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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,…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a…

Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…

Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling…

We propose a method for estimating the magnitude distribution of an acoustic field from spatially sparse magnitude measurements. Such a method is useful when phase measurements are unreliable or inaccessible. Physics-informed neural…

In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…

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…

We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based on an arbitrary problem-specific heuristic which may depend on the network and its gradients. In particular…

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…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

We introduce PINGS (Physics-Informed Neural Network for Fast Generative Sampling), a framework that amortizes diffusion sampling by training a physics-informed network to approximate reverse-time probability-flow dynamics, reducing sampling…

Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving forward and inverse problems governed by differential equations. However, their reliability when used in ill-posed inverse problems remains poorly…

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference Methods (FDMs), require a refined mesh to obtain stable and…

Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic…

Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial…