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Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…

I will demonstrate the effectiveness of Physics-Informed Neural Networks (PINNs) in solving partial differential equations (PDEs) when training data are scarce or noisy. The training data can be located either at the boundaries or within…

Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…

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) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

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…

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…

This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two…

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

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,…

Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

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…