Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …

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

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful
information from multiple tasks to improve generalization performance compared to single …

Solving partial differential equations (PDEs) using numerical methods is a ubiquitous task in
engineering and medicine. However, the computational costs can be prohibitively high …

Eddy-resolving turbulence simulations are essential for understanding and controlling
complex unsteady fluid dynamics, with significant implications for engineering and scientific …

Abstract We present Basis-to-Basis (B2B) operator learning, a novel approach for learning
operators on Hilbert spaces of functions based on the foundational ideas of function …

This work introduces reduced models based on Continuous Low Rank Adaptation
(CoLoRA) that pre-train neural networks for a given partial differential equation and then …

Operator learning has become a powerful tool in machine learning for modeling complex
physical systems governed by partial differential equations (PDEs). Although Deep Operator …

Operator learning focuses on approximating mappings G†: U→ V between infinite-
dimensional spaces of functions, such as u: Ω u→ R and v: Ω v→ R. This makes it …

This paper presents a methodology to learn surrogate models of steady state fluid dynamics
simulations on meshed domains, based on Implicit Neural Representations (INRs). The …