A globally convergent method to accelerate topology optimization using on-the-fly model reduction

by   Masayuki Yano, et al.

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite element simulation, which dominates the computational cost, with ROMs that reduce the cost of objective function and sensitivity evaluations by orders of magnitude. To guarantee convergence, we first introduce a trust-region method that employs generalized trust-region constraints and prove it is globally convergent. We then devise a class of globally convergent ROM-accelerated topology optimization methods informed by two theories: the aforementioned trust-region theory, which identifies the ROM accuracy conditions required to guarantee the method converges to a critical point of the original topology optimization problem; a posteriori error estimation theory for project-based ROMs, which informs ROM construction procedure to meet the accuracy conditions. This leads to trust-region methods that construct and update the ROM on-the-fly during optimization; the methods are guaranteed to converge to a critical point of the original, unreduced topology optimization problem, regardless of starting point. Numerical experiments on three different structural topology optimization problems demonstrate the proposed reduced topology optimization methods accelerate convergence to the optimal design by a factor of at least two.


page 21

page 23

page 25

page 27

page 28

page 30


A globally convergent method to accelerate large-scale optimization using on-the-fly model hyperreduction: application to shape optimization

We present a numerical method to efficiently solve optimization problems...

Entropic trust region for densest crystallographic symmetry group packings

Molecular crystal structure prediction (CSP) seeks the most stable perio...

A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization

In this contribution we propose and rigorously analyze new variants of a...

Topology Optimization Methods for 3D Structural Problems: A Comparative Study

The work provides an exhaustive comparison of some representative famili...

Computing a Sparse Projection into a Box

We describe a procedure to compute a projection of w ∈ℝ^n into the inter...

IRA assisted MMC-based topology optimization method

An Iterative Reanalysis Approximation (IRA) is integrated with the Movin...

TREGO: a Trust-Region Framework for Efficient Global Optimization

Efficient Global Optimization (EGO) is the canonical form of Bayesian op...

Please sign up or login with your details

Forgot password? Click here to reset