leibniz 0.2.0
Leibniz: a package providing facilities to express learnable differential equations based on PyTorch
Requires Python: >=3.9

# Leibniz

[![DOI](https://zenodo.org/badge/208940378.svg)](https://zenodo.org/badge/latestdoi/208940378)

Leibniz is a python package which provide facilities to express learnable differential equations with PyTorch

We also provide UNet, ResUNet and their variations, especially the Hyperbolic blocks for ResUNet.

Install
--------

```bash
pip install leibniz
```


How to use
-----------

### Physics-informed

As an example we solve a very simple advection problem, a box-shaped material transported by a constant steady wind.

![moving box](https://raw.githubusercontent.com/caiyunapp/leibniz/master/advection_3d.gif)


```python
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')
```

### UNet, ResUNet and variations

```python
from leibniz.unet import UNet
from leibniz.nn.layer.hyperbolic import HyperBottleneck
from leibniz.nn.activation import CappingRelu

unet = UNet(6, 1, normalizor='batch', spatial=(32, 64), layers=5, ratio=-1,
            vblks=[4, 4, 4, 4, 4], hblks=[1, 1, 1, 1, 1],
            scales=[-1, -1, -1, -1, -1], factors=[1, 1, 1, 1, 1],
            block=HyperBottleneck, relu=CappingRelu(), final_normalized=False)
```

We provide a ResUNet implementation, which is a UNet variation can insert ResNet blocks between layers.
The supported ResNet blocks are include
* Pure ResNet: Basic, Bottleneck block
* SENet variations: Basic, Bottleneck block
* Hyperbolic variations: Basic, Bottleneck block

We support 1d, 2d, 3d UNet.

normalizor are include:
* batch: BatchNorm
* layer: LayerNorm
* instance: InstanceNorm

Other hyperparameters are include:
* spatial: the sizes of the spatial dimentions
* ratio: the ratio to decide the intial number of channels into the UNet
* vblks: how many vertical blocks is inserted between two layers
* hblks: how many horizontal blocks is inserted in the skip connections
* scales: scale factors(power-2-based) on the spatial dimentions
* factors: expand or shrink factors(power-2-based) on the channels
* final_normalized: wheather to scale to final result between 0 to 1

### Piecewise Linear normalizor

Piecewise Linear normalizor provide an learnable monotonic peicewise linear functions and its inverse fucntion.
The API is shown as below

```python

from leibniz.nn.normalizor import PWLNormalizor

# on 3 channels, given 128 segmented pieces, and assuming the input data have a zero mean and 1.0 std
pwln = PWLNormalizor(3, 128, mean=0.0, std=1.0)

normed = pwln(input)
output = pwln.inverse(normed)
```

How to release
---------------

```bash
python3 setup.py sdist bdist_wheel
python3 -m twine upload dist/*

git tag va.b.c master
git push origin va.b.c
```

Contributors
------------

* Mingli Yuan ([Mountain](https://github.com/mountain))
* Xiang Pan ([Panpanx](https://github.com/Panpanx))
* Yi Liu ([YiLiu](https://github.com/YiLiu-Lly))

Acknowledge
-----------

We included source code with minor changes from [torchdiffeq](https://github.com/rtqichen/torchdiffeq) by Ricky Chen,
because of two purpose:
1. package torchdiffeq is not indexed by pypi
2. package torchdiffeq is very convenient and mandatory

All our contribution is based on Ricky's Neural ODE paper (NIPS 2018) and his package.