8803 eng reportzib 1 -- 2022-10-25 -- This work presents an innovative short to mid-term forecasting model that analyzes nonlinear complex spatial and temporal dynamics in energy networks under demand and supply balance constraints using Network Nonlinear Time Series (TS) and Mathematical Programming (MP) approach. We address three challenges simultaneously, namely, the adjacency matrix is unknown; the total amount in the network has to be balanced; dependence is unnecessarily linear. We use a nonparametric approach to handle the nonlinearity and estimate the adjacency matrix under the sparsity assumption. The estimation is conducted with the Mathematical Optimisation method. We illustrate the accuracy and effectiveness of the model on the example of the natural gas transmission network of one of the largest transmission system operators (TSOs) in Germany, Open Grid Europe. The obtained results show that, especially for shorter forecasting horizons, the proposed method outperforms all considered benchmark models, improving the average nMAPE for 5.1% and average RMSE for 79.6% compared to the second-best model. The model is capable of capturing the nonlinear dependencies in the complex spatial-temporal network dynamics and benefits from both sparsity assumption and the demand and supply balance constraint. 1438-0064 urn:nbn:de:0297-zib-88037 publish Milena Petkovic Milena Petkovic Nazgul Zakiyeva 22-19 eng uncontrolled nonlinear time series eng uncontrolled mathematical optimization eng uncontrolled energy networks OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING MODAL-Gesamt Petkovic, Milena Applied Algorithmic Intelligence Methods MODAL-EnergyLab Zakiyeva, Nazgul Applied Optimization https://opus4.kobv.de/opus4-zib/files/8803/ZIBReport_22_19.pdf