@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} } @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} } @inproceedings{PetkovicZakiyevaZittel, author = {Petkovic, Milena and Zakiyeva, Nazgul and Zittel, Janina}, title = {Statistical Analysis and Modeling for Detecting Regime Changes in Gas Nomination Time Series}, series = {Operations Research Proceedings 2021. OR 2021}, booktitle = {Operations Research Proceedings 2021. OR 2021}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-08623-6_29}, pages = {188 -- 193}, abstract = {As a result of the legislation for gas markets introduced by the European Union in 2005, separate independent companies have to conduct the transport and trading of natural gas. The current gas market of Germany, which has a market value of more than 54 billion USD, consists of Transmission System Operators (TSO), network users, and traders. Traders can nominate a certain amount of gas anytime and anywhere in the network. Such unrestricted access for the traders, on the other hand, increase the uncertainty in the gas supply management. Some customers' behaviors may cause abrupt structural changes in gas flow time series. In particular, it is a challenging task for the TSO operators to predict gas nominations 6 to 10 h-ahead. In our study, we aim to investigate the regime changes in time series of nominations to predict the 6 to 10 h-ahead of gas nominations.}, 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} } @article{HenningsPetkovicStreubel, author = {Hennings, Felix and Petkovic, Milena and Streubel, Tom}, title = {On the Numerical Treatment of Interlaced Target Values - Modeling, Optimization and Simulation of Regulating Valves in Gas Networks}, series = {Optimization and Engineering}, journal = {Optimization and Engineering}, publisher = {Springer Nature}, doi = {10.1007/s11081-023-09812-0}, abstract = {Due to the current and foreseeable shifts towards carbon dioxide neutral energy production, which will likely result in balancing fluctuating renewable energy generation by transforming power-to-gas-to-power as well as building a large-scale hydrogen transport infrastructure, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable. Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching. In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures. They provide direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves. Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network. That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas. In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process. Besides careful derivation, we compare simulation and optimization results with predictions of the widely adopted commercial simulation tool SIMONE, serving as our substitute for actual real-world transport operations.}, 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} } @article{LePetkovic, author = {Le, Thi Thai and Petkovic, Milena}, title = {Predicting Fluid Interface Instability in Energy Systems for Sustainable Energy Transition}, series = {Operations Research Proceedings}, journal = {Operations Research Proceedings}, abstract = {Due to the coexistence of different gases in underground storage, this work explores the interface stability's impact on energy storage, specifically during the injection and withdrawal of gases such as hydrogen and natural gas. A new approach of combing simulation and time series analysis is used to accurately predict instability modes in energy systems. Our simulation is based on the 2D Euler equations, solved using a second-order finite volume method with a staggered grid. The solution is validated by comparing them to experimental data and analytical solutions, accurately predicting the instability's behavior. We use time series analysis and state-of-the-art regime-switching methods to identify critical features of the interface dynamics, providing crucial insights into system optimization and design.}, language = {en} } @inproceedings{PetkovicZittel, author = {Petkovic, Milena and Zittel, Janina}, title = {Resilient Forecasting of High-Dimensional Network Time Series in the Energy Domain: A Hybrid Approach}, series = {Operations Research Proceedings 2023}, booktitle = {Operations Research Proceedings 2023}, abstract = {Energy systems are complex networks consisting of various interconnected components. Accurate energy demand and supply forecasts are crucial for efficient system operation and decision-making. However, high-dimensional data, complex network structures, and dynamic changes and disruptions in energy networks pose significant challenges for forecasting models. To address this, we propose a hybrid approach for resilient forecasting of network time series (HRF-NTS) in the energy domain. Our approach combines mathematical optimization methods with state-of-the-art machine learning techniques to achieve accurate and robust forecasts for high-dimensional energy network time series. We incorporate an optimization framework to account for uncertainties and disruptive changes in the energy system. The effectiveness of the proposed approach is demonstrated through a case study of forecasting energy demand and supply in a complex, large-scale natural gas transmission network. The results show that the hybrid approach outperforms alternative prediction models in terms of accuracy and resilience to structural changes and disruptions, providing stable, multi-step ahead forecasts for different short to mid-term forecasting horizons.}, 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{ZakiyevaPetkovic, author = {Zakiyeva, Nazgul and Petkovic, Milena}, title = {Modeling and Forecasting Gas Network Flows with Multivariate Time Series and Mathematical Programming Approach}, series = {Operations Research Proceedings 2021. OR 2021.}, booktitle = {Operations Research Proceedings 2021. OR 2021.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-08623-6_31}, pages = {200 -- 205}, abstract = {With annual consumption of approx. 95 billion cubic meters and similar amounts of gas just transshipped through Germany to other EU states, Germany's gas transport system plays a vital role in European energy supply. The complex, more than 40,000 km long high-pressure transmission network is controlled by several transmission system operators (TSOs) whose main task is to provide security of supply in a cost-efficient way. Given the slow speed of gas flows through the gas transmission network pipelines, it has been an essential task for the gas network operators to enhance the forecast tools to build an accurate and effective gas flow prediction model for the whole network. By incorporating the recent progress in mathematical programming and time series modeling, we aim to model natural gas network and predict gas in- and out-flows at multiple supply and demand nodes for different forecasting horizons. Our model is able to describe the dynamics in the network by detecting the key nodes, which may help to build an optimal management strategy for transmission system operators.}, 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} } @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} }