arXiv subjects

Geoffrey F. Bomarito

Publications and source records attributed to Geoffrey F. Bomarito.

8 recordsLinked to original sources

arXiv2026

Latent Generative Modeling of Random Fields from Limited Training Data

The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative models offer a powerful tool for sampling high- or infinite-dimensional uncertainties like random fields, but their reliance on large, dense training datasets limits their applicability in contexts where sufficient data is difficult or expensive to obtain. In this work, we propose a latent-space approach to generative modeling of random fields that incorporates domain knowledge to supplement limited training data. A constraint-aware variational autoencoder (VAE) with a function decoder is first used to learn compact latent representations of continuous functions that adhere to known physical or statistical constraints, even when training data is sparse or indirect. Generative modeling is then performed in the learned latent space, decoupling constraint enforcement from the sampling process. This decoupling enables expressive multi-step generative methods to be deployed in data-limited settings where existing constrained multi-step approaches are not directly applicable. The richer latent distributions captured by the generative model also overcome limitations of standard VAEs, which rely on simple parametric priors and struggle to represent complex, multimodal, or heavy-tailed distributions over functions. Efficacy is demonstrated on two challenging applications: wind velocity field reconstruction from sparse sensors and material property inference from indirect measurements. Results show the effectiveness of incorporating domain knowledge constraints for data-limited problems and the improved sample quality and robustness of the latent generative modeling approach versus directly sampling a constrained VAE.

cs.LG↗

arXiv2026

Automated Model Tuning for Multifidelity Uncertainty Propagation in Trajectory Simulation

Multifidelity uncertainty propagation combines the efficiency of low-fidelity models with the accuracy of a high-fidelity model to construct statistical estimators of quantities of interest. It is well known that the effectiveness of such methods depends crucially on the relative correlations and computational costs of the available computational models. However, the question of how to automatically tune low-fidelity models to maximize performance remains an open area of research. This work investigates automated model tuning, which optimizes model hyperparameters to minimize estimator variance within a target computational budget. Focusing on multifidelity trajectory simulation estimators, the cost-versus-precision tradeoff enabled by this approach is demonstrated in a practical, online setting where upfront tuning costs cannot be amortized. Using a real-world entry, descent, and landing example, it is shown that automated model tuning largely outperforms hand-tuned models even when the overall computational budget is relatively low. Furthermore, for scenarios where the computational budget is large, model tuning solutions can approach the best-case multifidelity estimator performance where optimal model hyperparameters are known a priori. Recommendations for applying model tuning in practice are provided and avenues for enabling adoption of such approaches for budget-constrained problems are highlighted.

stat.CO↗

arXiv2025

Bayesian Symbolic Regression via Posterior Sampling

Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian symbolic regression that approximates the posterior distribution over symbolic expressions, enhancing robustness and enabling uncertainty quantification for symbolic regression in the presence of noise. Differing from traditional genetic programming approaches, the SMC-based algorithm combines probabilistic selection, adaptive tempering, and the use of normalized marginal likelihood to efficiently explore the search space of symbolic expressions, yielding parsimonious expressions with improved generalization. When compared to standard genetic programming baselines, the proposed method better deals with challenging, noisy benchmark datasets. The reduced tendency to overfit and enhanced ability to discover accurate and interpretable equations paves the way for more robust symbolic regression in scientific discovery and engineering design applications.

cs.LG↗

arXiv2025

BISTRO -- A Bi-Fidelity Stochastic Gradient Framework using Trust-Regions for Optimization Under Uncertainty

Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model to accelerate convergence. Most existing bi-fidelity approaches, however, exploit either design-space curvature or random-space correlation, not both. We present BISTRO - a BI-fidelity Stochastic Trust-Region Optimizer for unconstrained optimization under uncertainty through a stochastic approximation procedure. This approach exploits the curvature information of a low-fidelity objective function to converge within a basin of a local minimum of the high-fidelity model where low-fidelity curvature information is no longer valuable. The method then switches to a variance-reduced stochastic gradient descent procedure. We provide convergence guarantees in expectation under certain regularity assumptions and ensure the best-case $\mathcal{O}(1/n)$ convergence rate for stochastic optimization. On benchmark problems and a 20-dimensional space shuttle reentry case, BISTRO converges faster than adaptive sampling and variance reduction procedures and cuts computational expense by up to 29x.

