@article{PetkovicChenGamrathetal., author = {Petkovic, Milena and Chen, Ying and Gamrath, Inken and Gotzes, Uwe and Hadjidimitrou, Natalia Selini and Zittel, Janina and Xu, Xiaofei and Koch, Thorsten}, title = {A hybrid approach for high precision prediction of gas flows}, series = {Energy Systems}, volume = {13}, journal = {Energy Systems}, doi = {10.1007/s12667-021-00466-4}, pages = {383 -- 408}, abstract = {About 23\% of the German energy demand is supplied by natural gas. Additionally, for about the same amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by transmissions system operators (TSOs). The number one priority of the TSOs is to ensure the security of supply. However, the TSOs have only very limited knowledge about the intentions and planned actions of the shippers (traders). Open Grid Europe (OGE), one of Germany's largest TSO, operates a high-pressure transport network of about 12,000 km length. With the introduction of peak-load gas power stations, it is of great importance to predict in- and out-flow of the network to ensure the necessary flexibility and security of supply for the German Energy Transition ("Energiewende"). In this paper, we introduce a novel hybrid forecast method applied to gas flows at the boundary nodes of a transport network. This method employs an optimized feature selection and minimization. We use a combination of a FAR, LSTM and mathematical programming to achieve robust high-quality forecasts on real-world data for different types of network nodes.}, language = {en} } @misc{PetkovicChenGamrathetal., author = {Petkovic, Milena and Chen, Ying and Gamrath, Inken and Gotzes, Uwe and Hadjidimitriou, Natalia Selini and Zittel, Janina and Xu, Xiaofei and Koch, Thorsten}, title = {A Hybrid Approach for High Precision Prediction of Gas Flows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73525}, abstract = {About 20\% of the German energy demand is supplied by natural gas. Ad- ditionally, for about twice the amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by so-called transmissions system operators or TSOs. The number one priority of the TSOs is to ensure security of supply. However, the TSOs have no knowledge of the intentions and planned actions of the shippers (traders). Open Grid Europe (OGE), one of Germany's largest TSO, operates a high- pressure transport network of about 12.000 km length. Since flexibility and security of supply is of utmost importance to the German Energy Transition ("Energiewende") especially with the introduction of peak-load gas power stations, being able to predict in- and out-flow of the network is of great importance. In this paper we introduce a new hybrid forecast method applied to gas flows at the boundary nodes of a transport network. The new method employs optimized feature minimization and selection. We use a combination of an FAR, LSTM DNN and mathematical programming to achieve robust high quality forecasts on real world data for different types of network nodes. Keywords: Gas Forecast, Time series, Hybrid Method, FAR, LSTM, Mathematical Optimisation}, language = {en} } @article{RoessigPetkovic, author = {R{\"o}ssig, Ansgar and Petkovic, Milena}, title = {Advances in Verification of ReLU Neural Networks}, series = {Journal of Global Optimization}, journal = {Journal of Global Optimization}, publisher = {Springer}, doi = {10.1007/s10898-020-00949-1}, abstract = {We consider the problem of verifying linear properties of neural networks. Despite their success in many classification and prediction tasks, neural networks may return unexpected results for certain inputs. This is highly problematic with respect to the application of neural networks for safety-critical tasks, e.g. in autonomous driving. We provide an overview of algorithmic approaches that aim to provide formal guarantees on the behavior of neural networks. Moreover, we present new theoretical results with respect to the approximation of ReLU neural networks. On the other hand, we implement a solver for verification of ReLU neural networks which combines mixed integer programming (MIP) with specialized branching and approximation techniques. To evaluate its performance, we conduct an extensive computational study. For that we use test instances based on the ACAS Xu System and the MNIST handwritten digit data set. Our solver is publicly available and able to solve the verification problem for instances which do not have independent bounds for each input neuron.}, language = {en} } @misc{PetkovicKochZittel, author = {Petkovic, Milena and Koch, Thorsten and Zittel, Janina}, title = {Deep learning for spatio-temporal supply and demand forecasting in natural gas transmission networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81221}, abstract = {Germany is the largest market for natural gas in the European Union, with an annual consumption of approx. 95 billion cubic meters. Germany's high-pressure gas pipeline network is roughly 40,000 km long, which enables highly fluctuating quantities of gas to be transported safely over long distances. Considering that similar amounts of gas are also transshipped through Germany to other EU states, it is clear that Germany's gas transport system is essential to the European energy supply. Since the average velocity of gas in a pipeline is only 25km/h, an adequate high-precision, high-frequency forecasting of supply and demand is crucial for efficient control and operation of such a transmission network. We propose a deep learning model based on spatio-temporal convolutional neural networks (DLST) to tackle the problem of gas flow forecasting in a complex high-pressure transmission network. Experiments show that our model effectively captures comprehensive spatio-temporal correlations through modeling gas networks and consistently outperforms state-of-the-art benchmarks on real-world data sets by at least 21\$\\%\$. The results demonstrate that the proposed model can deal with complex nonlinear gas network flow forecasting with high accuracy and effectiveness.}, language = {en} } @article{PetkovicKochZittel, author = {Petkovic, Milena and Koch, Thorsten and Zittel, Janina}, title = {Deep learning for spatio-temporal supply anddemand forecasting in natural gas transmission networks}, series = {Energy Science and Engineering}, journal = {Energy Science and Engineering}, doi = {https://doi.org/10.1002/ese3.932}, abstract = {Germany is the largest market for natural gas in the European Union, with an annual consumption of approx. 