Related papers: Quantifying constraint hierarchies in Bayesian PIN…

Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically…

We propose a consistent physics-informed neural networks (CPINNs) framework for elliptic obstacle problems formulated as variational inequalities. The method is based on a mixed loss functional that is rigorously aligned with the stability…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for…

The aim of this paper is to introduce a Mapping-based Hard-constrained Physics-Informed Neural Network (MH-PINN) for efficiently and accurately solving unbounded wave problems. First, we propose a coordinate mapping technique that…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…

This study investigates the use of an unsupervised, physics-informed deep learning framework to model a one-degree-of-freedom mass-spring system subjected to a nonlinear friction bow force and governed by a set of ordinary differential…

Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited,…

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure…

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed…

Neural networks and machine learning models for uncertainty quantification suffer from limited scalability and poor reliability compared to their deterministic counterparts. In industry-scale active learning settings, where generating a…

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…

This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…

Physics-informed neural networks (PINNs) have proven an effective tool for solving differential equations, in particular when considering non-standard or ill-posed settings. When inferring solutions and parameters of the differential…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

A physics-constrained neural network is presented for predicting the optical response of metasurfaces. Our approach incorporates physical laws directly into the neural network architecture and loss function, addressing critical challenges…