mlsanityData to 7 Oct 2026

A Fast Learning-Based Surrogate of Electrical Machines using a Reduced Basis

arXiv 2406.18990 ↗First posted 27 Jun 2024cs.LGcited by 0

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Abstract (arXiv)

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs, which are PDEs that depend on a set of parameters but are also temporal and spatial processes. Our contribution is a method hybridizing the Proper Orthogonal Decomposition and several Support Vector Regression machines. This method is conceived to work in real-time, thus aimed for being used in the context of digital twins, where a user can perform an interactive analysis of results based on the proposed surrogate. We present promising results on two use cases concerning electrical machines. These use cases are not toy examples but are produced an industrial computational code, they use meshes representing non-trivial geometries and contain non-linearities.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 19 of its 36 references that are in the map. First posted on arXiv 27 Jun 2024.

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References · 19

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  6. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  7. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  8. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  9. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  10. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  11. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
  12. 2022Message Passing Neural PDE Solverscited by 368
7 more
  1. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  2. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  3. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
  4. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 147
  5. 2018Deep Fluids: A Generative Network for Parameterized Fluid Simulationscited by 121
  6. 2019A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problemscited by 59
  7. 2020Building high accuracy emulators for scientific simulations with deep neural architecture searchcited by 36

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