From metronomes to celestial bodies, mechanics underpins how the world evolves in time and space. With consideration of this, a number of recent neural network models leverage inductive biases from classical mechanics to encourage model interpretability and ensure forecasted states are physical. However, in general, these models are designed to capture the dynamics of a single system with fixed physical parameters, from state-space measurements of a known configuration space. In this paper we introduce Symplectic Phase Space GAN (SPS-GAN) which can capture the dynamics of multiple systems, and generalize to unseen physical parameters from. Moreover, SPS-GAN does not require prior knowledge of the system configuration space. In fact, SPS-GAN can discover the configuration space structure of the system from arbitrary measurement types (e.g., state-space measurements, video frames). To achieve physically plausible generation, we introduce a novel architecture which embeds a Hamiltonian neural network recurrent module in a conditional GAN backbone. To discover the structure of the configuration space, we optimize the conditional time-series GAN objective with an additional physically motivated term to encourages a sparse representation of the configuration space. We demonstrate the utility of SPS-GAN for trajectory prediction, video generation and symmetry discovery. Our approach captures multiple systems and achieves performance on par with supervised models designed for single systems.

翻译：从节拍器到天体，力学原理支撑着世界在时空中的演化进程。基于这一认知，近期若干神经网络模型通过引入经典力学的归纳偏置来增强模型可解释性，并确保预测状态符合物理规律。然而，这些模型通常设计用于从已知构型空间的状态空间测量中，捕捉具有固定物理参数的单一系统动力学。本文提出的辛相空间生成对抗网络（SPS-GAN）能够同时捕捉多个系统的动力学特性，并可泛化至未见过的物理参数。此外，SPS-GAN无需预先获知系统构型空间信息，实际上能够从任意测量类型（如状态空间测量、视频帧）中发现系统的构型空间结构。为实现物理可解释的生成过程，我们提出一种新颖架构，将哈密顿神经网络循环模块嵌入条件生成对抗网络主干中。为发现构型空间的结构，我们在条件时间序列生成对抗网络目标函数中引入具有物理动机的附加项，以促进构型空间的稀疏表示。我们通过轨迹预测、视频生成和对称性发现等任务验证了SPS-GAN的有效性。该方法能够同时处理多个系统，其性能与专为单一系统设计的监督模型相当。