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Improving CFD simulations by local machine-learned correction

Peetak Mitra, Majid Haghshenas, Niccolo Dal Santo, Conor Daly, David P. Schmidt

TL;DR

The paper tackles the high computational cost of CFD by introducing a neural-network–based local discretization-error correction that augments coarse-mesh simulations. The correction is learned from fine-mesh ground truth and applied as a source term in the Navier–Stokes equations, enabling low-cost coarse simulations to approach high-fidelity results. Key contributions include a 3D engineering-relevant demonstration with numerical stability, a hybrid $L_2$/$L_1$ loss and Bayesian hyperparameter optimization, and reported $3$–$5\times$ speedups with minimal accuracy loss. This work strengthens the CFD cost/accuracy trade-off and points to scalable improvements for design-space explorations, especially when applied to larger problems and near-wall dynamics in turbulent flows.

Abstract

High-fidelity computational fluid dynamics (CFD) simulations for design space explorations can be exceedingly expensive due to the cost associated with resolving the finer scales. This computational cost/accuracy trade-off is a major challenge for modern CFD simulations. In the present study, we propose a method that uses a trained machine learning model that has learned to predict the discretization error as a function of largescale flow features to inversely estimate the degree of lost information due to mesh coarsening. This information is then added back to the low-resolution solution during runtime, thereby enhancing the quality of the under-resolved coarse mesh simulation. The use of a coarser mesh produces a non-linear benefit in speed while the cost of inferring and correcting for the lost information has a linear cost. We demonstrate the numerical stability of a problem of engineering interest, a 3D turbulent channel flow. In addition to this demonstration, we further show the potential for speedup without sacrificing solution accuracy using this method, thereby making the cost/accuracy trade-off of CFD more favorable.

Improving CFD simulations by local machine-learned correction

TL;DR

The paper tackles the high computational cost of CFD by introducing a neural-network–based local discretization-error correction that augments coarse-mesh simulations. The correction is learned from fine-mesh ground truth and applied as a source term in the Navier–Stokes equations, enabling low-cost coarse simulations to approach high-fidelity results. Key contributions include a 3D engineering-relevant demonstration with numerical stability, a hybrid / loss and Bayesian hyperparameter optimization, and reported – speedups with minimal accuracy loss. This work strengthens the CFD cost/accuracy trade-off and points to scalable improvements for design-space explorations, especially when applied to larger problems and near-wall dynamics in turbulent flows.

Abstract

High-fidelity computational fluid dynamics (CFD) simulations for design space explorations can be exceedingly expensive due to the cost associated with resolving the finer scales. This computational cost/accuracy trade-off is a major challenge for modern CFD simulations. In the present study, we propose a method that uses a trained machine learning model that has learned to predict the discretization error as a function of largescale flow features to inversely estimate the degree of lost information due to mesh coarsening. This information is then added back to the low-resolution solution during runtime, thereby enhancing the quality of the under-resolved coarse mesh simulation. The use of a coarser mesh produces a non-linear benefit in speed while the cost of inferring and correcting for the lost information has a linear cost. We demonstrate the numerical stability of a problem of engineering interest, a 3D turbulent channel flow. In addition to this demonstration, we further show the potential for speedup without sacrificing solution accuracy using this method, thereby making the cost/accuracy trade-off of CFD more favorable.
Paper Structure (9 sections, 3 equations, 5 figures, 2 tables)

This paper contains 9 sections, 3 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Machine learning algorithm
  4. Modified Governing Equations
  5. Problem setup
  6. Inputs
  7. Quantitative metrics
  8. Results
  9. Conclusions

Figures (5)

  • Figure 1: A schematic of the solution correction technique employed by the locally enhanced approach, nudging the low-fidelity solution towards the more accurate solutionwatt2021correcting.
  • Figure 2: The midplane clips suggest the locally enhanced simulation (right panel) is able to recover lost near wall information, thereby lowering errors and improving time to solution. The panel at the left is from the fine to coarse mesh mapping, the middle panel is from the coarse mesh simulation, and the right panel is from the network-enhanced simulation. Each plan shows the mid-clip plane colored by the velocity magnitude (scaled similarity). The network enhanced (right panel) recovers missing information (ground truth in the left panel) compared to the coarse mesh (middle panel) simulation.
  • Figure 3: The velocity magnitude difference between the mapped (ground truth) and the CFD simulations. The left panel shows the uncorrected coarse-mesh discrepancy. The locally enhanced simulation (right panel) is able to recover lost information in the near-wall region thereby improving solution accuracy. The differences in the velocity magnitude further confirm the earlier observation that the network enhanced (right panel) recovers missing information, and therefore has lower velocity magnitude differences.
  • Figure 4: Both panels indicate the local enhancement is able to provide better solutions at a lower cost, even for unseen run conditions. The timing plot on the left shows the relative improvement in the cost versus accuracy, as a result of the local enhancement. The size of the circles indicates the reduction factor of the cell count. The right panel shows the norm of the error at a range of Reynolds numbers, indicating the ability of the scheme to work at other Reynolds numbers.
  • Figure 5: Each panel shows plots of three different curves. One for the mapped field, one from the coarse mesh simulations, and one from the coarse mesh enhanced simulation. The left most panel shows the time-averaged behavior and indicates information recovery for the coarse mesh enhanced simulation and a consistent tracking of the mapped field (ground truth data). The middle and the right panel are from instantaneous Turbulent Kinetic Energy and Reynolds stress behavior in the near wall region. It is evident that the enhanced simulation recovers near wall behavior better compared to the low resolution coarse mesh simulation.