Related papers: Deep learning-based computational method for soft …

Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…

The ever-increasing data demand craves advancements in high-speed and energy-efficient computing hardware. Analog optical neural network (ONN) processors have emerged as a promising solution, offering benefits in bandwidth and energy…

Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations have been developed to simulate molecular systems, where an explicit description of changes in the electronic structure is necessary. However, QM/MM MD…

In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method (DGM) uses the PDE residual in the least-squares sense as the loss function…

Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions…

In molecular dynamics (MD), neural network (NN) potentials trained bottom-up on quantum mechanical data have seen tremendous success recently. Top-down approaches that learn NN potentials directly from experimental data have received less…

Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We introduce a…

Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…

We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved using dynamic…

This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…

This work introduces a novel deep learning-based architecture, termed the Deep Belief Markov Model (DBMM), which provides efficient, model-formulation agnostic inference in Partially Observable Markov Decision Process (POMDP) problems. The…

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving security-constrained direct current optimal power flow (SC-DCOPF) problems, which are critical for reliable and cost-effective power system operation.DeepOPF is inspired…

The multicomponent oxide solid solution is a versatile platform to tune the delicate balance between competing spin, charge, orbital, and lattice degrees of freedom for materials design and discovery. The development of compositionally…

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…

We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup…

Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform…

The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

In this paper, we present a deep learning-based (DL-based) algorithm, as a purely mathematical platform, for providing intuitive understanding of the properties of electromagnetic (EM) wave-matter interaction in nanostructures. This…

A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type principle is proposed…