# Input Convex Lipschitz Recurrent Neural Networks for Robust and Efficient Process Modeling and Optimization

arXiv: https://arxiv.org/abs/2401.07494 · HTML: https://mlsanity.com/paper/2401.07494/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 15 Jan 2024.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Lipschitz Recurrent Neural Networks](https://mlsanity.com/paper/2006.12070/) (2020)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [UnICORNN: A recurrent model for learning very long time dependencies](https://mlsanity.com/paper/2103.05487/) (2021)
- [Achieving robustness in classification using optimal transport with hinge regularization](https://mlsanity.com/paper/2006.06520/) (2020)
- [Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control](https://mlsanity.com/paper/1912.10360/) (2019)
- [Robust Machine Learning Modeling for Predictive Control Using Lipschitz-Constrained Neural Networks](https://mlsanity.com/paper/2308.13721/) (2023)
- [Spike-inspired Rank Coding for Fast and Accurate Recurrent Neural Networks](https://mlsanity.com/paper/2110.02865/) (2021)

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

- [SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions](https://mlsanity.com/paper/2604.22355/) (2026)

## Abstract (arXiv)

Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years, conventional neural networks often fail to address these two critical aspects simultaneously or even independently. Inspired by natural physical systems and established literature, input convex architectures are known to enhance computational efficiency in optimization tasks, whereas Lipschitz-constrained architectures improve robustness. However, combining these properties within a single model requires careful review, as inappropriate methods for enforcing one property can undermine the other. To overcome this, we introduce a novel network architecture, termed Input Convex Lipschitz Recurrent Neural Networks (ICL-RNNs). This architecture seamlessly integrates the benefits of convexity and Lipschitz continuity, enabling fast and robust neural network-based modeling and optimization. The ICL-RNN outperforms existing recurrent units in both computational efficiency and robustness. Additionally, it has been successfully applied to practical engineering scenarios, such as chemical process modeling and the modeling and control of Organic Rankine Cycle-based waste heat recovery systems. Source code is available at https://github.com/killingbear999/ICLRNN.