STRUPNET: structure-preserving neural networks

This package implements structure-preserving neural networks for learning dynamics of differential systems from data.

Installing

Install it using pip: pip install strupnet

SympNet: Symplectic neural networks

This package implements the symplectic neural networks found in [1] ("G" and "LA"-SympNets) and [2] ("H"-SympNets) as well as some new ones [3] ("P", "R" and "GR"-SympNets).

Basic example

import torch
from strupnet import SympNet

dim = 2 # degrees of freedom for the Hamiltonian system. x = (p, q) \in R^{2*dim}
sympnet = SympNet(dim=dim, layers=12, width=8)

timestep = torch.tensor([0.1]) # time-step 
x0 = torch.randn(2 * dim) # phase space coordinate x0 = (p0, q0) 

x1 = sympnet(x0, timestep) # defines a random but symplectic transformation from x0 to x1

The rest of your code is identical to you how you would train any module that inherits from torch.nn.Module.

VolNet: Volume-preserving neural networks

This module neural networks with unit Jacobian determinant. The VolNet is constructed from compositions of SympNets, and therefore requires you to pass through arguments that define one of the above SympNets. See the below example on how it's initialised.

Basic example

import torch
from strupnet import VolNet

dim = 3 # dimension of the ODE 

p_sympnet_kwargs = dict(
    method="P",
    layers=6,
    max_degree=4, # used for method='P' only, method='R' requires you to specify width.
)

volnet = VolNet(dim=DIM, **p_sympnet_kwargs)

timestep = torch.tensor([0.1]) # time-step 
x0 = torch.randn(3)

x1 = sympnet(x0, timestep) # defines a random but volume-preserving neural network mapping from x0 to x1

The rest of your code is identical to you how you would train any module that inherits from torch.nn.Module.

Example notebooks

See the examples/ folder for notebooks on basic implementation of SympNet and VolNet

References

[1] Jin, P., Zhang, Z., Zhu, A., Tang, Y. and Karniadakis, G.E., 2020. SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Neural Networks, 132, pp.166-179.

[2] Burby, J.W., Tang, Q. and Maulik, R., 2020. Fast neural Poincaré maps for toroidal magnetic fields. Plasma Physics and Controlled Fusion, 63(2), p.024001.

[3] In press.