# Input Convex Neural Networks for Building MPC

arXiv: https://arxiv.org/abs/2011.13227 · HTML: https://mlsanity.com/paper/2011.13227/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2020.

## Built on by (most cited first, 17 of 17)

- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Joint inference and input optimization in equilibrium networks](https://mlsanity.com/paper/2111.13236/) (2021)
- [Better Neural Network Expressivity: Subdividing the Simplex](https://mlsanity.com/paper/2505.14338/) (2025)
- [On Minimal Depth in Neural Networks](https://mlsanity.com/paper/2402.15315/) (2024)
- [On the Depth of Monotone ReLU Neural Networks and ICNNs](https://mlsanity.com/paper/2505.06169/) (2025)
- [Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC](https://mlsanity.com/paper/2110.15911/) (2021)
- [CDiNN -Convex Difference Neural Networks](https://mlsanity.com/paper/2103.17231/) (2021)
- [Structured Hammerstein-Wiener Model Learning for Model Predictive Control](https://mlsanity.com/paper/2107.04247/) (2021)
- [Real-Time Machine-Learning-Based Optimization Using Input Convex Long Short-Term Memory Network](https://mlsanity.com/paper/2311.07202/) (2023)
- [ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming](https://mlsanity.com/paper/2505.05261/) (2025)
- [Defining Neural Network Architecture through Polytope Structures of Dataset](https://mlsanity.com/paper/2402.02407/) (2024)
- [Efficient Data-Driven MPC for Demand Response of Commercial Buildings](https://mlsanity.com/paper/2401.15742/) (2024)
- [A Penalty-Based Guardrail Algorithm for Non-Decreasing Optimization with Inequality Constraints](https://mlsanity.com/paper/2405.01984/) (2024)
- [User-centric Vehicle-to-Grid Optimization with an Input Convex Neural Network-based Battery Degradation Model](https://mlsanity.com/paper/2505.11047/) (2025)
- [Control of dynamical systems with neural networks](https://mlsanity.com/paper/2510.12810/) (2025)
- [Dual Certified White-Box Inference for Input Convex Neural Networks](https://mlsanity.com/paper/2605.04722/) (2026)
- [Input convex neural networks as surrogates in mathematical optimisation](https://mlsanity.com/paper/2608.09707/) (2026)

## Abstract (arXiv)

Model Predictive Control in buildings can significantly reduce their energy consumption. The cost and effort necessary for creating and maintaining first principle models for buildings make data-driven modelling an attractive alternative in this domain. In MPC the models form the basis for an optimization problem whose solution provides the control signals to be applied to the system. The fact that this optimization problem has to be solved repeatedly in real-time implies restrictions on the learning architectures that can be used. Here, we adapt Input Convex Neural Networks that are generally only convex for one-step predictions, for use in building MPC. We introduce additional constraints to their structure and weights to achieve a convex input-output relationship for multistep ahead predictions. We assess the consequences of the additional constraints for the model accuracy and test the models in a real-life MPC experiment in an apartment in Switzerland. In two five-day cooling experiments, MPC with Input Convex Neural Networks is able to keep room temperatures within comfort constraints while minimizing cooling energy consumption.