Multi-Fidelity Training Reshapes Uncertainty Decomposition in Atomistic Models

Reduced-order models (ROMs) provide an efficient surrogate for complex multiscale systems, but their predictive accuracy is often compromised by truncation errors and the inadequate representation of interactions between resolved and unresolved scales. The missing effect of truncated (unresolved) scales on ROM (resolved) scales is often denoted as the closure problem. In this work, we formulate ROM closure modeling as a multi-fidelity (MF) learning problem and propose an uncertainty-aware MF framework based on conditional normalizing flow to enhance ROM predictive accuracy. The proposed approach learns a probabilistic mapping from low-fidelity (LF) ROM coefficients to high-fidelity (HF) coefficients, thereby improving predictive fidelity while quantifying the uncertainty associated with the learned closure. Two correction strategies are investigated: direct learning, in which HF coefficients are predicted directly from LF inputs, and residual learning, which learns the discrepancy between LF and HF coefficients and uses it to recover the corrected HF solution. The framework is demonstrated on a vortex merging problem governed by the two-dimensional Navier Stokes equations. Results show that both correction strategies improve ROM accuracy over uncorrected ROM, with residual learning achieving consistently better performance than direct learning. Moreover, the two proposed deep generative model-based strategies provide uncertainty quantification for the corrected ROM coefficients, which is critical for assessing prediction confidence and supporting the reliable use of ROMs in practical applications.

Deep neural networks, including large language models, have achieved remarkable performance across various tasks. However, they are prone to overconfidence during training or fine-tuning. In this work, we observe a consistent phenomenon across different models that the early model is better calibrated, while later training or fine-tuning yields marginal accuracy gains but substantially increases calibration errors. Our analysis suggests that the early model retains uncertainty awareness in both its predictions and features, which is gradually lost with continued training. To avoid training away this uncertainty awareness, we propose EUA-Cal, a novel method that exploits the Early model as an Uncertainty Anchor for Calibration. EUA-Cal introduces early prediction regularization to preserve early predictive uncertainty and prototype structure regularization to exploit uncertainty reflected in the early feature space, jointly mitigating overconfidence. Extensive experiments on image classification and multiple-choice question answering across eight diverse models demonstrate that EUA-Cal outperforms state-of-the-art calibration methods.

Diffusion models have seen wide adoption for 3D molecular generation, yet they offer no principled signal of when a generated molecule is likely to be of low quality. We propose a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. Building on a Laplace approximation of the denoising network, we measure the variability of the noise prediction across the generation trajectory. Empirically, we show that the resulting uncertainty score is informative of sample quality, exhibiting a negative correlation with established sample-level quality metrics. We further study how the proposed uncertainty score can be used to filter generated samples, improving model performance via test-time scaling.