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We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics-informed neural network and deep Ritz methods, we propose…

Physics-Informed Neural Networks (PINNs), which integrate deep learning with physical prior knowledge, have proven to be a powerful tool for studying the dynamics of high-dimensional nonlinear systems. The present work utilizes PINNs to…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these…

We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…

In this paper, we introduce a formulation of Physics-Informed Neural Networks (PINNs), based on learning the form of the Fourier decomposition, and a training methodology based on a spread of randomly chosen boundary conditions. By training…

Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this…

Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…

Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PDEs). However, achieving stable training and obtaining…

In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle problem. Prior work…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…