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Results for “f-divergence”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Stability and Convergence of Solutions to Stochastic Inverse Problems Using Approximate Probability Densities

Data-consistent inversion is designed to solve a class of stochastic inverse problems where the solution is a pullback of a probability measure specified on the outputs of a quantities of interest (QoI) map. Here, this work presents stability and convergence results for the case where finite QoI data result in an approximation of the solution as a density. Given their popularity in the literature, separate results are proven for three different approaches to measuring discrepancies between probability measures: f-divergences, integral probability metrics, and L p metrics. In the context of integral probability metrics, we also introduce a pullback probability metric that is well-suited for data-consistent inversion. This fills a theoretical gap in the convergence and stability results for data-consistent inversion that have mostly focused on convergence of solutions associated with approximate maps. Numerical results are included to illustrate key theoretical results with intuitive and reproducible test problems that include a demonstration of convergence in the measure-theoretic "almost" sense.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Regularization via f -Divergence: An Application to Multi-Oxide Spectroscopic Analysis

In this paper, we explore the application of convolutional neural networks (CNNs) for predicting the chemical composition of complex geologic samples in a simulated Martian atmospheric environment. Specifically, we aim to characterize oxide weight percentages (wt.%) of rock samples analyzed by remote Laser-Induced Breakdown Spectroscopy (LIBS), framing the problem as a multi-target regression task . Neural networks trained on LIBS spectra are prone to overfitting due to high spectral complexity, limited labeled data, and measurement noise. While regularization is critical for improving generalization, common methods (e.g., ℓ 2 regularization) impose constraints not directly tied to data distribution properties. We propose a novel regularization method based on a specific ƒ-divergence induced by a graph-based estimator, designed to constrain the distributional discrepancy between predictions and targets. This regularizer serves a dual purpose: (a) mitigating overfitting by enforcing a constraint on the distributional difference between predictions and noisy targets, and (b) acting as an auxiliary loss that penalizes large divergences. To enable backpropagation, we develop a differentiable approximation of this particular ƒ-divergence, making the method feasible for neural networks. Experiments on ChemCam and SuperCam LIBS calibration spectra show that mathematical equation-divergence regularization outperforms or matches standard regularization methods (ℓ 1 , ℓ 2 , dropout) and the classical baseline, partial least squares (PLS). Combining ƒ-divergence regularization with standard regularization yields further performance gains, indicating that distributional regularization is useful in this context giving a promising direction for robust model training in planetary science applications. Source code is publicly available at Klein and Li (2025), https://doi.org/10.11578/dc.20250530.7.

58 GEOSCIENCES↗