Seminar - Computational Mathematics

September 9, 2019
Tuesday, September 17, 2019 - 1:00pm to 2:00pm
Math Tower 154
Computational Mathematics Seminar

Title: Learning Dynamics with Neural Networks

Speaker: Tong Qin, OSU

Abstract: Recent years have seen great developments of the machine learning techniques, especially the deep learning, in areas like computer vision, signal processing, and recommendation systems. Such techniques, on the other hand, provides powerful tools for solving problems in traditional physical sciences by leveraging accumulated experimental data. In this talk, I will introduce our recent work on using neural networks to learn dynamics from data. In particular, basing on the one-step integral form of the ODEs, we propose to use the residual network (ResNet) as the basic building block for dynamics recovery. The ResNet block can be considered as an exact one-step integration for autonomous ODE systems. Then two other neural network architectures will be introduced, including the recurrent ResNet (RT-ResNet) and the recursive ResNet (RS-ResNet), both of which can be viewed as multi-step exact temporal integrations for ODEs. I will first use autonomous dynamical systems to illustrate the general framework. Extensions to dynamical systems with random or time-dependent parameters will also be discussed.

Seminar URL: https://people.math.osu.edu/xing.205/seminar.html

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