Stabilizing Test-Time Adaptation of High-Dimensional Simulation Surrogates via D-Optimal Statistics

TL;DR

This paper introduces a novel test-time adaptation framework for high-dimensional simulation surrogates using D-optimal statistics, significantly improving out-of-distribution performance with minimal computational overhead.

Contribution

It presents the first systematic approach for stable test-time adaptation in high-dimensional simulation regression problems using D-optimal statistics.

Findings

Achieved up to 7% out-of-distribution performance improvement.

Demonstrated effectiveness on SIMSHIFT and EngiBench benchmarks.

Provided a stable, principled method with negligible computational cost.

Abstract

Machine learning surrogates are increasingly used in engineering to accelerate costly simulations, yet distribution shifts between training and deployment often cause severe performance degradation (e.g., unseen geometries or configurations). Test-Time Adaptation (TTA) can mitigate such shifts, but existing methods are largely developed for lower-dimensional classification with structured outputs and visually aligned input-output relationships, making them unstable for the high-dimensional, unstructured and regression problems common in simulation. We address this challenge by proposing a TTA framework based on storing maximally informative (D-optimal) statistics, which jointly enables stable adaptation and principled parameter selection at test time. When applied to pretrained simulation surrogates, our method yields up to 7% out-of-distribution improvements at negligible computational cost. To the best of our knowledge, this is the first systematic demonstration of effective TTA for high-dimensional simulation regression and generative design optimization, validated on the SIMSHIFT and EngiBench benchmarks.