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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.

Deep learning for spatio-temporal supply and demand forecasting in natural gas transmission networks
(2021)

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.

Deep learning for spatio-temporal supply anddemand forecasting in natural gas transmission networks
(2021)

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.

With annual consumption of approx. 95 billion cubic me-ters and similar amounts of gas just transshipped through Germany toother EU states, Germany’s gas transport system plays a vital role inEuropean energy supply. The complex, more than 40,000 km long high-pressure transmission network is controlled by several transmission sys-tem operators (TSOs) whose main task is to provide security of supplyin a cost-efficient way. Given the slow speed of gas flows through the gastransmission network pipelines, it has been an essential task for the gasnetwork operators to enhance the forecast tools to build an accurate andeffective gas flow prediction model for the whole network. By incorpo-rating the recent progress in mathematical programming and time seriesmodeling, we aim to model natural gas network and predict gas in- andout-flows at multiple supply and demand nodes for different forecastinghorizons. Our model is able to describe the dynamics in the network bydetecting the key nodes, which may help to build an optimal manage-ment strategy for transmission system operators.

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.

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 hours ahead. In our study, we aim to investigate the regime changes in the time series of nominations to predict the 6 to 10 hours ahead of gas nominations.

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.

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.

Due to the current and foreseeable shifts in energy production, 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 full 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 commercial simulation tool SIMONE.