Neural Canonical Transformation with Symplectic Flows

09/30/2019
by   Shuo-Hui Li, et al.
0

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian. Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space. Since the canonical transformation preserves the Hamiltonian evolution, the model captures nonlinear collective modes in the learned latent representation. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model. The variational free energy calculation is based on the analytical form of physical Hamiltonian. While the phase space density estimation only requires samples in the coordinate space for separable Hamiltonians. We demonstrate appealing features of neural canonical transformation using toy problems including two-dimensional ring potential and harmonic chain. Finally, we apply the approach to real-world problems such as identifying slow collective modes in alanine dipeptide and conceptual compression of the MNIST dataset.

READ FULL TEXT

Authors

page 8

02/28/2021

Neural Network Approach to Construction of Classical Integrable Systems

Integrable systems have provided various insights into physical phenomen...
02/08/2018

Neural Network Renormalization Group

We present a variational renormalization group approach using deep gener...
03/19/2021

Joint Parameter Discovery and Generative Modeling of Dynamic Systems

Given an unknown dynamic system such as a coupled harmonic oscillator wi...
06/06/2020

Structure-preserving numerical methods for stochastic Poisson systems

We propose a class of numerical integration methods for stochastic Poiss...
10/28/2020

Forecasting Hamiltonian dynamics without canonical coordinates

Conventional neural networks are universal function approximators, but b...
06/11/2019

Learning Symmetries of Classical Integrable Systems

The solution of problems in physics is often facilitated by a change of ...
11/21/2021

Semiexplicit Symplectic Integrators for Non-separable Hamiltonian Systems

We construct a symplectic integrator for non-separable Hamiltonian syste...

Code Repositories

neuralCT

Pytorch implement of the paper Neural Canonical Transformation with Symplectic Flows


view repo
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.