We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical parameters. The iMODE method learns meta-knowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bi-level optimization framework: an outer level capturing the common force field form among studied dynamical system instances and an inner level adapting to individual system instances. A priori physical knowledge can be conveniently embedded in the neural network architecture as inductive bias, such as conservative force field and Euclidean symmetry. With the learned meta-knowledge, iMODE can model an unseen system within seconds, and inversely reveal knowledge on the physical parameters of a system, or as a Neural Gauge to "measure" the physical parameters of an unseen system with observed trajectories. We test the validity of the iMODE method on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.

翻译：我们提出了可解释的元神经常微分方程（iMODE）方法，用于从物理参数不同的多个动力系统的轨迹中快速学习可泛化（即非参数特定）的动力学。iMODE方法采用双层优化框架学习元知识——即动力系统实例力场的函数变化，而无需知晓物理参数：外层捕捉所研究动力系统实例间的共同力场形式，内层则适应单个系统实例。先验物理知识可便捷地嵌入神经网络架构作为归纳偏置，如保守力场和欧几里得对称性。凭借习得的元知识，iMODE可在数秒内建模未见系统，并逆向揭示系统物理参数信息，或作为"测量"具有观测轨迹的未见系统物理参数的神经量规。我们在双稳态系统、双摆、范德波尔振荡器、弹簧链和反应扩散系统上验证了iMODE方法的有效性。