# VpROM: A novel Variational AutoEncoder-boosted Reduced Order Model for the treatment of parametric dependencies in nonlinear systems

arXiv: https://arxiv.org/abs/2304.12437 · HTML: https://mlsanity.com/paper/2304.12437/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2023.

## Built on by (most cited first, 6 of 6)

- [VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification](https://mlsanity.com/paper/2405.20905/) (2024)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [Uncertainty Quantification for Reduced-Order Surrogate Models Applied to Cloud Microphysics](https://mlsanity.com/paper/2511.04534/) (2025)
- [KROM: Kernelized Reduced Order Modeling](https://mlsanity.com/paper/2603.00360/) (2026)
- [UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows](https://mlsanity.com/paper/2503.23236/) (2025)
- [Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation](https://mlsanity.com/paper/2602.23188/) (2026)

## Abstract (arXiv)

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition, however, such methods can become inefficient or fail in the case of parameteric or strongly nonlinear models. Such limitations are usually tackled via a library of local reduction bases each of which being valid for a given parameter vector. The success of such methods, however, is strongly reliant upon the method used to relate the parameter vectors to the local bases, this is typically achieved using clustering or interpolation methods. We propose the replacement of these methods with a Variational Autoencoder (VAE) to be used as a generative model which can infer the local basis corresponding to a given parameter vector in a probabilistic manner. The resulting VAE-boosted parametric ROM VpROM still retains the physical insights of a projection-based method but also allows for better treatment of problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.