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

• URL: http://arxiv.org/abs/2311.09740v3
• Date: Mon, 27 Nov 2023 03:09:21 GMT
• Title: Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations
• Authors: Rajat Kumar Sarkar, Ritam Majumdar, Vishal Jadhav, Sagar Srinivas Sakhinana, Venkataramana Runkana
• Abstract summary: We propose a novel definition of super-resolution tailored for PDE-based problems. We use coarse-grid simulated data as our input and predict fine-grid simulated outcomes. Our method enables the generation of fine-mesh solutions bypassing traditional simulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

Related papers

• Text2PDE: Latent Diffusion Models for Accessible Physics Simulation [7.16525545814044]
  We introduce several methods to apply latent diffusion models to physics simulation. We show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.
  arXiv  Detail & Related papers  (2024-10-02T01:09:47Z)
• Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates [3.909855210960908]
  We investigate and extend neural PDE solvers as a tool to aid in scaling simulations for two-phase flow problems. We extend existing numerical methods for this problem to a more complex setting involving varying geometries of the domain. We find that the investigated methods can accurately model the droplet dynamics with up to three orders of magnitude speed-up.
  arXiv  Detail & Related papers  (2024-05-27T15:18:12Z)
• PhyRecon: Physically Plausible Neural Scene Reconstruction [81.73129450090684]
  We introduce PHYRECON, the first approach to leverage both differentiable rendering and differentiable physics simulation to learn implicit surface representations. Central to this design is an efficient transformation between SDF-based implicit representations and explicit surface points. Our results also exhibit superior physical stability in physical simulators, with at least a 40% improvement across all datasets.
  arXiv  Detail & Related papers  (2024-04-25T15:06:58Z)
• PointSAGE: Mesh-independent superresolution approach to fluid flow predictions [0.0]
  High-resolution CFD simulations offer valuable insights into fluid behavior and flow patterns. As resolution increases, computational data requirements and time increase proportionately. We propose PointSAGE, a mesh-independent network to learn the complex fluid flow and directly predict fine simulations.
  arXiv  Detail & Related papers  (2024-04-06T12:49:09Z)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• MAgNet: Mesh Agnostic Neural PDE Solver [68.8204255655161]
  Climate predictions require fine-temporal resolutions to resolve all turbulent scales in the fluid simulations. Current numerical model solveers PDEs on grids that are too coarse (3km to 200km on each side) We design a novel architecture that predicts the spatially continuous solution of a PDE given a spatial position query.
  arXiv  Detail & Related papers  (2022-10-11T14:52:20Z)
• Multi-fidelity Hierarchical Neural Processes [79.0284780825048]
  Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2022-06-10T04:54:13Z)
• Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity [0.0]
  We leverage the governing equations and boundary conditions of the physical system to train the model without using any high-resolution labeled data. We demonstrate that the super-resolved fields match the accuracy of an advanced numerical solver running at 400 times the coarse mesh resolution.
  arXiv  Detail & Related papers  (2021-12-16T07:39:50Z)
• Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations [2.7892067588273517]
  We introduce a machine learning (ML) technique that corrects the numerical errors induced by a coarse-grid simulation of turbulent flows at high-Reynolds numbers. Our proposed simulation strategy is a hybrid ML-PDE solver that is capable of obtaining a meaningful high-resolution solution trajectory.
  arXiv  Detail & Related papers  (2020-09-30T19:29:21Z)
• Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction [79.81193813215872]
  We develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. We show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions.
  arXiv  Detail & Related papers  (2020-07-08T21:23:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.