用少量训练将确定性物理模拟器转为概率模型,提升预测可靠性。
Probabilistic Retrofitting of Learned Simulators
- 基于CRPS评分规则对预训练模型进行概率化改造,无需重训。
- 单系统模型可降20%-54%滚动CRPS,多系统基础模型提升达40%。
- 适配多种架构与动力系统,适合已有高性能确定性模型的团队。
主流偏微分方程(PDE)建模方法依赖确定性预测,但许多物理系统本质上具有混沌性和不确定性。尽管可从头训练概率模型,但计算成本高且无法利用已有高性能确定性模型的投入。本文提出一种高效训练策略,通过连续排名概率评分(CRPS)对预训练确定性模型进行概率化改造。该方法架构无关,仅需少量代码修改即可适配不同模型。在单一动力系统上,模型滚动CRPS降低20%-54%,方差归一化均方误差(VRMSE)提升最高30%;在多系统预训练的基础模型上,改造后CRPS改善达40%,VRMSE提升15%。结果表明,概率化PDE建模无需从头训练,仅需对现有确定性模型进行轻量级适配即可实现显著性能提升。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。