95 billion cubic meters. Germany's high-pressure gas pipeline network is roughly 40,000 km long, which enables highly fluctuating quantities of gas to be transported safely over long distances. Considering that similar amounts of gas are also transshipped through Germany to other EU states, it is clear that Germany's gas transport system is essential to the European energy supply. Since the average velocity of gas in a pipeline is only 25km/h, an adequate high-precision, high-frequency forecasting of supply and demand is crucial for efficient control and operation of such a transmission network. We propose a deep learning model based on spatio-temporal convolutional neural networks (DLST) to tackle the problem of gas flow forecasting in a complex high-pressure transmission network. Experiments show that our model effectively captures comprehensive spatio-temporal correlations through modeling gas networks and consistently outperforms state-of-the-art benchmarks on real-world data sets by at least 21\%. The results demonstrate that the proposed model can deal with complex nonlinear gas network flow forecasting with high accuracy and effectiveness.}, language = {en} } @inproceedings{PetkovicZittel, author = {Petkovic, Milena and Zittel, Janina}, title = {Forecasting and modeling the dynamics of large-scale energy networks under the supply and demand balance constraint}, series = {AIRO Springer Series: International Conference on Optimization and Decision Science}, booktitle = {AIRO Springer Series: International Conference on Optimization and Decision Science}, abstract = {With the emergence of "Big Data" the analysis of large data sets of high-dimensional energy time series in network structures have become feasible. However, building large-scale data-driven and computationally efficient models to accurately capture the underlying spatial and temporal dynamics and forecast the multivariate time series data remains a great challenge. Additional constraints make the problem more challenging to solve with conventional methods. For example, to ensure the security of supply, energy networks require the demand and supply to be balanced. This paper introduces a novel large-scale Hierarchical Network Regression model with Relaxed Balance constraint (HNR-RB) to investigate the network dynamics and predict multistep-ahead flows in the natural gas transmission network, where the total in- and out-flows of the network have to be balanced over a period of time. We concurrently address three main challenges: high dimensionality of networks with more than 100 nodes, unknown network dynamics, and constraint of balanced supply and demand in the network. The effectiveness of the proposed model is demonstrated through a real-world case study of forecasting demand and supply in a large-scale natural gas transmission network. The results demonstrate that HNR-RB outperforms alternative models for short- and mid-term horizons.}, language = {en} } @article{Dell’AmicoHadjidimitriouKochetal., author = {Dell'Amico, M. and Hadjidimitriou, Natalia Selini and Koch, Thorsten and Petkovic, Milena}, title = {Forecasting Natural Gas Flows in Large Networks}, series = {Machine Learning, Optimization, and Big Data. MOD 2017.}, volume = {Lecture Notes in Computer Science}, journal = {Machine Learning, Optimization, and Big Data. MOD 2017.}, number = {vol 10710}, doi = {https://doi.org/10.1007/978-3-319-72926-8_14}, pages = {158 -- 171}, abstract = {Natural gas is the cleanest fossil fuel since it emits the lowest amount of other remains after being burned. Over the years, natural gas usage has increased significantly. Accurate forecasting is crucial for maintaining gas supplies, transportation and network stability. This paper presents two methodologies to identify the optimal configuration o parameters of a Neural Network (NN) to forecast the next 24 h of gas flow for each node of a large gas network. In particular the first one applies a Design Of Experiments (DOE) to obtain a quick initial solution. An orthogonal design, consisting of 18 experiments selected among a total of 4.374 combinations of seven parameters (training algorithm, transfer function, regularization, learning rate, lags, and epochs), is used. The best result is selected as initial solution of an extended experiment for which the Simulated Annealing is run to find the optimal design among 89.100 possible combinations of parameters. The second technique is based on the application of Genetic Algorithm for the selection of the optimal parameters of a recurrent neural network for time series forecast. GA was applied with binary representation of potential solutions, where subsets of bits in the bit string represent different values for several parameters of the recurrent neural network. We tested these methods on three municipal nodes, using one year and half of hourly gas flow to train the network and 60 days for testing. Our results clearly show that the presented methodologies bring promising results in terms of optimal configuration of parameters and forecast error.}, language = {en} } @misc{ZakiyevaPetkovic, author = {Zakiyeva, Nazgul and Petkovic, Milena}, title = {High-dimensional high-frequency time series prediction with a mixed integer optimisation method}, series = {Operations Research Proceedings}, journal = {Operations Research Proceedings}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93114}, language = {en} } @article{ZakiyevaPetkovic, author = {Zakiyeva, Nazgul and Petkovic, Milena}, title = {High-dimensional high-frequency time series prediction with a mixed integer optimisation method}, series = {Operations Research Proceedings}, journal = {Operations Research Proceedings}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93068}, abstract = {We study a functional autoregressive model for high-frequency time series. We approach the estimation of the proposed model using a Mixed Integer Optimisation method. The proposed model captures serial dependence in the functional time series by including high-dimensional curves. We illustrate our methodology on large-scale natural gas network data. Our model provides more accurate day-ahead hourly out-of-sample forecast of the gas in and out-flows compared to alternative prediction models.}, language = {en} } @article{PetkovicZakiyeva, author = {Petkovic, Milena and Zakiyeva, Nazgul}, title = {Mathematical Optimization for Analyzing and Forecasting Nonlinear Network Time Series}, series = {Operations Research Proceedings 2022}, journal = {Operations Research Proceedings 2022}, abstract = {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, proposed method outperforms all considered benchmark models, improving the avarage nMAPE for 5.1\% and average RMSE for 79.6\% compared to the second-best model. The model is capable to capture the nonlinear dependencies in the complex spatial-temporal network dynamics and benefits from both sparsity assumption and the demand and supply balance constraint.}, language = {en} }