applied math

Joint Applied Math/Inverse Problems Seminar at Colorado State University

Thursday 3:00-4:00PM, Virtual on Zoom

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Zoom Meeting link  
Meeting ID: 966 1970 2488
Passcode: 376823

Spring 2022

Feb 03   Mar 10  

Feb 03   Back to top

Samy Wu Fung

Department of Applied Mathematics and Statistics, Colorado School of Mines

Title  Efficient Training of Infinite-Depth Neural Networks via Jacobian-Free Backpropagation

Abstract  A promising trend in deep learning replaces fixed depth models by approximations of the limit as network depth approaches infinity. This approach uses a portion of network weights to prescribe behavior by defining a limit condition. This makes network depth implicit, varying based on the provided data and an error tolerance. Moreover, existing implicit models can be implemented and trained with fixed memory costs in exchange for additional computational costs. In particular, backpropagation through implicit networks requires solving a Jacobian-based equation arising from the implicit function theorem. We propose a new Jacobian-free backpropagation (JFB) scheme that circumvents the need to solve Jacobian-based equations while maintaining fixed memory costs. This makes implicit depth models much cheaper to train and easy to implement. Numerical experiments on classification are provided.

Mar 10   Back to top

Chenfanfu Jiang

Department of Mathematics, University of California, Los Angeles

Title  Robust Optimization-based Solvers and Smooth Reformulations for 3D Contact

Abstract  Contact is ubiquitous and often unavoidable, and yet modeling contacting systems continues to stretch the limits of available computational tools. In part, this is due to the unique hurdles posed by contact problems. Several intricately intertwined physical and geometric factors make contact computations hard, especially in the presence of friction and nonlinear elasticity. In this talk, I will discuss our recent work on a new optimization-based finite element solver, which is constructed for mesh-based discretizations of nonlinear elastodynamic problems supporting large nonlinear deformations, implicit time-stepping with contact and friction. Built on top of a smooth barrier reformulation and a custom Newton-type optimization, it is a first-of-its-kind "plug-and-play" contact simulation framework that provides convergent and unconditionally feasible intersection-free trajectories. The method is greatly useful for applications in 3D animations, movie visual effects, and video games. The scheme also enables future studies of differentiable simulations of nonsmooth physics-constrained inverse problems in design, control, and robotics.