Leibniz is a package providing facilities to express learnable differential equations based on PyTorch
Leibniz is a python package which provide facilities to express learnable differential equations with PyTorch
pip install leibniz
How to use
As an example we solve an very simple advection problem, a box-shaped material transported by a constant steady wind.
import torch as th import leibniz as lbnz from leibniz.core.gridsys.regular3 import RegularGrid from leibniz.diffeq import odeint as odeint def binary(tensor): return th.where(tensor > lbnz.zero, lbnz.one, lbnz.zero) # setup grid system lbnz.bind(RegularGrid( basis='x,y,z', W=51, L=151, H=51, east=16.0, west=1.0, north=6.0, south=1.0, upper=6.0, lower=1.0 )) lbnz.use('x,y,z') # use xyz coordinate # giving a material field as a box fld = binary((lbnz.x - 8) * (9 - lbnz.x)) * \ binary((lbnz.y - 3) * (4 - lbnz.y)) * \ binary((lbnz.z - 3) * (4 - lbnz.z)) # construct a constant steady wind wind = lbnz.one, lbnz.zero, lbnz.zero # transport value by wind def derivitive(t, clouds): return - lbnz.upwind(wind, clouds) # integrate the system with rk4 pred = odeint(derivitive, fld, th.arange(0, 7, 1 / 100), method='rk4')
We included source code with minor changes from torchdiffeq by Ricky Chen, because of two purpose:
- package torchdiffeq is not indexed by pypi
- package torchdiffeq is very convenient and mandatory
All our contribution is based on Ricky's Neural ODE paper (NIPS 2018) and his package.
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