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Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many…
We propose a new machine-learning approach for fiber-optic communication systems whose signal propagation is governed by the nonlinear Schr\"odinger equation (NLSE). Our main observation is that the popular split-step method (SSM) for…
This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional…
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive…
Molecular Dynamics - Green's Functions Reaction Dynamics (MD-GFRD) is a multiscale simulation method for particle dynamics or particle-based reaction-diffusion dynamics that is suited for systems involving low particle densities. Particles…
This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…
Frugal Machine Learning (FML) refers to the practice of designing Machine Learning (ML) models that are efficient, cost-effective, and mindful of resource constraints. This field aims to achieve acceptable performance while minimizing the…
Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Due to the complexity in many-electron…
Vortex element methods are often used to efficiently simulate incompressible flows using Lagrangian techniques. Use of the FMM (Fast Multipole Method) allows considerable speed up of both velocity evaluation and vorticity evolution terms in…
Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from…
Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of…
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…
Long sequence neural memory remains a challenging problem. RNNs and their variants suffer from vanishing gradients, and Transformers suffer from quadratic scaling. Furthermore, compressing long sequences into a finite fixed representation…
Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…