Probabilistic state estimation in district heating grids using deep neural network

Probabilistic state estimation is critical for operating and controlling district heating grids efficiently. However, computational bottlenecks of traditional solvers limit the feasibility of uncertainty-aware Bayesian estimation. This paper proposes using deep neural networks (DNNs) to enable fast and accurate posterior estimation. Fullyconnected neural networks (FCNNs), convolutional neural networks (CNNs), and recurrent neural networks (RNNs) are evaluated as candidate approximators of the physical model. Markov chain Monte Carlo sampling in the heat exchange space is leveraged to generate posterior samples. Experiments on a benchmark heating grid demonstrate FCNNs can efficiently learn the mapping from heat exchanges to network states. A FCNN trained on 20 training epochs after hyperparameter optimization provides the best approximation accuracy and uncertainty estimates, outperforming prior methods based on Deep Neural Networks. The results highlight the potential of data -driven deep learning models for probabilistic state estimation. The proposed framework could enable real -time uncertainty-aware control and decision-making for future intelligent district heating grids.