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 M sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, U, and the total number of particles, 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 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.

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 identified.

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, while
recurrent neural networks solvers have not been extensively explored. We introduce a
reservoir computing (RC) architecture, an echo-state recurrent neural network capable
of discovering approximate solutions that satisfy ordinary differential equations (ODEs).
We suggest an approach to calculate time derivatives of recurrent neural network outputs
without 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 strongly
depends on finding the optimal hyper-parameters, which is a computationally expensive
process. We use Bayesian optimization to discover optimal sets in a high-dimensional
hyper-parameter space efficiently and numerically show that one set is robust and can
be 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 approach
by solving nonlinear systems of ODEs using a hybrid optimization method consisting of
gradient descent and Bayesian optimization. Evaluation of linear and nonlinear systems
of equations demonstrates the efficiency of the RC ODE solver.