Search Results for « Robust Uncertainty Quantification »

Physics-informed neural networks (PINNs) have emerged as powerful tools for solving partial differential equations, but their training remains challenging due to ill-conditioned loss landscapes. While adaptive methods like Adam dominate deep learning, they exhibit instability on stiff PDEs, and second-order methods are com- putationally prohibitive. We present EPANG-Gen (Enhanced Physics-Aware Natural Gradient with Generalization), a novel optimizer that combines memory-efficient eigen- decomposition with lightweight Bayesian uncertainty quantification. EPANG-Gen in- troduces three key innovations: (1) a randomized eigenspace estimator that approx- imates Hessian curvature with O(dk) memory (k ≪ d), (2) Bayesian R-LayerNorm for per-activation uncertainty estimation, and (3) adaptive rank selection (PASA) that dynamically adjusts to problem difficulty. We evaluate EPANG-Gen on four bench- mark PDEs—Poisson 1D, Burgers’ equation, Darcy flow, and Helmholtz 2D—and on the challenging Taylor-Green vortex at Re = 100, 000, a canonical 3D turbulence problem. Results show that EPANG-Gen matches Adam’s performance on the toughest turbulent regime while eliminating the 25% catastrophic failure rate of ADOPT across 72 runs. Ablation studies confirm that eigen-preconditioning improves performance by 11–35%. The built-in uncertainty estimates provide actionable confidence metrics at negligible cost. EPANG-Gen represents the first optimizer specifically designed for geo- metric and physical AI that combines theoretical convergence guarantees with practical robustness for safety-critical applications.

The monitoring of nuclear safeguards measurements consists of verifying the coherence between the operator declarations and the corresponding inspector measurements on the same nuclear items. Significant deviations may be present in the data, as consequence of problems with the operator and/or inspector measurement systems. However, they could also be the result of data falsification. In both cases, quantitative analysis and statistical outcomes may be negatively affected by their presence unless robust statistical methods are used. This article aims to investigate the benefits deriving from the introduction of robust procedures in the nuclear safeguards context. In particular, we will introduce a robust estimator for the estimation of the uncertainty components of the measurement error model. The analysis will prove the capacity of robust procedures to limit the bias in simulated and empirical contexts to provide more sounding statistical outcomes. For these reasons, the introduction of robust procedures may represent a step forward in the still ongoing development of reliable uncertainty quantification methods for error variance estimation.

Abstract The instantaneous reproduction number ( R t ) is a key measure of the rate of spread of an infectious disease. Correctly quantifying uncertainty in R t estimates is crucial for making well-informed decisions. Popular R t estimators leverage smoothing techniques to distinguish signal from noise. Examples include EpiEstim and EpiFilter, which are both controlled by a “smoothing parameter” that is traditionally selected by users. We demonstrate that the values of these smoothing parameters are unknown, vary markedly with epidemic dynamics, and show that data-driven smoothing is crucial for accurate uncertainty quantification of R t estimates. We derive model likelihoods for the smoothing parameters in both EpiEstim and EpiFilter and develop a Bayesian framework to automatically marginalise these parameters when fitting to epidemiological time-series data. This yields novel marginal posterior predictive distributions which prove integral to rigorous model evaluation. Applying our methods, we find that default parameterisations of these widely-used estimators can negatively impact R t inference, delaying detection of epidemic growth, and misrepresenting uncertainty (typically producing overconfident estimates), with implications for public health decision-making. Our extensions mitigate these issues, provide a principled approach to uncertainty quantification, improve the robustness of real-time R t inference, and facilitate model comparison using observable quantities.

Clinical prediction models trained on heterogeneous populations may exhibit disparities in predictive performance across patient subgroups, potentially reflecting differences in data availability, feature completeness, and representation in training data. Existing fairness-aware approaches can introduce performance-fairness trade-offs and commonly optimize group-level disparities without explicitly accounting for their subgroup-specific sources, limiting both their effectiveness and their clinical interpretability. This dissertation makes two methodological contributions. The first is a collaborative learning framework that treats demographic subgroups as clients and aggregates their model parameters using strategies that encode different assumptions about group contribution. Rather than optimizing an explicit group-fairness constraint, the framework preserves and integrates subgroup-specific information to improve equity while largely maintaining subgroup predictive performance. The second contribution is the localized conformal classifier, a neighborhood-adaptive conformal prediction framework for instance-level uncertainty quantification. By calibrating prediction sets according to the density and composition of a patient's local neighborhood in the feature space, the method communicates both the model's prediction and the uncertainty associated with that individual prediction. This information is particularly consequential when predictions inform clinical decision-making. Both contributions are evaluated across three clinical prediction tasks: 30-day mortality in ICU patients with sepsis, treatment non-completion in patients with substance use disorder, and hospital readmission after surgical resection in patients with colorectal cancer. Compared with reweighting and constrained optimization, collaborative learning achieves more favorable fairness-performance trade-offs with less degradation in predictive performance, and its variants consistently appear on the Pareto frontier across all three prediction tasks. A novel difficulty decomposition framework, derived from the localized conformal classifier's calibration scores, distinguishes sources of uncertainty arising from the local neighborhood from those specific to an individual prediction. SHAP attribution reveals how collaborative learning and fairness interventions alter the feature-attribution patterns in the underlying prediction models. Surrogate regression trees trained on the localized conformal classifier's difficulty scores relate neighborhood and instance difficulty to clinical features observable at the point of care. Clinical features remain strongly associated with instance-level difficulty under collaborative learning, whereas these associations weaken substantially after reweighting and are absent in some analyses. Across all three clinical contexts, local outcome heterogeneity is the most consistent driver of neighborhood-level predictive difficulty, while proximity to the decision boundary is the principal driver of instance-level difficulty. Together, these contributions provide a framework for developing and evaluating clinical prediction models that are not only accurate, but also more equitable across patient groups and more informative about the reliability of individual predictions.

Environmental forecasting involves the use of increasingly complex models to predict the response of ecosystems to external drivers or anthropogenic pressures. An ongoing challenge in this context is to quantify and reduce uncertainties in model inputs, parameters and structure, and to understand their impact on model predictions. In this talk, I will review our current methodological framework for assessing and reducing such model uncertainties, present their application in several case studies, and discuss current limitations and issues in the field. I will argue that structural uncertainty remains one of the most challenging problems in environmental forecasting. Hybrid approaches that combine machine learning or AI with process-based modelling approaches are among the most promising candidates to address this issue. I will conclude that the consistent consideration of all uncertainties is essential for the correct interpretation of model predictions and thus forms the basis for a responsible use of models in ecological forecasting.