相关论文: Estimating Parameter Fields in Multi-Physics PDEs …

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…

Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…

In many science and engineering settings, system dynamics are characterized by governing PDEs, and a major challenge is to solve inverse problems (IPs) where unknown PDE parameters are inferred based on observational data gathered under…

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…

Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…

The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often the variability of…

Partial differential equations (PDEs) are widely used to describe relevant phenomena in dynamical systems. In real-world applications, we commonly need to combine formal PDE models with (potentially noisy) observations. This is especially…

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

Deep neural networks (DNNs) have been widely used to solve partial differential equations (PDEs) in recent years. In this work, a novel deep learning-based framework named Particle Weak-form based Neural Networks (ParticleWNN) is developed…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…

Physics-informed Machine Learning has recently become attractive for learning physical parameters and features from simulation and observation data. However, most existing methods do not ensure that the physics, such as balance laws (e.g.,…

In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug…

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…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…