# RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure

arXiv: https://arxiv.org/abs/2311.10550 · HTML: https://mlsanity.com/paper/2311.10550/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 43 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 3 of 3)

- [On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds](https://mlsanity.com/paper/2101.03847/) (2021)
- [A globally convergent method to accelerate topology optimization using on-the-fly model reduction](https://mlsanity.com/paper/2004.05756/) (2020)
- [Data-driven framework for input/output lookup tables reduction: Application to hypersonic flows in chemical non-equilibrium](https://mlsanity.com/paper/2210.04269/) (2022)

## Abstract (arXiv)

Many engineering applications rely on the evaluation of expensive, non-linear high-dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order Nonlinear Approximation with Active Learning Procedure) to incrementally learn a fast and accurate reduced-order surrogate model of a target function on-the-fly as the application progresses. First, the combination of nonlinear auto-encoder, community clustering and radial basis function networks allows to learn an efficient and compact surrogate model with limited training data. Secondly, the active learning procedure overcome any extrapolation issue when evaluating the surrogate model outside of its initial training range during the online stage. This results in generalizable, fast and accurate reduced-order models of high-dimensional functions. The method is demonstrated on three direct numerical simulations of hypersonic flows in chemical nonequilibrium. Accurate simulations of these flows rely on detailed thermochemical gas models that dramatically increase the cost of such calculations. Using RONAALP to learn a reduced-order thermodynamic model surrogate on-the-fly, the cost of such simulation was reduced by up to 75% while maintaining an error of less than 10% on relevant quantities of interest.