Trust-Region Eigenvalue Filtering for Projected Newton

TL;DR

This paper presents an adaptive eigenvalue filtering strategy integrated into the Projected Newton method, improving stability and speed in deformable solid simulations by unifying different filtering approaches through trust-region ideas.

Contribution

The paper introduces a novel adaptive eigenvalue filtering approach for Projected Newton, unifying multiple strategies via trust-region concepts, with minimal implementation changes.

Findings

Outperforms stand-alone variants in deformable solid simulations

Requires only two lines of code change in existing frameworks

Effective stabilization and acceleration of optimization processes

Abstract

We introduce a novel adaptive eigenvalue filtering strategy to stabilize and accelerate the optimization of Neo-Hookean energy and its variants under the Projected Newton framework. For the first time, we show that Newton's method, Projected Newton with eigenvalue clamping and Projected Newton with absolute eigenvalue filtering can be unified using ideas from the generalized trust region method. Based on the trust-region fit, our model adaptively chooses the correct eigenvalue filtering strategy to apply during the optimization. Our method is simple but effective, requiring only two lines of code change in the existing Projected Newton framework. We validate our model outperforms stand-alone variants across a number of experiments on quasistatic simulation of deformable solids over a large dataset.