Related papers: Physics-informed neural networks for solving funct…

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…

We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…

Recent developments in acoustic signal processing have seen the integration of deep learning methodologies, alongside the continued prominence of classical wave expansion-based approaches, particularly in sound field reconstruction.…

The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…

With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

The equilibrium reconstruction of plasma is a core step in real-time diagnostic tasks in fusion research. This paper explores a multi-stage Physics-Informed Neural Networks(PINNs) approach to solve the Grad-Shafranov equation, achieving…

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…

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…

A physics-informed neural network (PINN) is developed, for the first time, to learn the time-dependent quasi-static magnetohydrodynamic (MHD) equations in axisymmetric tokamak geometry, without any experimental or synthetic data. The…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating…

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their…