# Neural-Network-Augmented Projection-Based Model Order Reduction for Mitigating the Kolmogorov Barrier to Reducibility of CFD Models

arXiv: https://arxiv.org/abs/2212.08939 · HTML: https://mlsanity.com/paper/2212.08939/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2022.

## Built on by (most cited first, 5 of 5)

- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Canonical and Noncanonical Hamiltonian Operator Inference](https://mlsanity.com/paper/2304.06262/) (2023)
- [Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds](https://mlsanity.com/paper/2305.15490/) (2023)
- [GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications](https://mlsanity.com/paper/2406.03569/) (2024)
- [KROM: Kernelized Reduced Order Modeling](https://mlsanity.com/paper/2603.00360/) (2026)

## Abstract (arXiv)

Inspired by our previous work on mitigating the Kolmogorov barrier using a quadratic approximation manifold, we propose in this paper a computationally tractable approach for combining a projection-based reduced-order model (PROM) and an artificial neural network (ANN) for mitigating the Kolmogorov barrier to reducibility of convection-dominated flow problems. The main objective the PROM-ANN concept that we propose is to reduce the dimensionality of the online approximation of the solution beyond what is possible using affine and quadratic approximation manifolds. In contrast to previous approaches for constructing arbitrarily nonlinear manifold approximations for nonlinear model reduction that exploited one form or another of ANN, the training of the PROM-ANN we propose in this paper does not involve data whose dimension scales with that of the high-dimensional model; and this PROM-ANN is hyperreducible using any well-established hyperreduction method. Hence, unlike many other ANN-based approaches, the PROM-ANN concept we propose in this paper is practical for large-scale and industry-relevant CFD problems. Its potential is demonstrated here for a parametric, shock-dominated, benchmark problem.