Inductive Domain Transfer In Misspecified Simulation-Based Inference

Simulation-based inference (SBI) of latent parameters in physical systems is often hindered by model misspecification -- the mismatch between simulated and real-world observations caused by inherent modeling simplifications.

RoPE, a recent SBI approach, addresses this challenge through a two-stage domain transfer process that combines semi-supervised calibration with optimal transport (OT)-based distribution alignment. However, RoPE operates in a fully transductive setting, requiring access to a batch of test samples at inference time, which limits scalability and generalization.

We propose a fully inductive and amortized SBI framework that integrates calibration and distributional alignment into a single, end-to-end trainable model. Our method leverages mini-batch OT with a closed-form coupling to align real and simulated observations that correspond to the same latent parameters, using both paired calibration data and unpaired samples.

A conditional normalizing flow is then trained to approximate the OT-induced posterior, enabling efficient inference without simulation access at test time. Across a range of synthetic and real-world benchmarks -- including complex medical biomarker estimation -- our approach matches or exceeds the performance of RoPE, while offering improved scalability and applicability in challenging, misspecified environments.