Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

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

Predicting the evolution of systems with spatio-temporal dynamics in response to external
stimuli is essential for scientific progress. Traditional equations-based approaches leverage …

High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional
subspace. Engineering applications for modeling, characterization, design, and control of …

Abstract Implicit Neural Spatial Representation (INSR) has emerged as an effective
representation of spatially-dependent vector fields. This work explores solving time …

The method of choice for integrating the time-dependent Fokker–Planck equation (FPE) in
high-dimension is to generate samples from the solution via integration of the associated …

Training neural networks sequentially in time to approximate solution fields of time-
dependent partial differential equations can be beneficial for preserving causality and other …

Training nonlinear parametrizations such as deep neural networks to numerically
approximate solutions of partial differential equations is often based on minimizing a loss …

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 …

Herein, we offer semi− analytic numerical procedures for the 1− D Tricomi− type time−
fractional equation (T− FTTE). We consider the Jacobi− shifted polynomials as basis …