A partial differential equation (PDE) involves a function $u(x_1, x_2, \dots, x_n)$ and its partial derivatives: $$ F\left(x_1, x_2, \dots, x_n, u, \frac{\partial u ...

Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended ...

Abstract: Neural operators are a class of neural networks to learn mappings between infinite-dimensional function spaces, and recent studies have shown that using neural operators to solve partial ...

Abstract: When planet bearing operates under a complex and variable environment, the fault signal is often coupled with signals from other transmission components and is influenced by the transmission ...

PDE-Transformer is a state-of-the-art neural architecture for physics simulations, specifically designed for partial differential equations (PDEs) on regular grids. This work will be presented at ICML ...