# Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations

arXiv: https://arxiv.org/abs/2311.09740 · HTML: https://mlsanity.com/paper/2311.09740/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasets](https://mlsanity.com/paper/2108.07667/) (2021)
- [PhySRNet: Physics informed super-resolution network for application in computational solid mechanics](https://mlsanity.com/paper/2206.15457/) (2022)
- [Deep learning at scale for subgrid modeling in turbulent flows](https://mlsanity.com/paper/1910.00928/) (2019)
- [Augmenting a Physics-Informed Neural Network for the 2D Burgers Equation by Addition of Solution Data Points](https://mlsanity.com/paper/2301.07824/) (2023)
- [Real-time Health Monitoring of Heat Exchangers using Hypernetworks and PINNs](https://mlsanity.com/paper/2212.10032/) (2022)

## Built on by (most cited first, 1 of 1)

- [PointSAGE: Mesh-independent superresolution approach to fluid flow predictions](https://mlsanity.com/paper/2404.04615/) (2024)

## Abstract (arXiv)

In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental contrast between downsampling high-resolution images and authentically emulating low-resolution physics. The former method conserves more of the underlying physics, surpassing the usual constraints of real-world scenarios. We propose a novel definition of super-resolution tailored for PDE-based problems. Instead of simply downsampling from a high-resolution dataset, we use coarse-grid simulated data as our input and predict fine-grid simulated outcomes. Employing a physics-infused UNet upscaling method, we demonstrate its efficacy across various 2D-CFD problems such as discontinuity detection in Burger's equation, Methane combustion, and fouling in Industrial heat exchangers. Our method enables the generation of fine-mesh solutions bypassing traditional simulation, ensuring considerable computational saving and fidelity to the original ground truth outcomes. Through diverse boundary conditions during training, we further establish the robustness of our method, paving the way for its broad applications in engineering and scientific CFD solvers.