Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant challenges, especially in the context of non-differentiable models, where the absence of likelihood model gradient information can result in high computational costs. To tackle this issue, we develop a novel Bayesian inference approach based on black box variational inference, utilizing importance sampling to reuse existing simulation model calls in the variational objective gradient estimation, without relying on forward model gradients. The novelty lies in a new batch-sequential sampling procedure, which only requires new model evaluations if the currently available model evaluations fail to yield a suitable approximation of the objective gradient. The resulting approach reduces computational costs by leading to variational parameter updates without requiring new model evaluations when possible, while adaptively increasing the number of model calls per iteration as needed. In combination with its black box nature, this new approach is suitable for inverse problems involving demanding physics-based models that lack model gradients. We demonstrate the efficiency gains of the proposed method compared to its baseline version, sequential Monte Carlo, and Markov-Chain Monte Carlo in diverse benchmarks, ranging from density matching to the Bayesian calibration of a nonlinear electro-chemo-mechanical model for solid-state batteries.

翻译：贝叶斯方法因其能够处理推断过程中固有的不确定性，在解决反问题方面尤为有效。然而，在采用这些方法时，若前向模型计算成本高昂，尤其是在模型不可微分的情况下，由于缺乏似然模型的梯度信息，可能导致极高的计算开销。为解决这一问题，我们提出了一种基于黑盒变分推断的新型贝叶斯推断方法，利用重要性采样在变分目标梯度估计中重复使用已有的仿真模型调用，而无需依赖前向模型的梯度。其创新点在于一种新的批量序贯采样流程：仅当当前可用的模型评估结果无法为客观梯度提供合适近似时，才需进行新的模型评估。该方法通过尽可能在不需新模型评估的情况下更新变分参数以降低计算成本，同时根据需要自适应地增加每次迭代的模型调用次数。结合其黑盒特性，这一新方法适用于涉及缺乏模型梯度的、基于物理的复杂模型的反问题。我们通过从密度匹配到固态电池非线性电化学-力学模型的贝叶斯校准等多种基准测试，展示了所提方法相较于其基线版本、序贯蒙特卡洛方法以及马尔可夫链蒙特卡洛方法在计算效率上的提升。