Related papers: A hybrid physics-informed neural network for nonli…
Fractional partial differential equations (FPDEs) can effectively represent anomalous transport and nonlocal interactions. However, inherent uncertainties arise naturally in real applications due to random forcing or unknown material…
Non-linear convection-reaction-diffusion (CRD) partial differential equations (PDEs) are crucial for modeling complex phenomena in fields such as biology, ecology, population dynamics, physics, and engineering. Numerical approximation of…
Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…
Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…
Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…
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…
Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…
Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity…
In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the…
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…
We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…
Neural networks offer powerful tools to solve partial differential equations (PDEs). We present a Variational Physics-Informed Neural Network (VPINN) designed for parabolic problems. Our approach combines a classical time discretization…
We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations…
We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the…
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…
When solving time-dependent partial differential equations(PDEs), traditional physics-informed neural networks (PINNs) have inherent limitations: due to the lack of temporal causality, the network is forced to learn the later-time control…