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

Siddhartha Mishra

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

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arxiv 1807.09519 v1 pith:RHA7HFIJ submitted 2018-07-25 math.NA cs.LGcs.NA

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

Siddhartha Mishra This is my paper

classification math.NA cs.LGcs.NA

keywords numericalmethodscomputationsdifferentialframeworklearningmachineparameters

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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.

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