Reconstructing Two-phase Flows Using Level-Set PINNs

  • Silva, Romulo (COPPE/Federal University of Rio de Janeiro)
  • Grave, Malú (COPPE/Federal University of Rio de Janeiro)
  • Coutinho, Alvaro (COPPE/Federal University of Rio de Janeiro)

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Inverse problems in fluid mechanics play an essential role in science and engineering, especially when it comes to optimal design, reconstruction of biomedical and geophysical flows, parameter estimation, and more. These inverse problems are often ill-posed, thus, it is challenging or sometimes even impossible to solve them using traditional methods. Moreover, the generation of simulated data for ill-posed inverse problems can become very costly since simulations need to be performed several times to either discover missing physics or calibrate the free parameters in the model. One possible alternative for solving these problems is through the use of Physics-Informed Neural Networks - PINNs [1], in which we approximate the problem’s solution using Neural Networks while incorporating the known data and physical laws when training it, and also easily enabling us to take advantage of computational resources like GPUs without much effort. Here, we show a Level-Set PINN-based framework for reconstructing the velocity field for two-phase flows. We apply the framework to reconstruct gas bubbles rising in viscous liquid problems, given only the bubble position. We use synthetic data generated by AMR/C simulations with a phase-field approach [2]. The only data provided is a set of snapshots containing the flow visualization [3], i.e., the phase field, from which we try to infer the velocities and pressure fields. Our approach does not require any reinitialization scheme, as is usual when using a level-set approach and traditional numerical methods. Such a scheme can reconstruct the flow quantities with reasonable accuracy, and it is straightforward to parallelize when using a data-parallel approach. [1] Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378:686–707, 2019. [2] M. Grave and A. L. Coutinho. Comparing the convected level-set and the allen–cahn phase-field methods in amr/c simulations of two-phase flows. Computers Fluids, 244:105569, 2022. [3] M. Raissi, A. Yazdani, and G. E. Karniadakis. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 367(6481):1026–1030, 2020.