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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.

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 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.

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.

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

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.

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.