Physics-informed machine-learning (PIML) enables the integration of domain knowledge
with machine learning (ML) algorithms, which results in higher data efficiency and more …

In this article, we propose physics-informed neural operators (PINO) that combine training
data and physics constraints to learn the solution operator of a given family of parametric …

The classical development of neural networks has primarily focused on learning map**s
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

Time-dependent partial differential equations (PDEs) are ubiquitous in science and
engineering. Recently, mostly due to the high computational cost of traditional solution …

Numerical simulation of fluids plays an essential role in modeling many physical
phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well …

One of the most promising applications of machine learning in computational physics is to
accelerate the solution of partial differential equations (PDEs). The key objective of machine …

This paper explores the recent advancements in enhancing Computational Fluid Dynamics
(CFD) tasks through Machine Learning (ML) techniques. We begin by introducing …

Abstract Machine learning models are gaining increasing popularity in the domain of fluid
dynamics for their potential to accelerate the production of high-fidelity computational fluid …

Partial differential equations (PDEs) see widespread use in sciences and engineering to
describe simulation of physical processes as scalar and vector fields interacting and …

This digital book contains a practical and comprehensive introduction of everything related
to deep learning in the context of physical simulations. As much as possible, all topics come …