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

arXiv: https://arxiv.org/abs/2602.15820 · HTML: https://mlsanity.com/paper/2602.15820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 71 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 30 of 46)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning](https://mlsanity.com/paper/1702.08811/) (2017)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Exploiting the Intrinsic Neighborhood Structure for Source-free Domain Adaptation](https://mlsanity.com/paper/2110.04202/) (2021)
- [Test-Time Adaptable Neural Networks for Robust Medical Image Segmentation](https://mlsanity.com/paper/2004.04668/) (2020)
- [Support and Invertibility in Domain-Invariant Representations](https://mlsanity.com/paper/1903.03448/) (2019)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [DELTA: degradation-free fully test-time adaptation](https://mlsanity.com/paper/2301.13018/) (2023)
- [Beyond Model Adaptation at Test Time: A Survey](https://mlsanity.com/paper/2411.03687/) (2024)

## Abstract (arXiv)

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.