Design-dependent regularization for simulator-misspecification correction

Develop and evaluate a design-dependent regularization penalty \(\lambda(\xi)\) for diffusion likelihood fine-tuning that preserves well-modeled experimental-design regions while permitting stronger correction in regions affected by simulator misspecification.

Background

The paper studies fine-tuning of a pretrained diffusion-based simulator surrogate using observed design–response pairs. In the analytic design-dependent misspecification experiment, fine-tuning improves predictions near an omitted discrepancy but degrades predictions in regions where the simulator was already accurate. Varying a global regularization strength $\lambda$ reveals a trade-off: stronger regularization limits adaptation and protects well-modeled regions, but also weakens correction where misspecification is present.

The authors therefore propose replacing a single global penalty with a design-dependent penalty $\lambda(\xi)$, allowing adaptation strength to vary across experimental conditions. The paper does not test this extension and leaves its evaluation unresolved.