SunBURST: Deterministic GPU-Accelerated Bayesian Evidence via Mode-Centric Laplace Integration

TL;DR

SunBURST is a GPU-accelerated deterministic algorithm that efficiently computes Bayesian evidence in high-dimensional problems by leveraging mode-centric geometric integration and Laplace approximation, achieving high accuracy and scalability.

Contribution

It introduces a novel GPU-native, deterministic method for Bayesian evidence calculation that replaces sampling with mode-centric geometric integration and Laplace approximation.

Findings

Achieves double-precision accuracy up to 1024 dimensions.

Exhibits sub-linear wall-clock scaling across tested dimensions.

Provides sub-percent accuracy in multimodal Gaussian mixtures.

Abstract

Bayesian evidence evaluation becomes computationally prohibitive in high dimensions due to the curse of dimensionality and the sequential nature of sampling-based methods. We introduce SunBURST, a deterministic GPU-native algorithm for Bayesian evidence calculation that replaces global volume exploration with mode-centric geometric integration. The pipeline combines radial mode discovery, batched L-BFGS refinement, and Laplace-based analytic integration, treating modes independently and converting large batches of likelihood evaluations into massively parallel GPU workloads. For Gaussian and near-Gaussian posteriors, where the Laplace approximation is exact or highly accurate, SunBURST achieves numerical agreement at double-precision tolerance in dimensions up to 1024 in our benchmarks, with sub-linear wall-clock scaling across the tested range. In multimodal Gaussian mixtures, conservative configurations yield sub-percent accuracy while maintaining favorable scaling. SunBURST is not intended as a universal replacement for sampling-based inference. Its design targets regimes common in physical parameter estimation and inverse problems, where posterior mass is locally well approximated by Gaussian structure around a finite number of modes. In strongly non-Gaussian settings, the method can serve as a fast geometry-aware evidence estimator or as a preprocessing stage for hybrid workflows. These results show that high-precision Bayesian evidence evaluation can be made computationally tractable in very high dimensions through deterministic integration combined with massive parallelism.