SFB Transregio 154

Mathematical Modelling, Simulation and Optimization using the example of Gas Networks

Project: TRR 154 – SFB Transregio 154
Project/grant No.:239904186
Supported by DFG (Deutsche Forschungsgemeinschaft/ German Research Foundation)
Duration: 2018 – 2026

SFB TRR154 Transregio – Mathematical modelling, simulation and optimization using the example of gas networks is focused to provide certified novel answers to these grand challenges, based on mathematical modeling, simulation and optimization. Given the amount of data and the potential of stochastic effects, this is a formidable task all by itself, regardless from the actual process of distributing the proper amount of gas with the required quality to the customer.

In order to achieve this goal new paradigms in the integration of these disciplines and in particular in the interplay between integer and nonlinear programming in the context of stochastic data have to be established and brought to bear. Clearly, without a specified underlying structure of the problems to face, such a breakthrough is rather unlikely. Thus, the particular network structure, the given hierarchical hybrid modeling in terms of switching algebraic, ordinary and partial differential-algebraic equations of hyperbolic type that is present in gas network transportation systems gives rise to the confidence that the challenges can be met by the team of the proposed Transregio-CRC.

TRR154 subprojects

C03: Nodal control and the turnpike phenomenon (since 2014 | 2022 – 2026)
PI: Martin Gugat (FAU), Rüdiger Schultz (University of Duisburg-Essen)
This project at DFG
Turnpike results provide connections between the solutions of transient and the corresponding stationary optimal control problems that are often used as models in the control of gas transport networks. In this way turnpike
results give a theoretical foundation for the approximation of transient optimal controls by the solutions of stationary optimal control problems that have a simpler structure. Turnpike studies can also be considered as
investigations of the structure of the transient optimal controls. In the best case the stationary optimal controls approximate the transient optimal controls exponentially fast.

C05: Observer-based data assimilation for time dependent flows on gas networks (since 2019)
PI: Martin Gugat (FAU), Jan Giesselmann (TU Darmstadt)
This project at DFG
This project studies data assimilation methods for models of compressible flows in gas networks. The basic idea of data assimilation is to include measurement data into simulations during runtime in order to make their results
more precise and more reliable. This can be achieved by augmenting the original model equations with control terms at nodes and on pipes that steer the solutions towards the measured data. This gives rise to a new system
called “observer”. This project is going to explore how much data is needed so that convergence of the observer towards the solution of the original system can be guaranteed, how fast this convergence is and how measurement
errors affect the solution.

C07: Random Batch Methods for Optimal Control of Network Dynamics (2022 – 2026)
PI: Falk Hante (Humboldt-Universität zu Berlin), Enrique Zuazua (FAU)
This project at DFG
This project focuses on hyperbolic and parabolic dynamics on networks and random batch methods for control. The aim is to restrict the overall network dynamics to subgraphs as a random batch for the computation of a stochastic gradient descent direction. We aim to develop a convergence theory and develop control methodologies of gas networks employing techniques of model predictive control. This approach can then readily be extended to incorporate uncertainties in the model by adapting concepts from the theory of simultaneous control of parameter-dependent systems.

Efficient Simulation and Optimal Control of Large-scale Hyperbolic Networks (September 2024 – February 2025)
Internal subproject.
Contact: Yue Wang, Enrique Zuazua (FAU)

Uncertainty
We analyze the (stationary and transient) gas transport with uncertain boundary data. This leads to optimization problems with probabilistic constraints. Our main methods to work with probabilistic constrained optimization
problems are the spheric-radial decomposition and kernel-density estimation.

People involved

Enrique Zuazua
Martin Gugat
Michael Schuster
Martín Hernández
Ziqian Li
Ziqi Wang

