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

Test-Time Adaptation (TTA) seeks to improve model robustness under distribution shifts by adapting parameters using unlabeled target data. However, in the absence of supervision, entropy-based adaptation is fundamentally underconstrained: multiple distinct parameter updates can achieve similarly low entropy while inducing drastically different decision boundaries. This phenomenon, known as underspecification, renders standard TTA brittle and prone to collapse into spurious modes. In this work, we reinterpret TTA through a posterior-inspired lens induced by entropy minimization, where low-entropy solutions define a pseudo-likelihood over parameters. Instead of committing to a single point estimate, we introduce a particle-based diversification framework that explores multiple plausible adaptation trajectories simultaneously. Our method can be viewed as a structured exploration of multiple plausible adaptation solutions, implemented through multi-level diversification at the output, parameter, optimizer, and input levels. Crucially, the framework acts as a plug-and-play wrapper compatible with existing TTA methods. Extensive experiments on challenging benchmarks demonstrate consistent gains in stability and robustness, achieving improvements of 3-4% under mixed shifts, 2-3% with batch size one, and 1-2.5% under label shifts, outperforming state-of-the-art baselines. Our results suggest that treating TTA as a multi-hypothesis inference problem, rather than a single-point optimization task, is key to mitigating underspecification and enabling reliable real-world deployment.

This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve computational efficiency in analyses such as uncertainty quantification and optimization that require many function calls. In order to address the challenge introduced by the high dimensionality of spatio-temporal output, a dimension reduction method is first employed to map the high-dimensional output to a low-dimensional latent space. This is followed by the construction of the surrogate model in the low-dimensional space. The prediction error in the original space, which includes both the reconstruction error and surrogate model error, is evaluated using different error metrics. Based on the prediction accuracy of the surrogate model, new training points are identified for adaptive improvement of the surrogate model. We present a novel adaptive sampling technique that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model. Thermo-mechanical analysis of a gas turbine engine blade is used to analyze the effectiveness of the proposed method.

Surrogate models are often chosen during development and then left in place as new measurements arrive. That practice becomes risky when noise, input support, or physical parameters change. We asked whether such changes call for a stateful adaptive controller, or whether it is enough to validate the candidate models again on each new batch. To study this question, we built RegimeShift-Surrogates, a reproducible streaming benchmark spanning eight analytic and dynamical tasks, four stationary or shifting regimes, ten held-out seeds, and eight classical, multilayer-perceptron, and Kolmogorov-Arnold network surrogates. The confirmatory run contains 30,720 model fits and 3,200 scored deployment windows. Choosing the model with the lowest validation loss in the current window yields mean log regret 0.091 against a per-window oracle; the best fixed model chosen in hindsight yields 0.192. The paired difference is -0.101 (hierarchical bootstrap 95% CI [-0.165, -0.040]; Holm-adjusted p = 0.0469), with revalidation ahead in 26 of 32 task-scenario combinations. None of the stateful alternatives, including exponential smoothing, dual-timescale adaptation, Page-Hinkley resets, or margin gating, improves the pooled result, and delayed bias correction makes it worse. Oracle choices also differ substantially by task: k-nearest neighbors dominate the damped oscillator, vanilla KAN is often selected for two-dimensional surfaces, and MLPs lead on the Runge and Van der Pol tasks. In this benchmark, fresh validation evidence is useful; carrying old evidence forward is often not.