# Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks

arXiv: https://arxiv.org/abs/2605.27756 · HTML: https://mlsanity.com/paper/2605.27756/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 75 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Deep Polynomial Neural Networks](https://mlsanity.com/paper/2006.13026/) (2020)
- [Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reduction](https://mlsanity.com/paper/2204.02462/) (2022)
- [Designing Inherently Interpretable Machine Learning Models](https://mlsanity.com/paper/2111.01743/) (2021)
- [Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning](https://mlsanity.com/paper/2202.05460/) (2022)
- [A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations](https://mlsanity.com/paper/2006.06154/) (2020)
- [A Quadratic Manifold for Model Order Reduction of Nonlinear Structural Dynamics](https://mlsanity.com/paper/1610.09902/) (2016)
- [Generalization of Quadratic Manifolds for Reduced Order Modeling of Nonlinear Structural Dynamics](https://mlsanity.com/paper/1610.09906/) (2016)
- [Kernel manifolds: nonlinear-augmentation dimensionality reduction using reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2509.00224/) (2025)
- [Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems](https://mlsanity.com/paper/2601.12161/) (2026)
- [Beyond the Kolmogorov Barrier: A Learnable Weighted Hybrid Autoencoder for Model Order Reduction](https://mlsanity.com/paper/2410.18148/) (2024)
- [NN-OpInf: an operator inference approach using structure-preserving composable neural networks](https://mlsanity.com/paper/2603.08488/) (2026)
- [Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework](https://mlsanity.com/paper/2605.14224/) (2026)

## Abstract (arXiv)

Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span. Such linear methods struggle, however, for data with slowly decaying Kolmogorov n-widths, such as advection-dominated and turbulent flows, which require many modes for accurate reconstruction; moreover, energy-based truncation can discard low-energy modes needed to capture small-scale features. Recent nonlinear manifold methods using polynomial mappings with alternating or greedy mode selection achieve better reconstruction with fewer modes, but fix the form of the nonlinear mapping a priori, limiting expressivity. In contrast, neural network (NN) manifolds offer greater expressivity yet employ energy-based selection. We present SparseModesNet, a dimensionality reduction framework that employs linear encoding and nonlinear NN decoding. The decoder leverages LassoNet, a method enforcing hierarchical sparsity through a residual connection with a linear skip layer, to simultaneously select informative modes and learn a nonlinear mapping that minimizes reconstruction error. On benchmark advection-dominated and chaotic flows, SparseModesNet matches or exceeds state-of-the-art performance. For turbulent channel flow at friction Reynolds number Reτ = 5200, our method reduces reconstruction error by 51-78% compared to existing polynomial manifold methods while maintaining interpretability through physically meaningful mode selection.