math.OC↗

arXiv2024

Covariance Expressions for Multi-Fidelity Sampling with Multi-Output, Multi-Statistic Estimators: Application to Approximate Control Variates

We provide a collection of results on covariance expressions between Monte Carlo based multi-output mean, variance, and Sobol main effect variance estimators from an ensemble of models. These covariances can be used within multi-fidelity uncertainty quantification strategies that seek to reduce the estimator variance of high-fidelity Monte Carlo estimators with an ensemble of low-fidelity models. Such covariance expressions are required within approaches like the approximate control variate and multi-level best linear unbiased estimator. While the literature provides these expressions for some single-output cases such as mean and variance, our results are relevant to both multiple function outputs and multiple statistics across any sampling strategy. Following the description of these results, we use them within an approximate control variate scheme to show that leveraging multiple outputs can dramatically reduce estimator variance compared to single-output approaches. Synthetic examples are used to highlight the effects of optimal sample allocation and pilot sample estimation. A flight-trajectory simulation of entry, descent, and landing is used to demonstrate multi-output estimation in practical applications.

stat.CO↗

arXiv2021

Entropy-based adaptive design for contour finding and estimating reliability

In reliability analysis, methods used to estimate failure probability are often limited by the costs associated with model evaluations. Many of these methods, such as multifidelity importance sampling (MFIS), rely upon a computationally efficient, surrogate model like a Gaussian process (GP) to quickly generate predictions. The quality of the GP fit, particularly in the vicinity of the failure region(s), is instrumental in supplying accurately predicted failures for such strategies. We introduce an entropy-based GP adaptive design that, when paired with MFIS, provides more accurate failure probability estimates and with higher confidence. We show that our greedy data acquisition strategy better identifies multiple failure regions compared to existing contour-finding schemes. We then extend the method to batch selection, without sacrificing accuracy. Illustrative examples are provided on benchmark data as well as an application to an impact damage simulator for National Aeronautics and Space Administration (NASA) spacesuits.

stat.ME↗

arXiv2020

On the Optimization of Approximate Control Variates with Parametrically Defined Estimators

Multi-model Monte Carlo methods, such as multi-level Monte Carlo (MLMC) and multifidelity Monte Carlo (MFMC), allow for efficient estimation of the expectation of a quantity of interest given a set of models of varying fidelities. Recently, it was shown that the MLMC and MFMC estimators are both instances of the approximate control variates (ACV) framework [Gorodetsky et al. 2020]. In that same work, it was also shown that hand-tailored ACV estimators could outperform MLMC and MFMC for a variety of model scenarios. Because there is no reason to believe that these hand-tailored estimators are the best among a myriad of possible ACV estimators, a more general approach to estimator construction is pursued in this work. First, a general form of the ACV estimator variance is formulated. Then, the formulation is utilized to generate parametrically-defined estimators. These parametrically-defined estimators allow for an optimization to be pursued over a larger domain of possible ACV estimators. The parametrically-defined estimators are tested on a large set of model scenarios, and it is found that the broader search domain enabled by parametrically-defined estimators leads to greater variance reduction.

stat.CO↗

arXiv2020

Inverse Estimation of Elastic Modulus Using Physics-Informed Generative Adversarial Networks

While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations (PDEs) using auto differentiation. By relating observed data to unobserved quantities of interest through PDEs, PI-GANs allow for the estimation of underlying probability distributions without their direct measurement (i.e. inverse problems). The scalable nature of GANs allows high-dimensional, spatially-dependent probability distributions (i.e., random fields) to be inferred, while incorporating prior information through PDEs allows the training datasets to be relatively small. In this work, PI-GANs are demonstrated for the application of elastic modulus estimation in mechanical testing. Given measured deformation data, the underlying probability distribution of spatially-varying elastic modulus (stiffness) is learned. Two feed-forward deep neural network generators are used to model the deformation and material stiffness across a two dimensional domain. Wasserstein GANs with gradient penalty are employed for enhanced stability. In the absence of explicit training data, it is demonstrated that the PI-GAN learns to generate realistic, physically-admissible realizations of material stiffness by incorporating the PDE that relates it to the measured deformation. It is shown that the statistics (mean, standard deviation, point-wise distributions, correlation length) of these generated stiffness samples have good agreement with the true distribution.

eess.IV↗