Related papers: Mesh-Informed Neural Networks for Operator Learnin…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex…

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can…

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…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

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…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

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…

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 numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

Self-supervised learning methods like masked autoencoders (MAE) have shown significant promise in learning robust feature representations, particularly in image reconstruction-based pretraining task. However, their performance is often…

The residual loss in Physics-Informed Neural Networks (PINNs) alters the simple recursive relation of layers in a feed-forward neural network by applying a differential operator, resulting in a loss landscape that is inherently different…

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Spatiotemporal partial differential equations (PDEs) find extensive application across various scientific and engineering fields. While numerous models have emerged from both physics and machine learning (ML) communities, there is a growing…

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…