Probabilistic Retrofitting of Learned Simulators

TL;DR

This paper introduces a simple, architecture-agnostic method to convert existing deterministic PDE models into probabilistic models using retrofitting with CRPS, significantly improving uncertainty quantification without retraining from scratch.

Contribution

The authors propose a retrofitting approach that transforms pre-trained deterministic PDE models into probabilistic models efficiently, applicable across various architectures and scales.

Findings

Achieved 20-54% reduction in rollout CRPS.

Improved VRMSE by up to 30% on single systems.

Enhanced CRPS by up to 40% on PDE foundation models.

Abstract

Dominant approaches for modelling Partial Differential Equations (PDEs) rely on deterministic predictions, yet many physical systems of interest are inherently chaotic and uncertain. While training probabilistic models from scratch is possible, it is computationally expensive and fails to leverage the significant resources already invested in high-performing deterministic backbones. In this work, we adopt a training-efficient strategy to transform pre-trained deterministic models into probabilistic ones via retrofitting with a proper scoring rule: the Continuous Ranked Probability Score (CRPS). Crucially, this approach is architecture-agnostic: it applies the same adaptation mechanism across distinct model backbones with minimal code modifications. The method proves highly effective across different scales of pre-training: for models trained on single dynamical systems, we achieve 20-54% reductions in rollout CRPS and up to 30% improvements in variance-normalised RMSE (VRMSE) relative to compute-matched deterministic fine-tuning. We further validate our approach on a PDE foundation model, trained on multiple systems and retrofitted on the dataset of interest, to show that our probabilistic adaptation yields an improvement of up to 40% in CRPS and up to 15% in VRMSE compared to deterministic fine-tuning. Validated across diverse architectures and dynamics, our results show that probabilistic PDE modelling need not require retraining from scratch, but can be unlocked from existing deterministic backbones with modest additional training cost.