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space_time_pde

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MeshfreeFlowNet: Physical Constrained Space Time Super-Resolution

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[![DOI](https://zenodo.org/badge/226422310.svg)](https://zenodo.org/badge/latestdoi/226422310)
# MeshfreeFlowNet

By: [Chiyu "Max" Jiang*](http://maxjiang.ml/), [Soheil Esmaeilzadeh*](https://soheilesm.github.io/), [Kamyar Azizzadenesheli](https://www.cs.purdue.edu/homes/kamyar/), [Karthik Kashinath](http://www.nersc.gov/about/nersc-staff/data-analytics-services/karthik-kashinath/), [Mustafa Mustafa](https://www.nersc.gov/about/nersc-staff/data-analytics-services/mustafa-mustafa/), [Hamdi Tchelepi](https://profiles.stanford.edu/hamdi-tchelepi), [Philip Marcus](http://www.me.berkeley.edu/people/faculty/philip-s-marcus), [Prabhat](http://www.nersc.gov/about/nersc-staff/data-analytics-services/prabhat/), [Anima Anandkumar](http://tensorlab.cms.caltech.edu/users/anima/) (* Denotes Equal Contributions)

Published at International Conference for High Performance Computing, Networking, Storage and Analysis (SC20). Best Student Paper Award Finalist.

\[[Project Website](http://www.maxjiang.ml/proj/meshfreeflownet)\] \[[Paper](https://arxiv.org/pdf/2005.01463.pdf)\] \[[Video](https://youtu.be/mjqwPch9gDo)\] \[[Addtional Video - APS DFD 2020 Presentation](https://www.youtube.com/watch?v=anZ_gLrvnYs&t=538s&ab_channel=SoheilEsmaeilzadeh)\]
 
![teaser](https://raw.githubusercontent.com/maxjiang93/space_time_pde/master/doc/meshfreeflownet_wide.png "meshfreeflownet_teaser")

This is the code repository for the MeshfreeFlowNet: physical constrained space time super-resolution. Code implemented in PyTorch.

## Introduction
MeshfreeFlowNet is a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet allows for: (i) the output to be sampled at all spatio-temporal resolutions, (ii) a set of Partial Differential Equation (PDE) constraints to be imposed, and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal domains owing to its fully convolutional encoder.

## Repo highlights
Here are a few reasons why you might be interested in using our code:
* We provide a general PyTorch-ready PDE layer that (i) allows evaluation of arbitrary combinations of partial differential equations (ii) provides a user-friendly interface that parses equations from human-readable string. (iii) computes gradient through any black-box function written using pytorch. Easy to plug-and-play into any physics informed ML projects. Find documentation and examples under [`src/`](src).
* We provide general layers for 3D U-Nets, continuous decoding network (using IM-NET backbone), and the interpolation layer.
* We provide scripts to reproduce the results in our paper.

---

### In case of using the code or finding the paper impactful in your research please consider citing:

@article{Jiang2020,
    archivePrefix = {arXiv},
    arxivId = {2005.01463},
    author = {Jiang, Chiyu Max and Esmaeilzadeh, Soheil and Azizzadenesheli, Kamyar and Kashinath, 
    Karthik and Mustafa, Mustafa and Tchelepi, Hamdi A. and Marcus, Philip and Prabhat and Anandkumar, Anima},
    eprint = {2005.01463},
    title = {{MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework}},
    url = {http://arxiv.org/abs/2005.01463},
    year = {2020}
    }

space_time_pde

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