# Minimum Reduced-Order Models via Causal Inference

arXiv: https://arxiv.org/abs/2407.00271 · HTML: https://mlsanity.com/paper/2407.00271/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 128 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Extracting Sparse High-Dimensional Dynamics from Limited Data](https://mlsanity.com/paper/1707.08528/) (2017)
- [Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows](https://mlsanity.com/paper/1907.09909/) (2019)
- [Sparse Identification of Nonlinear Dynamical Systems via Reweighted ℓ1-regularized Least Squares](https://mlsanity.com/paper/2005.13232/) (2020)
- [Data-driven super-parameterization using deep learning: Experimentation with multi-scale Lorenz 96 systems and transfer-learning](https://mlsanity.com/paper/2002.11167/) (2020)
- [How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification](https://mlsanity.com/paper/1905.08061/) (2019)
- [A Randomized Algorithm for Approximating the Log Determinant of a Symmetric Positive Definite Matrix](https://mlsanity.com/paper/1503.00374/) (2015)
- [A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization](https://mlsanity.com/paper/2208.09104/) (2022)
- [Entropic Causal Inference for Neurological Applications](https://mlsanity.com/paper/2010.04247/) (2020)
- [Efficient Construction of Local Parametric Reduced Order Models Using Machine Learning Techniques](https://mlsanity.com/paper/1511.02909/) (2015)
- [ERFit: Entropic Regression Fit Matlab Package, for Data-Driven System Identification of Underlying Dynamic Equations](https://mlsanity.com/paper/2010.02411/) (2020)
- [Estimating Global Identifiability Using Conditional Mutual Information in a Bayesian Framework](https://mlsanity.com/paper/2304.02025/) (2023)

## Built on by (most cited first, 2 of 2)

- [Probing forced responses and causality in data-driven climate emulators: conceptual limitations and the role of reduced-order models](https://mlsanity.com/paper/2506.22552/) (2025)
- [Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Network](https://mlsanity.com/paper/2507.08749/) (2025)

## Abstract (arXiv)

Constructing sparse, effective reduced-order models (ROMs) for high-dimensional dynamical data is an active area of research in applied sciences. In this work, we study an efficient approach to identifying such sparse ROMs using an information-theoretic indicator called causation entropy. Given a feature library of possible building block terms for the sought ROMs, the causation entropy ranks the importance of each term to the dynamics conveyed by the training data before a parameter estimation procedure is performed. It thus allows for an efficient construction of a hierarchy of ROMs with varying degrees of sparsity to effectively handle different tasks. This article examines the ability of the causation entropy to identify skillful sparse ROMs when a relatively high-dimensional ROM is required to emulate the dynamics conveyed by the training dataset. We demonstrate that a Gaussian approximation of the causation entropy still performs exceptionally well even in presence of highly non-Gaussian statistics. Such approximations provide an efficient way to access the otherwise hard to compute causation entropies when the selected feature library contains a large number of candidate functions. Besides recovering long-term statistics, we also demonstrate good performance of the obtained ROMs in recovering unobserved dynamics via data assimilation with partial observations, a test that has not been done before for causation-based ROMs of partial differential equations. The paradigmatic Kuramoto-Sivashinsky equation placed in a chaotic regime with highly skewed, multimodal statistics is utilized for these purposes.