Related papers: Noise-aware Physics-informed Machine Learning for …

Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

For Prognostics and Health Management (PHM) of Lithium-ion (Li-ion) batteries, many models have been established to characterize their degradation process. The existing empirical or physical models can reveal important information regarding…

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the…

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…

Variational quantum algorithms are promising for near-term quantum computing, but are severely limited by hardware noise and the substantial circuit overhead required for error mitigation methods such as Zero-Noise Extrapolation (ZNE). We…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical constraints into the loss function. However, standard optimizers such as Adam often…

Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity…

In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…

Atomic resolution STEM images often suffer from noise due to low electron doses and instrument imperfections, hence it is challenging to obtain critical structural details required for material analysis. To address the problem, we propose a…

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

Physics-informed neural network (PINN) has been a prevalent framework for solving PDEs since proposed. By incorporating the physical information into the neural network through loss functions, it can predict solutions to PDEs in an…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…