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
本研究探究世界模型所需硬编码的通用物理结构，提出从学习能量与固定可逆算子生成动力学的方法，在多个物理系统中实现稳定性、干预正确性及对扰动的鲁棒性，并以少量参数高效恢复本构关系。
AI 中文摘要
世界模型从记录的轨迹中学习预测物理系统如何演化，然而它所模仿的系统所遵循的物理定律既未被完全提供，也未被可靠地遵守。该模型可能在长时间滚动中产生能量、漂移或发散，并可能使用训练期间观察到的定律来回答关于定律变化的查询。我们探究必须将多少通用物理结构硬编码到世界模型中，以及随后能从数据中学习多少特定于系统的物理，才能同时满足四个属性：与第二定律兼容的耗散、对物理参数干预的正确响应、稳定性延伸到训练时域的一百倍，以及对扰动的鲁棒性。所施加的结构是通用的：动力学通过固定的可逆算子从学习能量的梯度生成，能量被限制在约束类中，单向端口可以移除能量但绝不能注入能量，驱动通道是已知的，被干预的参数通过可分离映射进入。模型学习能量泛函、本构关系、耗散率和耦合。在电磁腔、粒子网格单元和浅水流体中，具有约九千个参数的模型以单位斜率恢复本构函数，使用单组权重将守恒世界与耗散世界区分开四个数量级，并将符号、幅度、速率和重力的变化转移到未见过的值，而具有相同容量但不具备相同结构的模型则表现不佳或更差。恢复非线性本构定律时保留其曲率，并在保留的干预上比收敛的线性模型预测好2-17倍。
英文摘要
A world model learns to forecast how a physical system evolves from recorded trajectories, yet the systems it imitates obey physical laws that are neither fully supplied nor reliably respected. The model may create energy, drift or diverge over long rollouts, and answer a changed law query using the law observed during training. We ask how much general physical structure must be hard coded into a world model, and how much system-specific physics can then be learned from data, for four properties to hold simultaneously: second law compatible dissipation, correct responses to interventions on physical parameters, stability out to one hundred times the training horizon, and robustness to disturbances. The imposed structure is general: dynamics are generated from the gradient of a learned energy through a fixed reversible operator, the energy is restricted to a confining class, a one way port can remove energy but never inject it, the drive channel is known, and the intervened parameter enters through a separable map. The model learns the energy functional, constitutive relations, dissipation rate, and couplings. Across an electromagnetic cavity, a particle in cell grid, and a shallow-water fluid, models with roughly nine thousand parameters recover constitutive functions with unit slope, separate conserving from dissipating worlds by four orders of magnitude using a single set of weights, and transfer changes in sign, magnitude, rate, and gravity to unseen values, where equal-capacity models without the same structure perform at chance or worse. A nonlinear constitutive law is recovered with its curvature preserved and predicts a held-out intervention $2$-$17\times$ better than a converged linear model.
