相关论文: Physics-Informed Neural Networks for Weakly Compre…

Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

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) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

We introduce a physics-informed neural network (PINNs) framework for modelling the spatial distribution of chromodynamic fields induced by quark-antiquark pairs, based on lattice Monte Carlo simulations. In contrast to conventional neural…

Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore,…

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly…

The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…

Modeling water flow in unsaturated soils is vital for describing various hydrological and ecological phenomena. Soil water dynamics is described by well-established physical laws (Richardson-Richards equation (RRE)). Solving the RRE is…

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…

Physics-informed neural networks (PINNs) have emerged as a major research focus. However, today's PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often…

Multi-fluid flows are found in various industrial processes, including metal injection molding and 3D printing. The accuracy of multi-fluid flow modeling is determined by how well interfaces and capillary forces are represented. In this…

Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the…

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…

In this article, our goal is to solve two-parameter singular perturbation problems (SPPs) in one- and two-dimensions using an adapted Physics-Informed Neural Networks (PINNs) approach. Such problems are of major importance in engineering…

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…

The Zakharov-Kuznetsov equation, originally a three dimensional mathematical model of plasma with a uniform magnetic field, is a direct extension of the KdV equation into higher dimensions and is a typical quasi-integrable system.…

Physics-Informed Neural Networks (PINNs) solve forward PDEs by minimizing residual losses from the governing equations with initial and boundary conditions, but they often struggle with discontinuities such as shocks. In contrast, finite…