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Flow reconstruction by multiresolution optimization of a discrete loss with automatic differentiation.

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We developed multiresolution Optimizing a DIscrete Loss (mODIL), a fast computational method for solving fluid mechanics inverse problems. This powerful technique significantly reduces computational cost compared to Physics-Informed Neural Networks (PINNs).

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Area of Science:

  • Computational fluid dynamics
  • Inverse problems
  • Optimization methods

Background:

  • Inverse problems in fluid mechanics are crucial for understanding and predicting fluid behavior.
  • Existing methods for solving these problems can be computationally expensive and prone to local minima.
  • The Optimizing a DIscrete Loss (ODIL) framework offers a deterministic approach to inverse problems.

Purpose of the Study:

  • To present a potent and accelerated computational method for solving inverse problems in fluid mechanics.
  • To improve the efficiency and robustness of gradient-based optimization for grid-based parameters.
  • To reduce the computational cost compared to existing methods like Physics-Informed Neural Networks (PINNs).

Main Methods:

  • Introduction of a multigrid decomposition technique to accelerate gradient-based optimization.
  • Integration of the multigrid technique into the Optimizing a DIscrete Loss (ODIL) framework, creating multiresolution ODIL (mODIL).
  • Utilization of automatic differentiation for efficient gradient calculation within the mODIL framework.
  • Demonstration on diverse problems: Burgers equation, thermal conductivity inference, and 3D body shape reconstruction from wake velocity.

Main Results:

  • mODIL accelerates the original ODIL framework by an order of magnitude.
  • mODIL demonstrates improved avoidance of local minima during optimization.
  • Comparative study shows mODIL has 3-5 orders of magnitude lower computational cost than PINNs on benchmark problems.
  • Successful application to various inverse and flow reconstruction tasks, including complex 3D scenarios.

Conclusions:

  • mODIL is a highly potent, fast, and consistent method for addressing inverse problems in fluid mechanics.
  • The developed technique offers significant computational advantages over established methods like PINNs.
  • mODIL facilitates easier implementation through automatic differentiation and improved optimization performance.