Kyla D. Jones | Searcharxiv

arXiv2026

Bayesian reversal of the liquid level trajectory in a draining tank for pollution forensics

Storage tanks for hazardous liquids are common in industry and agriculture. During a pollution incident, liquid may drain from a storage tank through a small hole, crack, or pipe. After containing the leak, estimating the discharged volume of liquid is essential for public safety, regulatory assessment, and remediation. When the original inventory of liquid is unknown, this constitutes an inverse problem. In this work, we present a framework for inferring the initial liquid level in a partially drained tank from the observed final liquid level after a pollution incident and an estimate of the drainage duration. Because the drainage dynamics, model parameters, and observations are uncertain, we employ Bayesian statistical inversion to combine prior physical knowledge with experimental liquid level time series data to predict the initial liquid level with quantified uncertainty. We use a physics-based model based on Torricelli's law to describe the tank-draining dynamics and augment it with an empirical discrepancy function to account for missing or imperfectly modeled physics. In our experiments with a tank draining of water, we found that our inferred initial liquid level was accurate, although uncertainty increased with drainage duration. Beyond its application to pollution forensics, this work may also serve as a hands-on classroom project illustrating dynamic modeling, model discrepancy, and Bayesian inference.

stat.AP↗

arXiv2026

BITS for GAPS: Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates

We introduce Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates (BITS for GAPS), a framework enabling information-theoretic experimental design of Gaussian process-based surrogate models. Unlike standard methods, which use fixed or point-estimated hyperparameters in acquisition functions, our approach propagates hyperparameter uncertainty into the sampling criterion through Bayesian hierarchical modeling. In this framework, a latent function receives a Gaussian process prior, while hyperparameters are assigned additional priors to capture the modeler's knowledge of the governing physical phenomena. Consequently, the acquisition function incorporates uncertainties from both the latent function and its hyperparameters, ensuring that sampling is guided by both data scarcity and model uncertainty. We further establish theoretical results in this context: a closed-form approximation and a lower bound of the posterior differential entropy. We demonstrate the framework's utility for hybrid modeling with a vapor-liquid equilibrium case study. Specifically, we build a surrogate model for latent activity coefficients in a binary mixture. We construct a hybrid model by embedding the surrogate into an extended form of Raoult's law. This hybrid model then informs distillation design. This case study shows how partial physical knowledge can be translated into a hierarchical Gaussian process surrogate. It also shows that using BITS for GAPS increases expected information gain and predictive accuracy by targeting high-uncertainty regions of the Wilson activity model. Overall, BITS for GAPS is a generalized uncertainty-aware framework for adaptive data acquisition in complex physical systems.

stat.ML↗