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.

翻译：贝叶斯证据评估因维度灾难和基于采样方法的序列性，在高维情况下变得计算上不可行。本文提出SunBURST，一种用于贝叶斯证据计算的确定性GPU原生算法，它用模式中心几何积分替代全局体积探索。该流程结合了径向模式发现、批量L-BFGS优化和基于拉普拉斯的解析积分，独立处理各模式，并将大批量似然评估转化为大规模并行的GPU计算任务。对于拉普拉斯近似精确或高度准确的高斯及近高斯后验分布，在我们的基准测试中，SunBURST在维度高达1024时达到双精度容差范围内的数值一致性，且在测试范围内呈现亚线性实际时间缩放。在多峰高斯混合模型中，保守配置可实现亚百分比精度，同时保持良好缩放性。SunBURST并非旨在普遍替代基于采样的推断方法，其设计针对物理参数估计和反问题中常见的场景——这些场景中后验质量可通过有限数量模式周围的高斯结构进行局部良好近似。在强非高斯场景中，该方法可作为快速几何感知证据估计器，或作为混合工作流的预处理阶段。这些结果表明，通过确定性积分与大规模并行计算相结合，高精度贝叶斯证据评估在极高维度下可以实现计算可行性。