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The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often…

Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically…

We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…

A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data…

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

We develop a self-adaptive physics-informed neural network (PINN) framework that reliably solves forward Darcy flow and performs accurate permeability inversion in heterogeneous porous media. In the forward setting, the PINN predicts…

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…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

In this study, we propose a novel approach, termed boundary integrated neural networks (BINNs), for analyzing in-plane crack problems within the framework of linear elastic fracture mechanics. The proposed approach integrates artificial…

The dynamics of one-dimensional quantum droplets and the landing applications of deep learning are recent research hotspots. In this work, we propose a novel time piecewise physics-informed neural networks (PINNs) to study complex dynamics…

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

Underwater explosion modeling faces a critical challenge of simultaneously resolving shock waves and gas-liquid interfaces, as traditional methods struggle to balance accuracy and computational efficiency. To address this, we develop a…

Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achieving accurate long-time integration for these equations…

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has…

This paper introduces scour physics-inspired neural networks (SPINNs), a hybrid physics-data-driven framework for bridge scour prediction using deep learning. SPINNs integrate physics-based, empirical equations into deep neural networks and…

Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale…

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…