Inductive Domain Transfer In Misspecified Simulation-Based Inference

Simulation-based inference (SBI) has evolved as a vital tool for estimating parameters in complex physical systems where likelihood functions are difficult or impossible to compute directly. Early methods like Approximate Bayesian Computation (ABC) relied on rejection sampling, which was computationally expensive. Neural posterior estimation (NPE) and related techniques introduced neural networks to learn posterior distributions efficiently from simulated data, significantly advancing the field. However, these methods are sensitive to model misspecification—discrepancies between the simulator and real-world data—which can bias inference results. Recent methods like RoPE incorporated domain transfer strategies, combining semi-supervised calibration with optimal transport (OT) to mitigate this issue. Despite improvements, RoPE’s transductive nature limits its scalability and generalization to unseen data. As applications grow more complex, especially in medical imaging and environmental modeling, there is a pressing need for scalable, inductive SBI methods that can handle severe model mismatch and operate efficiently without repeated simulation.

The core challenge in SBI under model misspecification is achieving accurate, robust inference for individual test samples without relying on large test batches or repeated simulations. Existing methods like RoPE require access to test data in batches, which hampers scalability and real-time application. Additionally, the reliance on separate calibration and distribution alignment stages can limit the model’s ability to fully exploit the complementary strengths of pointwise and distributional alignment. Furthermore, high computational costs and sensitivity to hyperparameters hinder practical deployment, especially in high-dimensional or severely misspecified environments. Addressing these issues necessitates a unified, scalable framework capable of inductive inference, leveraging minimal calibration data and eliminating the need for repeated simulation during testing.

FRISBI introduces several key innovations: 1) It derives a closed-form solution for mini-batch OT, enabling efficient joint training of the encoder gϕ with both calibration and distribution alignment objectives. 2) It integrates these objectives into a single end-to-end training process, improving robustness and leveraging their mutual strengths. 3) It employs a conditional normalizing flow qξ to approximate the OT-based posterior mixture, allowing fast, simulation-free inference at test time. 4) The framework supports large unpaired datasets and small calibration sets, making it highly scalable and adaptable to real-world environments with model mismatch. These innovations collectively enable fully inductive, robust SBI, overcoming the limitations of prior transductive methods like RoPE.

• �� Train encoder gϕ using a joint objective combining a variant of entropic OT with a supervised calibration loss, optimizing both pointwise and distributional alignment.
• �� Derive a closed-form solution for the OT coupling, enabling efficient stochastic gradient descent (SGD) updates per sample.
• �� Incorporate large unpaired datasets and calibration pairs to refine the encoder and OT plan iteratively.
• �� Train a conditional normalizing flow qξ to approximate the OT-induced posterior mixture, using samples from the calibrated distribution.
• �� During inference, encode test observations with gϕ, then sample from qξ to obtain the posterior, eliminating the need for simulation access.
• �� Hyperparameters γ and λ control regularization and supervision strength, tuned via cross-validation. The entire training process supports scalable, single-sample inference with minimal computational overhead.

The framework was evaluated on synthetic pendulum models, controlled physical experiments (wind tunnel, light tunnel), and real medical data (cardiac output estimation). Baselines included RoPE, NPE, and OT-only methods. Metrics such as log-posterior probability (LPP) and coverage area under the curve (ACAUC) assessed accuracy and calibration. Experiments varied calibration set sizes (10, 50, 200, 1000), demonstrating that FRISBI maintains high performance with limited calibration data. Hyperparameters γ=0.5 and λ tuned for stability. Results showed consistent superiority over baselines, especially in small calibration regimes and severe model mismatch scenarios, validating the method’s robustness and scalability.

FRISBI achieved approximately 15% higher LPP and 20% lower ACAUC compared to RoPE across benchmarks. It maintained stable performance with small calibration sets, outperforming transductive methods in single-sample inference. The method demonstrated robustness in high-dimensional, misspecified environments, with significant improvements in calibration and accuracy metrics. These results confirm the effectiveness of joint training and posterior amortization, enabling practical, real-time applications in complex scientific tasks.

This method is suitable for real-time parameter estimation in medical diagnostics, environmental monitoring, and engineering systems. It requires minimal calibration data and no repeated simulation at inference, making it ideal for resource-constrained or high-stakes scenarios. Long-term, it can facilitate autonomous scientific discovery, adaptive modeling, and complex system control, especially where model fidelity is limited or data is scarce.

The approach assumes calibration data reasonably represents the target domain; large domain shifts may reduce accuracy. Hyperparameter tuning remains critical, and high-dimensional parameter spaces pose computational challenges. In cases of extreme model mismatch or insufficient calibration, performance may degrade. Future work should focus on robustness enhancements, scalability, and extending to multi-modal, multi-task applications.