A growing body of work leverages the Hamiltonian formalism as an inductive
bias for physically plausible neural network based video generation. The
structure of the Hamiltonian ensures conservation of a learned quantity (e.g.,
energy) and imposes a phase-space interpretation on the low-dimensional
manifold underlying the input video. While this interpretation has the
potential to facilitate the integration of learned representations in
downstream tasks, existing methods are limited in their applicability as they
require a structural prior for the configuration space at design time. In this
work, we present a GAN-based video generation pipeline with a learned
configuration space map and Hamiltonian neural network motion model, to learn a
representation of the configuration space from data. We train our model with a
physics-inspired cyclic-coordinate loss function which encourages a minimal
representation of the configuration space and improves interpretability. We
demonstrate the efficacy and advantages of our approach on the Hamiltonian
Dynamics Suite Toy Physics dataset.

使用 Gan 神经网络以及 Hamiltonian 动力学模型，在无需预先设计结构假设的情况下，学习配置空间，并通过周期坐标损失函数提高可解释性，以在视频生成中实现高效和有优势的方法。

Hamiltonian GAN

The Hamiltonian formalism plays a central role in classical and quantum
physics. Hamiltonians are the main tool for modelling the continuous time
evolution of systems with conserved quantities, and they come equipped with
many useful properties, like time reversibility and smooth interpolation in
time. These properties are important for many machine learning problems - from
sequence prediction to reinforcement learning and density modelling - but are
not typically provided out of the box by standard tools such as recurrent
neural networks. In this paper, we introduce the Hamiltonian Generative Network
(HGN), the first approach capable of consistently learning Hamiltonian dynamics
from high-dimensional observations (such as images) without restrictive domain
assumptions. Once trained, we can use HGN to sample new trajectories, perform
rollouts both forward and backward in time and even speed up or slow down the
learned dynamics. We demonstrate how a simple modification of the network
architecture turns HGN into a powerful normalising flow model, called Neural
Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive
densities. We hope that our work serves as a first practical demonstration of
the value that the Hamiltonian formalism can bring to deep learning.

本文介绍了哈密顿生成网络 (HGN) 和神经哈密顿流 (NHF)，这是第一种能够从高维度观察中连续地学习哈密顿动力学而无需限制性条件的方法，它能够可靠地从机器学习的角度解决很多问题。