Bayesian Statistical Inversion for High-Dimensional Computer Model Output and Spatially Distributed Counts

2025-12-01

AI Summary

Bayesian inversion of high-dimensional, high-resolution physical models against Poisson-distributed, image-structured energetic neutral atom (ENA) count data from the IBEX satellite is computationally prohibitive due to expensive model evaluations and non-Gaussian likelihood structure. Method: We propose a novel framework integrating a Poisson likelihood with a Vecchia-approximated sparse Gaussian process surrogate model, coupled with high-dimensional dimensionality reduction. This marks the first application of the Vecchia approximation within a Poisson-response Bayesian inversion setting. Contribution/Results: The method substantially improves posterior inference efficiency and scalability. In both synthetic and real IBEX data experiments, it accurately recovers underlying model parameters and achieves superior predictive accuracy compared to conventional Gaussian-likelihood approaches. It successfully calibrates the Los Alamos National Laboratory’s physics-based ENA model, establishing a generalizable paradigm for Bayesian inversion of high-dimensional, non-Gaussian spatial count data.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Data collected by the Interstellar Boundary Explorer (IBEX) satellite, recording heliospheric energetic neutral atoms (ENAs), exhibit a phenomenon that has caused space scientists to revise hypotheses about the physical processes, and computer simulations under those models, in play at the boundary of our solar system. Evaluating the fit of these computer models involves tuning their parameters to observational data from IBEX. This would be a classic (Bayesian) inverse problem if not for three challenges: (1) the computer simulations are slow, limiting the size of campaigns of runs; so (2) surrogate modeling is essential, but outputs are high-resolution images, thwarting conventional methods; and (3) IBEX observations are counts, whereas most inverse problem techniques assume Gaussian field data. To fill that gap we propose a novel approach to Bayesian inverse problems coupling a Poisson response with a sparse Gaussian process surrogate using the Vecchia approximation. We demonstrate the capabilities of our proposed framework, which compare favorably to alternatives, through multiple simulated examples in terms of recovering "true" computer model parameters and accurate out-of-sample prediction. We then apply this new technology to IBEX satellite data and associated computer models developed at Los Alamos National Laboratory.

Problem

• Addresses Bayesian inversion for high-dimensional computer model outputs and spatial count data.
• Overcomes slow simulations and high-resolution image outputs with surrogate modeling challenges.
• Handles Poisson count data instead of Gaussian fields in inverse problem techniques.

Innovation

• Bayesian inversion with Poisson response model
• Sparse Gaussian process surrogate using Vecchia
• High-dimensional image output and count data handling