Bridged SBI: Correcting Biased Low-Fidelity Posteriors for Cost-Efficient High-Fidelity Inference
Authors: Gahee Kim, Yuki Kadokawa, Sandro M. Alcantara Tacora, Taro Abe, Daisuke Endo, Genki Yamauchi, Takeshi Hashimoto, Takamitsu Matsubara
Abstract
Accurate calibration of particle-based simulators is crucial for robotic earthwork simulation, but analytical calibration is challenging due to this task's highly nonlinear particle dynamics and the black-box nature of conventional simulators. Although simulation-based inference (SBI) can estimate posterior distributions over simulation parameters solely from forward simulations, applying SBI directly to high-fidelity (HF) particle simulators is often computationally prohibitive. Low-fidelity (LF) simulators with coarser particles can reduce this cost, but changes in particle size and particle count shift the parameter values needed to reproduce the same observation, producing biased LF posteriors. We propose Bridged SBI, which leverages a biased but informative LF posterior to guide HF inference. This method first uses inexpensive LF simulations to identify a coarse high-density parameter region, and then it learns a local residual bridge to transport LF posterior samples toward HF-consistent regions by correcting the LF--HF discrepancy. We analyze how sequential multi-fidelity SBI (Naive-MF) can suffer from LF-induced posterior miscoverage when it directly relies on the LF posterior without discrepancy correction. We then show that Bridged SBI is designed to alleviate this issue by explicitly modeling the LF--HF discrepancy through residual correction. Experiments on both sim-to-sim particle-parameter calibration and real-to-sim calibration with real soil observation show that Bridged SBI produces more accurate and reliable HF posteriors than HF-only SBI or the Naive-MF baseline, especially under limited HF simulation costs.
The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site neural surrogate of the simulator and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.
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.
Arunkumar V, Manoranjan Gandhudi, Gangadharan G. R. +2
Simulation-based inference (SBI) provides amortized Bayesian parameter inference from simulator-generated data without requiring explicit likelihood evaluation. Its reliability can degrade under model misspecification, where real-world observations are not well represented by the simulator used for training. Existing methods using unlabeled real-world data often align simulated and real-world data distributions, but marginal alignment alone does not directly preserve parameter-relevant information needed for posterior inference. We propose SPIN, an SBI framework with parameter-relevant information-preserving domain transfer using unlabeled, unpaired real-world observations. During training, SPIN translates labeled simulator observations toward the real-world domain and back to the simulator domain, using the original simulator labels to encourage domain transfer that preserves parameter-relevant mutual information. At test time, the learned real-to-simulator transport maps real-world observations into the simulator domain for posterior inference, without requiring real-world parameter labels or paired real--simulator observations. Across controlled synthetic and physical real-world benchmarks, SPIN improves real-world posterior inference, with the improvement becoming clearer as misspecification increases.