Related papers: Thermodynamically consistent physics-informed neur…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
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,…
Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are…
The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been…
Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent…
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…
We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss function so that its neural network solutions produce…
We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…
Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to…
Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…
Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
In this paper, we introduce a novel framework for combining scientific knowledge within physics-based models and recurrent neural networks to advance scientific discovery in many dynamical systems. We will first describe the use of outputs…
We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multi-body dynamics. Unlike other approaches, e.g., Fully-connected Neural Network…
Current, realistic numerical simulations of the solar atmosphere reproduce observations in a statistical sense; they do not replicate observations such as a movie of solar granulation. Inversions on the other hand reproduce observations by…
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…
We establish a unified theoretical framework addressing the stability, consistency, and convergence of neural networks under realistic training conditions, specifically, in the presence of non-IID data, geometric constraints, and embedded…
One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…
Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…
We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solving differential equations that is completely meshless. This…