Related papers: A deep neural network approach to solve the Dirac …

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…

In Changjun Fan et al. [Nature Communications https://doi.org/10.1038/s41467-023-36363-w (2023)], the authors present a deep reinforced learning approach to augment combinatorial optimization heuristics. In particular, they present results…

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…

In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…

Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

We extend our hybrid linear-method/accelerated-descent variational Monte Carlo optimization approach to excited states and investigate its efficacy in double excitations. In addition to showing a superior statistical efficiency when…

In cognitive decoding, researchers aim to characterize a brain region's representations by identifying the cognitive states (e.g., accepting/rejecting a gamble) that can be identified from the region's activity. Deep learning (DL) methods…

In this paper we consider solutions of the Dirac equation at ultra high energies. The study provides new insights including features overlooked thus far and also new ramifications.

Evaluating failure probability for complex engineering systems is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and, hence, requires numerous repeated simulations of a complex…

Deep learning offers promising new ways to accurately model aleatoric uncertainty in robotic state estimation systems, particularly when the uncertainty distributions do not conform to traditional assumptions of being fixed and Gaussian. In…

To solve the Dirac equation with the finite difference method, one has to face up to the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order…

In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…

In this article, we studied the system of (2+1) dimensional Dirac equation in time-dependent noncommutative phase-space. Exactly, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse…

When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…