相关论文: Physics-Informed Neural Networks for Discovering L…

Physics-informed neural networks (PINNs) have attracted a lot of attention in scientific computing as their functional representation of partial differential equation (PDE) solutions offers flexibility and accuracy features. However, their…

The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical…

Physics-Informed Neural Networks (PINNs) have recently emerged as a novel approach to simulate complex physical systems on the basis of both data observations and physical models. In this work, we investigate the use of PINNs for various…

Shear wave elastography (SWE) enables the measurement of elastic properties of soft materials, including soft tissues, in a non-invasive manner and finds broad applications in a variety of disciplines. The state-of-the-art SWE methods…

Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…

The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs. We propose a modularized approach and study the choices of…

Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…

Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…

Given their ability to effectively learn non-linear mappings and perform fast inference, deep neural networks (NNs) have been proposed as a viable alternative to traditional simulation-driven approaches for solving high-dimensional…

Physics-informed neural networks (PINNs) have recently emerged as effective methods for solving partial differential equations (PDEs) in various problems. Substantial research focuses on the failure modes of PINNs due to their frequent…

Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical…

The perturbation theory is developed for joint statistics of the advanced and retarded Green's functions of the 1D Schrodinger equation with a piecewise-constant random potential. Using this method, analytical expressions are obtained for…

Physics-Informed Neural Networks (PINNs) have become a prominent application of deep learning in scientific computation, as they are powerful approximators of solutions to nonlinear partial differential equations (PDEs). There have been…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism…

The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity…