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Machine Learning Optimized Approach for Parameter Selection in MESHFREE Simulations

Paulami Banerjee, Mohan Padmanabha, Chaitanya Sanghavi, Isabel Michel, Simone Gramsch

TL;DR

A novel ML-optimized approach is introduced, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time.

Abstract

Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a comprehensive overview of our research combining Machine Learning (ML) and Fraunhofer's MESHFREE software (www.meshfree.eu), a powerful tool utilizing a numerical point cloud in a Generalized Finite Difference Method (GFDM). This tool enables the effective handling of complex flow domains, moving geometries, and free surfaces, while allowing users to finely tune local refinement and quality parameters for an optimal balance between computation time and results accuracy. However, manually determining the optimal parameter combination poses challenges, especially for less experienced users. We introduce a novel ML-optimized approach, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time. This research contributes valuable insights into parameter optimization in meshfree simulations, enhancing accessibility and usability for a broader user base in scientific and engineering applications.

Machine Learning Optimized Approach for Parameter Selection in MESHFREE Simulations

TL;DR

A novel ML-optimized approach is introduced, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time.

Abstract

Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a comprehensive overview of our research combining Machine Learning (ML) and Fraunhofer's MESHFREE software (www.meshfree.eu), a powerful tool utilizing a numerical point cloud in a Generalized Finite Difference Method (GFDM). This tool enables the effective handling of complex flow domains, moving geometries, and free surfaces, while allowing users to finely tune local refinement and quality parameters for an optimal balance between computation time and results accuracy. However, manually determining the optimal parameter combination poses challenges, especially for less experienced users. We introduce a novel ML-optimized approach, using active learning, regression trees, and visualization on MESHFREE simulation data, demonstrating the impact of input combinations on results quality and computation time. This research contributes valuable insights into parameter optimization in meshfree simulations, enhancing accessibility and usability for a broader user base in scientific and engineering applications.
Paper Structure (18 sections, 9 equations, 10 figures, 5 tables)

This paper contains 18 sections, 9 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Numerics Based on GFDM
  3. Point Cloud Management
  4. Differential Operators
  5. Physical Model
  6. Research Question
  7. Parameter Selection
  8. Use Case and Description of the Underlying Data
  9. Simulation Setup
  10. Data Generation
  11. Initial Data Exploration
  12. Approach
  13. Parameter Range Selection Using Active Learning
  14. Conformal Prediction using Ensemble Regression Models
  15. Results and Key Findings
  16. ...and 3 more sections

Figures (10)

  • Figure 1: Geometrical setup of the 3D flow around a cylinder
  • Figure 2: Point cloud and resulting interaction radius distribution for Hmin$\ =8.5e-3m$ and Hmax$\ =3.9e-2m$
  • Figure 3: Comparison of the temporal evolution of drag (red line) and lift (blue line) coefficients for a selected data sample with the corresponding ranges for the benchmarks in Schaefer1996 (dashed lines)
  • Figure 4: Correlation matrix for the selected parameters, drag and lift coefficients, as well as computation time
  • Figure 5: Cause-and-effect relationship between Hmax and lift coefficient $C_\mathrm{L}$ (blue dots) and benchmark range in Schaefer1996 (red dashed line)
  • ...and 5 more figures