Physics-informed ANNs for dynamic, distributed and stochastic systems (SmartANN)

PN 5-12

Project description

We look at learning the physics behind experimental data for unknown spatio-temporal systems (Machine Physics Learning, MPL). MPL runtime demands are currently close to inhibitive for real-world systems, making parallelization via domain decomposition and other HPC techniques indispensable, and leading to load balancing problems still unsolved in HPC. In particular, we generalize the Finite Volume Neural Network (FINN) developed previously in the project PN 5-6, by including numerical techniques such as unstructured grids and adaptivity. Based on FINN, we develop an adaptive and flexible learning of differential operators using, e.g., dedicated flux and state kernels in neural networks to represent arbitrary forms of numerical discretization stencils. Additionally, we will develop a concept to estimate the combined (numerical forward and learning inverse) error of MPL and extend FINN towards multilevel PDE representation. By combining FINN, modern numerics and HPC, we make learning of computationally demanding physical problems tractable.

Project information

Project title Physics-informed ANNs for dynamic, distributed and stochastic systems (SmartANN)
Project leaders Sergey Oladyshkin (Dominik Göddeke)
Project staff Elena Kiseleva, doctoral researcher
Project duration February 2023 - October 2025
Project number PN 5-12

Publications PN 5-12

  1. 2024

    1. C. Homs-Pons et al., “Coupled Simulation and Parameter Inversion for Neural System  and Electrophysiological Muscle Models,” GAMM-Mitteilungen, Mar. 2024, doi: 10.1002/gamm.202370009.

  2. 2023

    1. K. Mouris et al., “Stability criteria for Bayesian calibration of reservoir sedimentation models,” Modeling Earth Systems and Environment, 2023, doi: 10.1007/s40808-023-01712-7.
    2. P.-C. Bürkner, I. Kröker, S. Oladyshkin, and W. Nowak, “The sparse Polynomial Chaos expansion: a fully Bayesian approach with joint priors on the coefficients and global selection of terms,” Journal of Computational Physics, p. 112210, 2023, doi: https://doi.org/10.1016/j.jcp.2023.112210.
    3. M. F. Morales Oreamuno, S. Oladyshkin, and W. Nowak, “Information-Theoretic Scores for Bayesian Model Selection and Similarity Analysis: Concept and Application to a Groundwater Problem,” Water Resources Research, vol. 59, no. 7, Art. no. 7, Jul. 2023, doi: 10.1029/2022WR033711.
    4. S. Oladyshkin, T. Praditia, I. Kroeker, F. Mohammadi, W. Nowak, and S. Otte, “The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory,” Neural Networks, vol. 166, pp. 85–104, Sep. 2023, doi: 10.1016/j.neunet.2023.06.036.
    5. R. Kohlhaas, I. Kröker, S. Oladyshkin, and W. Nowak, “Gaussian active learning on multi-resolution arbitrary polynomial chaos emulator: concept for bias correction, assessment of surrogate reliability and its application to the carbon dioxide benchmark,” Computational Geosciences, vol. 27, no. 3, Art. no. 3, 2023, doi: doi:10.1007/s10596-023-10199-1.
    6. C. C. Horuz et al., “Physical Domain Reconstruction with Finite Volume Neural Networks,” Applied Artificial Intelligence, vol. 37, no. 1, Art. no. 1, 2023, doi: https://doi.org/10.1080/08839514.2023.2204261.
    7. I. Kröker, S. Oladyshkin, and I. Rybak, “Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems,” Computational Geosciences, 2023, doi: 10.1007/s10596-023-10236-z.
    8. S. Schwindt et al., “Bayesian calibration points to misconceptions in three-dimensional hydrodynamic reservoir modelling,” Water Resources Research, vol. 59, p. e2022WR033660, 2023, doi: https://doi.org/10.1029/2022WR033660.
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