# Automated Manifold Learning for Reduced Order Modeling

arXiv: https://arxiv.org/abs/2506.01741 · HTML: https://mlsanity.com/paper/2506.01741/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Automated Machine Learning on Graphs: A Survey](https://mlsanity.com/paper/2103.00742/) (2021)
- [Identifying the latent space geometry of network models through analysis of curvature](https://mlsanity.com/paper/2012.10559/) (2020)
- [Neighborhood Growth Determines Geometric Priors for Relational Representation Learning](https://mlsanity.com/paper/1910.05565/) (2019)
- [TabNAS: Rejection Sampling for Neural Architecture Search on Tabular Datasets](https://mlsanity.com/paper/2204.07615/) (2022)
- [Efficient AutoML Pipeline Search with Matrix and Tensor Factorization](https://mlsanity.com/paper/2006.04216/) (2020)
- [Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems](https://mlsanity.com/paper/2404.17535/) (2024)

## Built on by (most cited first, 1 of 1)

- [MEDAL: Manifold Embedding Distillation via Autoencoder Learning](https://mlsanity.com/paper/2605.24244/) (2026)

## Abstract (arXiv)

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we investigate the use of Geometric Representation Learning for the data-driven discovery of system dynamics from spatial-temporal data. We propose to encode similarity structure in such data in a spatial-temporal proximity graph, to which we apply a range of classical and deep learning-based manifold learning approaches to learn reduced order dynamics. We observe that while manifold learning is generally capable of recovering reduced order dynamics, the quality of the learned representations varies substantially across different algorithms and hyperparameter choices. This is indicative of high sensitivity to the inherent geometric assumptions of the respective approaches and suggests a need for careful hyperparameter tuning, which can be expensive in practise. To overcome these challenges, we propose a framework for Automated Manifold Learning, which selects a manifold learning approach and corresponding hyperparameter choices based on representative subsamples of the input graph. We demonstrate that the proposed framework leads to performance gains both in scalability and in the learned representations' accuracy in capturing local and global geometric features of the underlying system dynamics.