Related papers: Hamiltonian Learning via Inverse Physics-Informed …

Scientific machine learning (SciML) methods such as physics-informed neural networks (PINNs) are used to estimate parameters of interest from governing equations and small quantities of data. However, there has been little work in assessing…

Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to…

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations…

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…

In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with…

Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

Predicting the remaining useful life (RUL) of rotating machinery is critical for industrial safety and maintenance, but existing methods struggle with scarce target-domain data and unclear degradation dynamics. We propose a Meta-Learning…

Physics-informed neural networks (PINNs) have recently emerged as a promising framework for integrating data-driven learning with physical knowledge. In this work, we propose a coupled PINN approach for the joint reconstruction of indoor…

Extracting Hamiltonian parameters from available experimental data is a challenge in quantum materials. In particular, real-space spectroscopy methods such as scanning tunneling spectroscopy allow probing electronic states with atomic…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems. Recently, equivariant message…

Efficient characterization of quantum devices is a significant challenge critical for the development of large scale quantum computers. We consider an experimentally motivated situation, in which we have a decent estimate of the…

The Hessian matrix (second derivatives) encodes far richer local curvature of the potential energy surface than energies and forces alone. However, training machine-learning interatomic potentials (MLIPs) with full Hessians is often…

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

In this article, we employ multiscale physics-informed neural networks (MscalePINNs) for the inverse design of finite-size photonic materials with stealthy hyperuniform (SHU) disordered geometries. Specifically, we show that MscalePINNs can…