In-situ adaptive reduction of nonlinear multiscale structural dynamics models

TL;DR

This paper introduces an in-situ, adaptive nonlinear model reduction framework that updates local reduced-order bases dynamically during simulations, significantly improving efficiency and robustness in multiscale solid mechanics computations.

Contribution

It presents a novel online adaptive approach for nonlinear model reduction using a database of local bases, enhancing accuracy and efficiency in multiscale dynamic simulations.

Findings

Achieves up to tenfold acceleration in 3D multiscale computations

Maintains high accuracy with dynamic local basis updates

Reduces offline computational costs through in-situ adaptation

Abstract

Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried parameter point lies in an unexplored region of the parameter space. This paper addresses this issue by presenting an in-situ, adaptive framework for nonlinear model reduction where computations are performed by default online, and shifted offline as needed. The framework is based on the concept of a database of local Reduced-Order Bases (ROBs), where locality is defined in the parameter space of interest. It achieves accuracy by updating on-the-fly a pre-computed ROB, and approximating the solution of a dynamical system along its trajectory using a sequence of most-appropriate local ROBs. It achieves efficiency by managing the dimension of a local ROB, and incorporating hyperreduction in the process. While sufficiently comprehensive, the framework is described in the context of dynamic multiscale computations in solid mechanics. In this context, even in a nonparametric setting of the macroscale problem and when all offline, online, and adaptation overhead costs are accounted for, the proposed computational framework can accelerate a single three-dimensional, nonlinear, multiscale computation by an order of magnitude, without compromising accuracy.