Go to ICLR 2025 Conference homepageSemi-Supervised Neural Network Model For Quadratic Multiparametric Programming
Neural Networks (NN) with ReLU activation functions have been used as surrogate models for multiparametric quadratic problems (mp-QP) for a wide range of engineering applications. Researchers have suggested leveraging the piecewise affine property of deep NN models to solve mp-QP with linear constraints, which also exhibit piecewise affine behaviour. However, traditional deep NN applications to mp-QP fall short of providing optimal and feasible predictions, even when trained with large datasets. This study introduces a semi-supervised NN (SSNN) architecture that directly represents the mathematical structure of the global solution function. In contrast to generic NN training approaches, the proposed SSNN method derives a large proportion of model weights directly from the physical characteristics of the system, producing solutions with higher accuracy despite training on significantly smaller data sets. Since many energy management problems are formulated as QP, the proposed approach has been applied in energy systems to demonstrate proof of concept. Model performance in terms of solution accuracy and speed of the predictions was compared against a commercial solver and a generic NN model based on classical training. Results show KKT sufficient conditions for SSNN consistently outperform generic NN architectures with classical training using far less data. A similar performance advantage is shown using extreme, out-of-training distribution test data. Given its advantages of speed and reliability, the SSNN model can quickly produce optimal and feasible solutions within a second for millions of input parameters sampled from a distribution of stochastic demands and renewable generator dispatches, which can be used for simulations and long term planning.