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        "author": "Mingli Yuan",
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        "description": "# Leibniz\n\n[![Build Status](https://api.travis-ci.com/caiyunapp/leibniz.svg?branch=master)](http://travis-ci.com/caiyunapp/leibniz) \n\nLeibniz is a python package which provide facilities to express learnable differential equations with PyTorch\n\n\nInstall\n--------\n\n```bash\npip install leibniz\n```\n\n\nHow to use\n-----------\n\nAs an example we solve an very simple advection problem, a box-shaped material transported by a constant steady wind.\n\n![moving box](https://raw.githubusercontent.com/caiyunapp/leibniz/master/advection_3d.gif)\n\n\n```python\nimport torch as th\nimport leibniz as lbnz\n\nfrom leibniz.core.gridsys.regular3 import RegularGrid\nfrom leibniz.diffeq import odeint as odeint\n\n\ndef binary(tensor):\n    return th.where(tensor > lbnz.zero, lbnz.one, lbnz.zero)\n\n# setup grid system\nlbnz.bind(RegularGrid(\n    basis='x,y,z',\n    W=51, L=151, H=51,\n    east=16.0, west=1.0,\n    north=6.0, south=1.0,\n    upper=6.0, lower=1.0\n))\nlbnz.use('x,y,z') # use xyz coordinate\n\n# giving a material field as a box \nfld = binary((lbnz.x - 8) * (9 - lbnz.x)) * \\\n      binary((lbnz.y - 3) * (4 - lbnz.y)) * \\\n      binary((lbnz.z - 3) * (4 - lbnz.z))\n\n# construct a constant steady wind\nwind = lbnz.one, lbnz.zero, lbnz.zero\n\n# transport value by wind\ndef derivitive(t, clouds):\n    return - lbnz.upwind(wind, clouds)\n\n# integrate the system with rk4\npred = odeint(derivitive, fld, th.arange(0, 7, 1 / 100), method='rk4')\n```\n\nContributors\n------------\n\n* Mingli Yuan ([Mountain](https://github.com/mountain))\n* Xiang Pan ([Panpanx](https://github.com/Panpanx))\n\nAcknowledge\n-----------\n\nWe included source code with minor changes from [torchdiffeq](https://github.com/rtqichen/torchdiffeq) by Ricky Chen,\nbecause of two purpose:\n1. package torchdiffeq is not indexed by pypi\n2. package torchdiffeq is very convenient and mandatory\n\nAll our contribution is based on Ricky's Neural ODE paper (NIPS 2018) and his package.\n\n\n\n\n",
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