# Convex Hybrid Modeling: An Operator-Based Approach

arXiv: https://arxiv.org/abs/2605.23151 · HTML: https://mlsanity.com/paper/2605.23151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 15 of 15)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Understanding neural networks with reproducing kernel Banach spaces](https://mlsanity.com/paper/2109.09710/) (2021)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Partition-based formulations for mixed-integer optimization of trained ReLU neural networks](https://mlsanity.com/paper/2102.04373/) (2021)
- [OMLT: Optimization & Machine Learning Toolkit](https://mlsanity.com/paper/2202.02414/) (2022)
- [Koopman Operators in Robot Learning](https://mlsanity.com/paper/2408.04200/) (2024)
- [Accelerating optimization over the space of probability measures](https://mlsanity.com/paper/2310.04006/) (2023)
- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [EDMD-Based Robust Observer Synthesis for Nonlinear Systems](https://mlsanity.com/paper/2509.09812/) (2025)
- [Koopman Operator for Stability Analysis: Theory with a Linear--Radial Product Reproducing Kernel](https://mlsanity.com/paper/2511.06063/) (2025)
- [Koopman-based Estimation of Lyapunov Functions: Theory on a Reproducing Kernel Hilbert Space](https://mlsanity.com/paper/2603.01403/) (2026)
- [Dissipativity Analysis of Nonlinear Systems: A Linear--Radial Kernel-based Approach](https://mlsanity.com/paper/2604.01373/) (2026)

## Abstract (arXiv)

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear ones, promoting the use of operator theory, which ``universally'' represents a nonlinear system by a nonparametric operator. On the other hand, interpretability requires by a ``non-universal'', parametric nonlinear model family satisfying first principles; these constraints tend to complicate the learning procedure. This paper considers hybrid modeling by formulating convex learning problems that account for interpretability systematically and give surrogate models efficiently. Three settings are discussed -- (i) regularization around a particular ``reference model'', (ii) restriction on an ``interpretable subspace'', and more generally, (iii) restriction on a ``interpretable manifold'' that is nonlinearly parameterized. In the more general setting, by introducing an operator-theoretic technique to re-parameterize models in the ``lifted'' parameters (``canonical features'', potentially infinite-dimensional), the system is regarded as a kernel-based mixture of interpretable models. Application to both static and dynamic models are exemplified in numerical studies.