Related papers: Sequential learning based PINNs to overcome tempor…

PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical…

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task…

Current PINN implementations with sequential learning strategies often experience some weaknesses, such as the failure to reproduce the previous training results when using a single network, the difficulty to strictly ensure continuity and…

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

Solving the two-dimensional shallow water equations is a fundamental problem in flood simulation technology. In recent years, physics-informed neural networks (PINNs) have emerged as a novel methodology for addressing this problem. Given…

This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods…

The electromagnetic inverse scattering problem (ISP), due to its inherent strong nonlinearity and severe ill-posedness, has long been a core challenge in microwave imaging. In recent years, physics-informed neural networks (PINNs) have…

Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…

This research explores neural network-based numerical approximation of two-dimensional convection-dominated singularly perturbed problems on square, circular, and elliptic domains. Singularly perturbed boundary value problems pose…

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher differential…

Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain…

Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PDEs). However, achieving stable training and obtaining…

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…

This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite…

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…