# Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems

arXiv: https://arxiv.org/abs/2307.14874 · HTML: https://mlsanity.com/paper/2307.14874/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2023.

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

- [CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations](https://mlsanity.com/paper/2402.14646/) (2024)
- [Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges](https://mlsanity.com/paper/2602.11378/) (2026)
- [Nonlinear model reduction for transport-dominated problems](https://mlsanity.com/paper/2602.01397/) (2026)
- [History-aware adaptive reduced-order models via incremental singular value decomposition](https://mlsanity.com/paper/2605.28684/) (2026)
- [In-context learning from self-generated trajectories for adaptive model reduction](https://mlsanity.com/paper/2607.02937/) (2026)

## Abstract (arXiv)

Online adaptive model reduction efficiently reduces numerical models of transport-dominated problems by updating reduced spaces over time, which leads to nonlinear approximations on latent manifolds that can achieve a faster error decay than classical linear model reduction methods that keep reduced spaces fixed. Critical for online adaptive model reduction is coupling the full and reduced model to judiciously gather data from the full model for adapting the reduced spaces so that accurate approximations of the evolving full-model solution fields can be maintained. In this work, we introduce lookahead data-gathering strategies that predict the next state of the full model for adapting reduced spaces towards dynamics that are likely to be seen in the immediate future. Numerical experiments demonstrate that the proposed lookahead strategies lead to accurate reduced models even for problems where previously introduced data-gathering strategies that look back in time fail to provide predictive models. The proposed lookahead strategies also improve the robustness and stability of online adaptive reduced models.