# Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

arXiv: https://arxiv.org/abs/2007.12167 · HTML: https://mlsanity.com/paper/2007.12167/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2020.

## Built on by (most cited first, 11 of 11)

- [Nonlinear proper orthogonal decomposition for convection-dominated flows](https://mlsanity.com/paper/2110.08295/) (2021)
- [Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling](https://mlsanity.com/paper/2111.06173/) (2021)
- [textitFastSVD-ML-ROM: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications](https://mlsanity.com/paper/2207.11842/) (2022)
- [Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles](https://mlsanity.com/paper/2302.09748/) (2023)
- [Multi-fidelity physics constrained neural networks for dynamical systems](https://mlsanity.com/paper/2402.02031/) (2024)
- [Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint](https://mlsanity.com/paper/2409.00458/) (2024)
- [An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes](https://mlsanity.com/paper/2202.06170/) (2022)
- [Conditional variational autoencoder with Gaussian process regression recognition for parametric models](https://mlsanity.com/paper/2305.09625/) (2023)
- [Sim+Real: Joint Simulation-Experiment Training Improves Balanced Prediction in Physical Systems](https://mlsanity.com/paper/2610.01974/) (2026)
- [Calibrated Principal Component Regression](https://mlsanity.com/paper/2510.19020/) (2025)
- [Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design](https://mlsanity.com/paper/2604.14424/) (2026)

## Abstract (arXiv)

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. We assess the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.