FD-Net with Auxiliary Time Steps: Fast Prediction of PDEs using Hessian-Free Trust-Region Methods

Sila Gulgec, Zheng Shi, Neil Deshmukh, Shamim N Pakzad, Martin Takáč
October, 2019 Research, Academic Space
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Image credit: FD-Net

Abstract

Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate future dynamical behavior. The methodology designs the filter sizes such that they mimic the finite difference between the neighboring points. By learning the governing equation, the network predicts the future evolution of the solution by using only a few trainable parameters. In this paper, we provide numerical results to compare the efficiency of the second-order Trust-Region Conjugate Gradient (TRCG) method with the first-order ADAM optimizer.

Type
Conference paper
Publication
NeurIPS 2019 Workshop (Beyond First Order Methods in ML)
Deep Learning Adaptive Algorithms
Zheng Shi
Zheng Shi
Team Lead, Data Science | Ph.D., Machine Learning & Optimization

Deep Learning, Machine Learning, Optimization Algorithms, and Data Science.