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Apr 28, 2020
May 1, 2020



By: Chiyu "Max" Jiang*, Soheil Esmaeilzadeh*, Kamyar Azizzadenesheli, Karthik Kashinath, Mustafa Mustafa, Hamdi Tchelepi, Philip Marcus, Prabhat, Anima Anandkumar (* Denotes Equal Contributions)

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

[Project Website] [Paper] [Video] [Addtional Video - APS DFD 2020 Presentation]


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


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/.
  • 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:

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 = {},
year = {2020}