Related papers: Unified generalization analysis for physics inform…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

This work proposes a Physics-informed Neural Network framework with Graph Embedding (GPINN) to perform PINN in graph, i.e. topological space instead of traditional Euclidean space, for improved problem-solving efficiency. The method…

Deep neural networks (DNNs) are powerful black-box function approximators which have been shown to yield improved performance compared to traditional neural network (NN) architectures. However, black-box algorithms do not incorporate known…

We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

Neural networks, while powerful, often lack interpretability. Physics-Informed Neural Networks (PINNs) address this limitation by incorporating physics laws into the loss function, making them applicable to solving Ordinary Differential…

Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…

Physics-Informed Neural Networks (PINNs) have been shown to be an effective way of incorporating physics-based domain knowledge into neural network models for many important real-world systems. They have been particularly effective as a…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to…

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction…

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in…

As a promising framework for resolving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have received widespread attention from industrial and scientific fields. However, lack of expressive ability and…

We study the training and performance of physics-informed learning for initial and boundary value problems (IBVP) with physics-informed neural networks (PINNs) from a statistical learning perspective. Specifically, we restrict ourselves to…

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,…

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…