[2603.01949] Probabilistic Retrofitting of Learned Simulators

Computer Science > Machine Learning arXiv:2603.01949 (cs) [Submitted on 2 Mar 2026] Title:Probabilistic Retrofitting of Learned Simulators Authors:Cristiana Diaconu, Miles Cranmer, Richard E. Turner, Tanya Marwah, Payel Mukhopadhyay View a PDF of the paper titled Probabilistic Retrofitting of Learned Simulators, by Cristiana Diaconu and 4 other authors View PDF HTML (experimental) 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...