Non-intrusive model reduction of advection-dominated hyperbolic problems using neural network shift augmented manifold transformations
<|reference_start|>Non-intrusive model reduction of advection-dominated hyperbolic problems using neural network shift augmented manifold transformations: Advection-dominated problems are commonly noticed in nature, engineering systems, and a wide range of industrial processes. For these problems, linear approximation methods (proper orthogonal decomposition and reduced basis method) are not suitable, as the Kolmogorov $n$-width decay is slow, leading to inefficient and inaccurate reduced order models. There are few non-linear approaches to accelerate the Kolmogorov $n$-width decay. In this work, we use a neural-network shift augmented transformation technique, that employs automatic-shit detection and detects the optimal non-linear transformation of the full-order model solution manifold $\mathcal{M}$. We exploit a deep-learning framework to derive parameter-dependent bijective mapping between the manifold $\mathcal{M}$ and the transformed manifold $\tilde{\mathcal{M}}$. It consists of two neural networks, 1) ShiftNet, to employ automatic-shift detection by learning the shift-operator, which finds the optimal shifts for numerous snapshots of the full-order solution manifold, to accelerate the Kolmogorov $n$-width decay, and 2) InterpNet, which learns the reference configuration and can reconstruct the field values of the same, for each shifted grid distribution. We construct non-intrusive reduced order models on the resulting transformed linear subspaces and employ automatic-shift detection for predictions. We test our methodology on advection-dominated problems, such as 1D travelling waves, 2D isentropic convective vortex and 2D two-phase flow test cases. This work leads to the development of the complete NNsPOD-ROM algorithm for model reduction of advection-dominated problems, comprising both offline-online stages.<|reference_end|>
@article{gowrachari2024non-intrusive,
    title={Non-intrusive model reduction of advection-dominated hyperbolic problems
  using neural network shift augmented manifold transformations},
    author={Harshith Gowrachari, Nicola Demo, Giovanni Stabile and Gianluigi Rozza},
    journal={arXiv preprint arXiv:2407.18419},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18419},
    primaryClass={math.NA cs.NA physics.flu-dyn}
}