# Rank-Minimizing and Structured Model Inference

arXiv: https://arxiv.org/abs/2302.09521 · HTML: https://mlsanity.com/paper/2302.09521/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 19 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms](https://mlsanity.com/paper/2002.09726/) (2020)
- [Data-driven Structured Realization](https://mlsanity.com/paper/1611.02072/) (2016)
- [Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows](https://mlsanity.com/paper/2010.06701/) (2020)
- [Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation](https://mlsanity.com/paper/1910.00110/) (2019)
- [Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations](https://mlsanity.com/paper/2005.05890/) (2020)
- [Data-driven balancing of linear dynamical systems](https://mlsanity.com/paper/2104.01006/) (2021)
- [Quadrature-Based Vector Fitting: Implications For H2 System Approximation](https://mlsanity.com/paper/1403.4655/) (2014)
- [Structured vector fitting framework for mechanical systems](https://mlsanity.com/paper/2110.09220/) (2021)
- [Structured Optimization-Based Model Order Reduction for Parametric Systems](https://mlsanity.com/paper/2209.05101/) (2022)

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

- [Hankel Singular Value Regularization for Highly Compressible State Space Models](https://mlsanity.com/paper/2510.22951/) (2025)

## Abstract (arXiv)

While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and engineering. This work introduces a method that infers models from data with physical insights encoded in the form of structure and that minimizes the model order so that the training data are fitted well while redundant degrees of freedom without conditions and sufficient data to fix them are automatically eliminated. The models are formulated via solution matrices of specific instances of generalized Sylvester equations that enforce interpolation of the training data and relate the model order to the rank of the solution matrices. The proposed method numerically solves the Sylvester equations for minimal-rank solutions and so obtains models of low order. Numerical experiments demonstrate that the combination of structure preservation and rank minimization leads to accurate models with orders of magnitude fewer degrees of freedom than models of comparable prediction quality that are learned with structure preservation alone.