arXiv subjects

Rileigh Bandy

Publications and source records attributed to Rileigh Bandy.

4 recordsLinked to original sources

arXiv2026

Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches

Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first stage uses data assimilation to infer state and closure trajectories from observations. The second stage trains a machine learning closure model offline using the assimilated data, thereby avoiding repeated simulator calls during training. In this work, we investigate the cost and accuracy tradeoffs between embedded and staged data-driven closure modeling approaches for a synthetic epidemiological SIQR model with a nonlinear state-dependent quarantine closure. The results illustrate a practical accuracy-efficiency trade-off: for this exemplar, embedded training provides the strongest average accuracy, while the staged approach yields comparable qualitative behavior with a moderate increase in error, substantially fewer model evaluations, and improved optimization robustness.

cs.LG↗

arXiv2026

Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.

cs.CE↗

arXiv2026

Inference in the presence of model-form uncertainties: Leveraging a prediction-oriented approach to improve uncertainty characterization

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and machine learning communities have developed prediction-oriented inference approaches that provide better calibrated uncertainties and adapt to the level of misspecification present. However, these approaches have yet to be demonstrated in the context of complex scientific applications where phenomena of interest are governed by physics-based models. Such settings often involve single realizations of high-dimensional spatio-temporal data and nonlinear, computationally expensive parameter-to-observable maps. This work investigates variational prediction-oriented inference in problems exhibiting these relevant features; namely, we consider a polynomial model and a contaminant transport problem governed by advection-diffusion equations. The prediction-oriented loss is formulated as the log-predictive probability of the calibration data. We study the effects of increasing misspecification and noise, and we assess approximations of the predictive density using Monte Carlo sampling and component-wise kernel density estimation. A novel aspect of this work is applying prediction-oriented inference to the calibration of model-form uncertainty (MFU) representations, which are embedded physics-based modifications to the governing equations that aim to reduce (but rarely eliminate) model misspecification. The computational results demonstrate that prediction-oriented frameworks can provide better uncertainty characterizations in comparison to standard inference while also being amenable to the calibration of MFU representations.

cs.CE↗

arXiv2025

Hybrid Physics-Data Enrichments to Represent Uncertainty in Reduced Gas-Surface Chemistry Models for Hypersonic Flight

During hypersonic flight, air reacts with a planetary re-entry vehicle's thermal protection system (TPS), creating reaction products that deplete the TPS. Reliable assessment of TPS performance depends on accurate ablation models. New finite-rate gas-surface chemistry models are advancing state-of-the-art in TPS ablation modeling, but model reductions that omit chemical species and reactions may be necessary in some cases for computational tractability. This work develops hybrid physics-based and data-driven enrichments to improve the predictive capability and quantify uncertainties in such low-fidelity models while maintaining computational tractability. We focus on discrepancies in predicted carbon monoxide production that arise because the low-fidelity model tracks only a subset of reactions. To address this, we embed targeted enrichments into the low-fidelity model to capture the influence of omitted reactions. Numerical results show that the hybrid enrichments significantly improve predictive accuracy while requiring the addition of only three reactions.

cs.CE↗