# LC-SVD-DLinear: A low-cost physics-based hybrid machine learning model for data forecasting using sparse measurements

arXiv: https://arxiv.org/abs/2411.17433 · HTML: https://mlsanity.com/paper/2411.17433/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 68 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 5 of 5)

- [ModelFLOWs-app: data-driven post-processing and reduced order modelling tools](https://mlsanity.com/paper/2305.17150/) (2023)
- [Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors](https://mlsanity.com/paper/1902.07358/) (2019)
- [Forecasting through deep learning and modal decomposition in two-phase concentric jets](https://mlsanity.com/paper/2212.12731/) (2022)
- [A predictive physics-aware hybrid reduced order model for reacting flows](https://mlsanity.com/paper/2301.09860/) (2023)
- [Low-cost singular value decomposition with optimal sensor placement](https://mlsanity.com/paper/2311.09791/) (2023)

## Abstract (arXiv)

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost variant of singular value decomposition (LC-SVD) with the DLinear architecture, which decomposes the input features-specifically, the temporal coefficients-into trend and seasonality components, enabling a shallow neural network to capture the non-linear dynamics of the temporal data. This methodology uses under-resolved data, which can either be input directly into the hybrid model or downsampled from high resolution using two distinct techniques provided by the methodology. Working with under-resolved cases helps reduce the overall computational cost. Additionally, we present a variant of the method, LC-HOSVD-DLinear, which combines a low-cost version of the high-order singular value decomposition (LC-HOSVD) algorithm with the DLinear network, designed for high-order data. These approaches have been validated using two datasets: first, a numerical simulation of three-dimensional flow past a circular cylinder at Re = 220; and second, an experimental dataset of turbulent flow passing a circular cylinder at Re = 2600. The combination of these datasets demonstrates the robustness of the method. The forecasting and reconstruction results are evaluated through various error metrics, including uncertainty quantification. The work developed in this article will be included in the next release of ModelFLOWs-app