arXiv subjects

Rebecca Morrison

Publications and source records attributed to Rebecca Morrison.

7 recordsLinked to original sources

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↗

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↗

arXiv2025

Conditional Independence Estimates for the Generalized Nonparanormal

For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class of non-Gaussian distributions -- those derived from diagonal transformations of a Gaussian -- information about the conditional independence structure can still be inferred from the precision matrix, provided the data meet certain criteria, analogous to the Gaussian case. We call such transformations of the Gaussian as the generalized nonparanormal. The functions that define these transformations are, in a broad sense, arbitrary. We also provide a simple and computationally efficient algorithm that leverages this theory to recover conditional independence structure from the generalized nonparanormal data. The effectiveness of the proposed algorithm is demonstrated via synthetic experiments and applications to real-world data.

cs.LG↗

arXiv2025

Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach

Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical model, which encodes these dependencies, by assuming that the variables follow a distribution with a simple parametric form. Moreover, the computational cost of many algorithms scales poorly for high-dimensional distributions, as they need to estimate all the edges in the graph simultaneously. In this work, we propose a scalable algorithm to infer the conditional independence relationships of each variable by exploiting the local Markov property. The proposed method, named Localized Sparsity Identification for Non-Gaussian Distributions (L-SING), estimates the graph by using flexible classes of transport maps to represent the conditional distribution for each variable. We show that L-SING includes existing approaches, such as neighborhood selection with Lasso, as a special case. We demonstrate the effectiveness of our algorithm in both Gaussian and non-Gaussian settings by comparing it to existing methods. Lastly, we show the scalability of the proposed approach by applying it to high-dimensional non-Gaussian examples, including a biological dataset with more than 150 variables.

cs.LG↗

arXiv2024

Exact mean and covariance formulas after diagonal transformations of a multivariate normal

Consider $\boldsymbol X \sim \mathcal{N}(\boldsymbol 0, \boldsymbol \Sigma)$ and $\boldsymbol Y = (f_1(X_1), f_2(X_2),\dots, f_d(X_d))$. We call this a diagonal transformation of a multivariate normal. In this paper we compute exactly the mean vector and covariance matrix of the random vector $\boldsymbol Y.$ This is done two different ways: One approach uses a series expansion for the function $f_i$ and the other a transform method. We compute several examples, show how the covariance entries can be estimated, and compare the theoretical results with numerical ones.

math.ST↗

arXiv2023

Analytic solutions to nonlinear ODEs via spectral power series

Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic solutions to a class of nonlinear, homogeneous ODEs with linear and quadratic terms on the right-hand side. We formulate a power series expansion of each state variable, whose function depends on the eigenvalues of the linearized system, and solve for the coefficients using some linear algebra and combinatorics. Various experiments exhibit quickly decaying coefficients, such that a good approximation to the true solution consists of just a few terms.

math.DS↗

arXiv2011

Optimal Data Split Methodology for Model Validation

The decision to incorporate cross-validation into validation processes of mathematical models raises an immediate question - how should one partition the data into calibration and validation sets? We answer this question systematically: we present an algorithm to find the optimal partition of the data subject to certain constraints. While doing this, we address two critical issues: 1) that the model be evaluated with respect to predictions of a given quantity of interest and its ability to reproduce the data, and 2) that the model be highly challenged by the validation set, assuming it is properly informed by the calibration set. This framework also relies on the interaction between the experimentalist and/or modeler, who understand the physical system and the limitations of the model; the decision-maker, who understands and can quantify the cost of model failure; and the computational scientists, who strive to determine if the model satisfies both the modeler's and decision maker's requirements. We also note that our framework is quite general, and may be applied to a wide range of problems. Here, we illustrate it through a specific example involving a data reduction model for an ICCD camera from a shock-tube experiment located at the NASA Ames Research Center (ARC).

physics.data-an↗