A machine learning framework for data driven acceleration of computations of differential equations

Autor:	Mishra, Siddhartha
Rok vydání:	2018
Předmět:	Mathematics - Numerical Analysis Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of trainable parameters. These parameters are determined in an offline training process by (approximately) minimizing suitable (possibly non-convex) loss functions by (stochastic) gradient descent methods. The proposed algorithm is designed to be always consistent with the underlying differential equation. Numerical experiments involving both linear and non-linear ODE and PDE model problems demonstrate a significant gain in computational efficiency over standard numerical methods.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1807.09519 Zobrazit plný text záznamu View this record from Arxiv