发表机构
Stony Brook University; Georgia Institute of Technology; Westlake University（石溪大学; 佐治亚理工学院; 西湖大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示物理世界模型中，辛积分器保证长时域稳定性，显式线性因子化实现反事实泛化，两者可分离且可独立设计。
AI 中文摘要
一个学习得到的模拟器能够准确复现其训练条件，但一旦这些条件发生变化，它会在两种不同的方式上失效。在长时间推演中，小的误差不断累积，直到轨迹偏离物理上合理的行为；在对某个物理参数进行干预时，模型可能继续遵循训练期间所见的规律，而非被干预后的规律。我们表明，这两种失效需要不同的结构性补救措施。用辛积分器演化学习到的能量，可以保持保守动力学的几何结构，并使推演在长达训练时域100倍的范围内保持有界且物理上有意义，而同等容量的预测器、能量正则化的预测器以及调优的神经ODE则发散。相反，通过显式的线性因子化来编码物理耦合，使模型能够遵循从未见过的耦合符号，而无约束的参数化则仍锁定在训练规律上。关键在于，这两种机制是可分离的：移除负责长时域稳定性的结构，反事实迁移保持完整；而移除因子化的耦合则破坏反事实迁移，却不消除稳定性。这种双重分离，通过每次移除或替换一个结构组件的匹配对照实验确立，不仅存在于头条的三体系统中，而且在物理状态必须从像素而非直接提供时仍然可见。结果为物理世界模型提供了一个具体的设计原则：长时域稳定性和变化规律泛化源于不同的结构性承诺，且每一者都可以在不需要另一者的情况下被有意施加。
英文摘要
A learned simulator can reproduce its training conditions accurately yet fail in two distinct ways once those conditions change. Over long rollouts, small errors accumulate until the trajectory drifts away from physically plausible behavior; under an intervention on a physical parameter, the model may continue to follow the law seen during training rather than the intervened one. We show that these two failures require different structural remedies. Evolving a learned energy with a symplectic integrator preserves the geometry of the conservative dynamics and keeps rollouts bounded and physically meaningful for up to $100\times$ the training horizon, while equal-capacity predictors, an energy-regularized predictor, and a tuned neural ODE diverge. By contrast, encoding the physical coupling through an explicit linear factorization enables the model to follow a never-seen sign of that coupling, whereas an unrestricted parameterization remains locked to the training law. Crucially, the two mechanisms are separable: removing the structure responsible for long-horizon stability leaves counterfactual transfer intact, while removing the factorized coupling destroys counterfactual transfer without eliminating stability. This double dissociation, established with matched controls that remove or replace one structural component at a time, persists beyond the headline three-body system and remains visible when the physical state must be inferred from pixels rather than provided directly. The result is a concrete design principle for physical world models: long-horizon stability and changed-law generalization arise from distinct structural commitments, and each can be imposed deliberately without requiring the other.
