Fast Bayesian equipment condition monitoring via simulation based inference: applications to heat exchanger health

Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistical frameworks, describe how machine-learning-based SBI methods, such as neural posterior estimation and neural likelihood estimation, can be used for parameter estimation within these frameworks, and show that the same methods can also be applied to Empirical Bayes or unfolding tasks. We also discuss how to validate inference results and the limitations of SBI with machine learning.

Mechanistic epidemiological models are widely used to support infectious disease forecasting and public-health decision making. Bayesian calibration of such models is commonly performed using Markov chain Monte Carlo (MCMC), which can become computationally expensive for high-dimensional nonlinear systems and repeated near-real-time analyses. Here, we investigate simulation-based inference (SBI) using neural posterior estimation as a scalable alternative for Bayesian calibration of a mechanistic SECIR epidemiological model using COVID-19 intensive care unit (ICU) occupancy data from Germany during 2020. We compared SBI and MCMC across multiple epidemic phases using both 31-day inference windows and a substantially more challenging 201-day reconstruction problem involving multiple transmission change points. Posterior agreement was evaluated quantitatively using Wasserstein distances and Kullback-Leibler divergences together with posterior predictive checks. Across the 31-day windows, SBI recovered posterior distributions in strong agreement with MCMC while accurately reproducing observed ICU trajectories. In the 201-day setting, SBI preserved the dominant posterior structure despite increased uncertainty. SBI, by combining CPU and GPU resources, substantially reduced computational runtime compared with MCMC, which was restricted to running on CPUs. Whereas MCMC required approximately 1000 seconds for the 31-day inference problems, SBI achieved comparable posterior and predictive performance in approximately 60-70 seconds on a single GPU. For the 201-day inference problem, SBI required an average of 157 seconds, while the MCMC runs took over 19,000 seconds. Our results demonstrate that SBI provides a rapid and computationally efficient framework for Bayesian calibration of mechanistic epidemiological models, supporting repeated near-real-time inference and rapid outbreak analysis.

Simulation-based inference (SBI) of latent parameters is often hindered by simulator misspecification, the mismatch between simulated and real-world observations caused by inherent modeling simplifications. RoPE, the recent state-of-the-art for robust SBI, addresses this through optimal transport between learned representations of real and simulated observations, but requires ground-truth parameter calibration pairs that are typically unavailable in the very settings where SBI is needed. What practitioners do have is unstructured side-information such as regime labels, instruction text, and policy bulletins. We propose Misspecification-Aware Simulation-Based Inference (MA-SBI), a calibration-free framework that turns this side-channel into a posterior correction. A learned corrector maps side-channel text to an observation-space shift applied before any pre-trained amortized posterior, requiring no retraining and no parameter ground-truth. Our main theorem bounds achievable bias reduction by the mutual information between misspecification and side-channel, with a non-vacuous constant that extends to all sub-Gaussian noise via Donsker-Varadhan. On hide-the-calibration benchmarks, MA-SBI with text alone matches the oracle posterior across 10 seeds and two backbones (TOST equivalence), while RoPE given more data does not. The two approaches are complementary: where misspecification is structural and recoverable from parameter pairs, RoPE dominates, as the theory predicts. A stochastic variant improves posterior-predictive log-likelihood on real COVID and OxCGRT epidemiological data, and correctly leaves the posterior unchanged on a well-specified cognitive-science corpus.