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Data-efficient operator learning for solving high Mach number fluid flow problems

arXiv 2311.16860 ↗First posted 28 Nov 2023cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

We consider the problem of using SciML to predict solutions of high Mach fluid flows over irregular geometries. In this setting, data is limited, and so it is desirable for models to perform well in the low-data setting. We show that Neural Basis Functions (NBF), which learns a basis of behavior modes from the data and then uses this basis to make predictions, is more effective than a basis-unaware baseline model. In addition, we identify continuing challenges in the space of predicting solutions for this type of problem.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 12 of its 22 references that are in the map. First posted on arXiv 28 Nov 2023.

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References · 12

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,223
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,989
  3. 2021Characterizing possible failure modes in physics-informed neural networkscited by 637
  4. 2019DeepXDE: A deep learning library for solving differential equationscited by 618
  5. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 538
  6. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 522
  7. 2020ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learningcited by 201
  8. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 88
  9. 2014A Stochastic Quasi-Newton Method for Large-Scale Optimizationcited by 68
  10. 2021LocoProp: Enhancing BackProp via Local Loss Optimizationcited by 15
  11. 2022Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equationscited by 4
  12. 2022Neural Basis Functions for Accelerating Solutions to High Mach Euler Equationscited by 2

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