = {Metamaterials constitute a relatively new field which is very promisingbecause it exhibits properties that may not be readily found in nature. Oneof promising lines of research is the study of novel characteristics of the prop-agation of electromagnetic (EM) waves in gradient refractive index (GRIN)lenses. In this Thesis, three geometrical optics methods as well as a wavenumerical method have been developed for the investigation of EM wavespropagation through media with certain refractive indices. Furthermore, westudy the propagation of EM waves through specific geometrical configura-tions as well as through complex random networks of GRIN lenses, such asLuneburg (LL) and Luneburg Hole (LH) lenses. We show that waveguides,which are formed by LLs, offer the capability of better controlling the prop-agation characteristics of EM waves.
In addition, we show that branchedflows and extreme events can arise in such complex photonic systems.In addition to GRIN lenses networks, we use the discrete nonlinear Schr ̈o-dinger equation to investigate the propagation of an EM wavepacket throughcertain configurations of optical fiber lattices and investigate the effects ofrandomness and nonlinearity in the diffusion exponent.
Finally, we study surface plasmon polaritons (SPPs). We investigate howthe presence of active (gain) dielectrics change the dispersion relation andenhance the propagation length of SPPs. We finally show that the use of anactive dielectric with gain, which compensates for metal absorption losses,enhances substantially the plasmon propagation.},
	url = {http://elocus.lib.uoc.gr//dlib/6/9/9/metadata-dlib-1423129321-297195-26444.tkl$\#$},
	author = {Marios Mattheakis}
}
@conference {250621,
	title = {Enhanced surface plasmon polariton propagation induced by active dielectrics},
	booktitle = {Expert from the Proceedings of the 2014 COMSOL conference in Cambridge},
	year = {2014},
	month = {17-17 Sep.},
	publisher = {COMSOL},
	organization = {COMSOL},
	address = {Cambridge, UK},
	abstract = {We present numerical simulations for the propagation of surface plasmon polaritons (SPPs) in a dielectric-metal-dielectric waveguide using COMSOL multiphysics software. We show that the use of an active dielectric with gain that compensates metal absorption losses enhances substantially plasmon propagation. Furthermore, the introduction of the active material induces, for a specific gain value, a root in the imaginary part of the propagation constant leading to infinite propagation of the surface plasmon. The computational approaches analyzed in this work can be used to define and tune the optimal conditions for surface plasmon polariton amplification and propagation.},
	url = {http://www.comsol.com/paper/enhanced-surface-plasmon-polariton-propagation-induced-by-active-dielectrics-18183},
	author = {C. Athanasopoulos and M Mattheakis and G. P. Tsironis}
}
@article {2040-8986-16-10-102003,
	title = {Small-world networks of optical fiber lattices},
	journal = {Journal of Optics},
	volume = {16},
	year = {2014},
	month = {2014},
	pages = {102003},
	abstract = {We use a simple dynamical model and explore coherent dynamics of wavepackets in complex networks of optical fibers. We start from a symmetric lattice and through the application of a Monte{\textendash}Carlo criterion we introduce structural disorder and deform the lattice into a small-world network regime. We investigate in the latter both structural (correlation length) as well as dynamical (diffusion exponent) properties and find that both exhibit a rapid crossover from the ordered to the fully random regime. For a critical value of the structural disorder parameter\&nbsp;ρ≈0.25\&nbsp;transport changes from ballistic to sub-diffusive due to the creation strongly connected local clusters and channels of preferential transport in the small world regime.},
	url = {http://stacks.iop.org/2040-8986/16/i=10/a=102003},
	author = {F Perakis and M Mattheakis and G. P. Tsironis}
}
@article {2040-8986-14-11-114006,
	title = {Luneburg lens waveguide networks},
	journal = {Journal of Optics},
	volume = {14},
	year = {2012},
	month = {2012},
	pages = {114006},
	abstract = {We investigate certain configurations of Luneburg lenses that form light propagating and guiding networks. We study single Luneburg lens dynamics and apply the single lens ray tracing solution to various arrangements of multiple lenses. The wave propagating features of the Luneburg lens networks are also verified through direct numerical solutions of Maxwell{\textquoteright}s equations. We find that Luneburg lenses may form efficient waveguides for light propagation and guiding. The additional presence of nonlinearity improves the focusing characteristics of the networks.},
	url = {http://stacks.iop.org/2040-8986/14/i=11/a=114006},
	author = {M M Mattheakis and G. P. Tsironis and V I Kovanis}
}
