Related papers: Solving Heterogeneous Agent Models with Physics-in…

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…

Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

The growing computational demands of artificial intelligence (AI) in addressing climate change raise significant concerns about inefficiencies and environmental impact, as highlighted by the Jevons paradox. We propose an attention-enhanced…

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…

In complex engineering systems such as electro-thermal-fluid coupling, rapid and accurate prediction of multi-physics fields is essential for advanced applications like digital twins and real-time condition monitoring. Traditional numerical…

This paper puts forward the vision of creating a library of neural-network-based models for power system simulations. Traditional numerical solvers struggle with the growing complexity of modern power systems, necessitating faster and more…

I will demonstrate the effectiveness of Physics-Informed Neural Networks (PINNs) in solving partial differential equations (PDEs) when training data are scarce or noisy. The training data can be located either at the boundaries or within…

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

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…

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

Neutrino oscillations provide crucial insights into fundamental particle physics, with two-flavor approximations effectively describing reactor and atmospheric phenomena. This paper investigates the application of Physics-Informed Neural…

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…

Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

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…

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

Solving partial differential equations (PDEs) using neural methods has been a long-standing scientific and engineering research pursuit. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional…