Related papers: Improved Physics-informed neural networks loss fun…

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

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…

Physics-Based Loss Scaling (PBLS) is introduced for Mixed-Formulation PINNs (MF-PINNs) applied to the neutron diffusion equation. In particular, we propose a new \textit{scaled} loss function based on the material cross sections, which is…

In our recently proposed Integrated Finite Element Neural Network (I-FENN) framework (Pantidis and Mobasher, 2023) we showcased how PINNs can be deployed on a finite element-level basis to swiftly approximate a state variable of interest,…

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

Partitioned neural network functions are used to approximate the solution of partial differential equations. The problem domain is partitioned into non-overlapping subdomains and the partitioned neural network functions are defined on the…

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

The residual loss in Physics-Informed Neural Networks (PINNs) alters the simple recursive relation of layers in a feed-forward neural network by applying a differential operator, resulting in a loss landscape that is inherently different…

In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with…

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be…

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity data. PINNs incorporate all available information into a…

We report a new approach to flow field tomography that uses the Navier-Stokes and advection-diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a…

We introduce Physics Informed Symbolic Networks (PISN) which utilize physics-informed loss to obtain a symbolic solution for a system of Partial Differential Equations (PDE). Given a context-free grammar to describe the language of symbolic…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

This paper concerns solving the steady radiative transfer equation with diffusive scaling, using the physics informed neural networks (PINNs). The idea of PINNs is to minimize a least-square loss function, that consists of the residual from…

Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the…