# Efficient reformulations of ReLU deep neural networks for surrogate modelling in power system optimisation

arXiv: https://arxiv.org/abs/2601.14673 · HTML: https://mlsanity.com/paper/2601.14673/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [Constrained Monotonic Neural Networks](https://mlsanity.com/paper/2205.11775/) (2022)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [An Alternative Method for Solving Security-Constrained Unit Commitment with Neural Network Based Battery Degradation Model](https://mlsanity.com/paper/2207.00650/) (2022)
- [A Neural Network-Based Distributional Constraint Learning Methodology for Mixed-Integer Stochastic Optimization](https://mlsanity.com/paper/2211.11392/) (2022)
- [Efficient constraint learning for data-driven active distribution network operation](https://mlsanity.com/paper/2208.03940/) (2022)
- [Optimal offering strategy for an aggregator across multiple products of European day-ahead market](https://mlsanity.com/paper/2208.12431/) (2022)
- [Inclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning](https://mlsanity.com/paper/2210.01540/) (2022)
- [Linearization of ReLU Activation Function for Neural Network-Embedded Optimization: Optimal Day-Ahead Energy Scheduling](https://mlsanity.com/paper/2310.01758/) (2023)

## Abstract (arXiv)

The ongoing decarbonisation of power systems is driving an increasing reliance on distributed energy resources, which introduces complex and nonlinear interactions that are difficult to capture in conventional optimisation models. As a result, machine learning based surrogate modelling has emerged as a promising approach, but integrating machine learning models such as ReLU deep neural networks (DNNs) directly into optimisation often results in nonconvex and computationally intractable formulations. This paper proposes a linear programming (LP) reformulation for a class of convexified ReLU DNNs with non-negative weight matrices beyond the first layer, enabling a tight and tractable embedding of learned surrogate models in optimisation. We evaluate the method using a case study on learning the prosumer's responsiveness within an aggregator bidding problem in the Danish tertiary capacity market. The proposed reformulation is benchmarked against state-of-the-art alternatives, including piecewise linearisation (PWL), MIP-based embedding, and other LP relaxations. Across multiple neural network architectures and market scenarios, the convexified ReLU DNN achieves solution quality comparable to PWL and MIP-based reformulations while significantly improving computational performance and preserving model fidelity, unlike penalty-based reformulations. The results demonstrate that convexified ReLU DNNs offer a scalable and reliable methodology for integrating learned surrogate models in optimisation, with applicability to a wide range of emerging power system applications.