# Convex Parameterizations and Fidelity Bounds for Nonlinear Identification and Reduced-Order Modelling

arXiv: https://arxiv.org/abs/1701.06652 · HTML: https://mlsanity.com/paper/1701.06652/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2017.

## Built on by (most cited first, 8 of 8)

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- [Learning Stable and Passive Neural Differential Equations](https://mlsanity.com/paper/2404.12554/) (2024)
- [R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networks](https://mlsanity.com/paper/2504.01250/) (2025)
- [React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN](https://mlsanity.com/paper/2506.01226/) (2025)
- [Distributed Identification of Contracting and/or Monotone Network Dynamics](https://mlsanity.com/paper/2107.14309/) (2021)

## Abstract (arXiv)

Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error minimization, leads to optimization problems that are generally non-convex in the model parameters and suffer from multiple local minima. In this work we present methods which address these problems through convex optimization, based on Lagrangian relaxation, dissipation inequalities, contraction theory, and semidefinite programming. We demonstrate the proposed methods with a model order reduction task for electronic circuit design and the identification of a pneumatic actuator from experiment.