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Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…

A physics-informed neural network is presented for poroelastic problems with coupled flow and deformation processes. The governing equilibrium and mass balance equations are discussed and specific derivations for two-dimensional cases are…

We provide an approach enabling one to employ physics-informed neural networks (PINNs) for uncertainty quantification. Our approach is applicable to systems where observations are scarce (or even lacking), these being typical situations…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Flash floods in urban areas occur with increasing frequency. Detecting these floods would greatlyhelp alleviate human and economic losses. However, current flood prediction methods are eithertoo slow or too simplified to capture the flood…

This paper introduces for the first time, to our knowledge, a framework for physics-informed neural networks in power system applications. Exploiting the underlying physical laws governing power systems, and inspired by recent developments…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

Traditional numerical methods often struggle with the complexity and scale of modeling pollutant transport across vast and dynamic oceanic domains. This paper introduces a Physics-Informed Neural Network (PINN) framework to simulate the…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Physics-informed neural networks have gained popularity as a deep-learning based parametric partial differential equation solver. Especially for engineering applications, this approach is promising because a single neural network could…

Physics-informed neural networks have been widely applied to learn general parametric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems…

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…

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…