Leibniz is a package providing facilities to express learnable differential equations based on PyTorch
Project description
Leibniz
Leibniz is a python package which provide facilities to express learnable differential equations with PyTorch
Install
pip install leibniz
How to use
As an example we solve a very simple advection problem, a box-shaped material transported by a constant steady wind.
import torch as th
import leibniz as lbnz
from leibniz.core3d.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')
How to release
python3 setup.py sdist bdist_wheel
python3 -m twine upload dist/*
git tag va.b.c master
git push origin va.b.c
Contributors
Acknowledge
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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