Related papers: Physics-informed deep learning links geodetic data…
Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited,…
The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…
The measurement of deep water gravity wave elevations using in-situ devices, such as wave gauges, typically yields spatially sparse data. This sparsity arises from the deployment of a limited number of gauges due to their installation…
A novel deep learning technique called Physics Informed Neural Networks (PINNs) is adapted to study steady groundwater flow in unconfined aquifers. This technique utilizes information from underlying physics represented in the form of…
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.…
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…
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…
The emergence of neural networks constrained by physical governing equations has sparked a new trend in deep learning research, which is known as Physics-Informed Neural Networks (PINNs). However, solving high-dimensional problems with…
A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…
This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…
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…
A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schr\"{o}dinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution…
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…
In this paper, we study physics-informed neural networks (PINN) to approximate solutions to one-dimensional boundary value problems for linear elliptic equations and establish robust error estimates of PINN regardless of the quantities of…
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…
We propose a consistent physics-informed neural networks (CPINNs) framework for elliptic obstacle problems formulated as variational inequalities. The method is based on a mixed loss functional that is rigorously aligned with the stability…
We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…
Traditional numerical methods often struggle with the complexity and scale of modeling pollutant transport across vast and dynamic oceanic domains. This paper introduces a Physics-Informed Neural Network (PINN) framework to simulate the…