Publications

K. Liu, E. Zuazua (2025) Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics, Math. Models Methods Appl. Sci., https://arxiv.org/html/2412.01619v1
M. Gugat (2025) Boundary stabilization of quasi-linear hyperbolic systems with varying time delay, SIAM Journal on Control and Optimization, Vol. 63, No. 1, pp. 452-471. https://doi.org/10.1137/24M1648570
Z. Li, Z. Wang, E. Zuazua (2025) A Potential Game Perspective in Federated Learning, https://dx.doi.org/10.48550/arXiv.2411.11793
Y. Song, Z. Wang, E. Zuazua (2025) FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning, Neural Networks, Vol. 181, No. 106772, ISSN: 0893-6080, DOI: 10.1016/j.neunet.2024.106772
Z. Li, K. Liu, L. Liverani, E. Zuazua (2025) Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
Z. Wang, E. Zuazua (2025) Approximate and Weighted Data Reconstruction Attack in Federated Learning
A. Alcalde, G. Fantuzzi, E. Zuazua (2025) Exact Sequence Classification with Hardmax Transformers, https://arxiv.org/abs/2502.02270
T. Crin-Barat, N. De Nitti, E. Zuazua (2025) On the decay of one-dimensional locally and partially dissipative hyperbolic systems, ESAIM:COCV, https://arxiv.org/abs/2206.00555
F. Zakaria, I. Ftouhi, E. Zuazua (2025) Optimal L^p-approximation of convex sets by convex subsets, https://arxiv.org/abs/2501.00928
M. Hernandez, E. Zuazua (2025) Deep Neural Networks: Multi-Classification and Universal Approximation, https://arxiv.org/abs/2409.06555v1
M. Gugat, M. Schuster, J. Sokolowski (2024) The location problem for compressor stations in pipeline networks, Mathematics and Mechanics of Complex Systems, Vol. 12, No. 4, pp. 507–546, https://doi.org/10.2140/memocs.2024.12.507
D. Ruiz-Balet, E. Zuazua (2024) Pattern control via diffusion interaction
M. Gugat (2024) Stabilization of a cyclic network of strings by nodal control, Journal of Evolution Equations, Vol. 25, No. 4, https://doi.org/10.1007/s00028-024-01030-0
M. Hernandez, E. Zuazua (2024) Uniform Turnpike Property and Singular Limits, Acta Appl Math, Vol. 190, No. 3, https://doi.org/10.1007/s10440-024-00640-7
A. Alcalde, G. Fantuzzi, E. Zuazua (2024) Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis
M. Hernandez, M. Lazar, S. Zamorano (2024) Averaged observations and turnpike phenomenon for parameter-dependent systems, https://arxiv.org/pdf/2404.17455
B. Dehman, E. Zuazua (2024) Boundary sidewise observability of the wave equation, J. Eur. Math. Soc. (JEMS)
A. Ulke, M. Schuster, S. Göttlich (2024) Steady State Blended Gas Flow on Networks: Existence and Uniqueness of Solutions
M. Schuster (2024) On the Convergence of Optimization Problems with Kernel Density Estimated Probabilistic Constraints
D.W.M. Veldman, E. Zuazua (2024) Local Stability and Convergence of Unconstrained Model Predictive Control
S. Zamorano, E. Zuazua (2024) Tracking controllability for finite-dimensional linear systems
N. De Nitti, D. Serre, E. Zuazua (2024) Pointwise constraints for scalar conservation laws with positive wave velocity
Z. Wang, Y. Song, E. Zuazua (2024) Approximate and Weighted Data Reconstruction Attack in Federated Learning, arXiv:2308.06822
C. Esteve, B. Geshkovski, D. Pighin, E. Zuazua (2024) Large-time asymptotics in deep learning, hal-02912516
G. Wang, Y. Zhang, E. Zuazua (2024) Observability for heat equations with time-dependent analytic memory, Arch Rational Mech Anal, Vol. 248, No. 115, https://doi.org/10.1007/s00205-024-02058-9
E. Zuazua (2024) Progress and future directions in machine learning through control theory Proceedings book FGS 2024, pp. 116, https://hdl.handle.net/10651/74677
A. Alvarez-Lopez, R. Orive-Illera, E. Zuazua (2024) Optimized classification with Neural ODEs via separability, Neural Networks, Vol. 180, 106640, arXiv:2312.13807
D.W.M. Veldman, A. Borkowski, E. Zuazua (2024) Stability and Convergence of a Randomized Model Predictive Control Strategy, IEEE Trans. Automat., Vol. 69, No. 9, pp. 6253-6260, 10.1109/TAC.2024.3375253
A. Alvarez-Lopez, A. Hadj Slimane, E. Zuazua (2024) Interplay between depth and width for interpolation in neural ODEs, Neural Networks, Vol. 180, pp. 106-640, https://doi.org/10.1016/j.neunet.2024.106640, ISSN 0893-6080, arXiv.2401.09902
J. Lecarós, J. Lopez-Rios, G.I. Montecinos, E. Zuazua (2024) Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements, Math. Meth. Appl. Sci., pp. 1–32, https://doi.org/10.1002/mma.10251
T. Crin-Barat, L-Y. Shou, E. Zuazua (2024) Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system, Ann. Inst. Henri Poincare (C) Anal. Non Lineaire, https://doi.org/10.4171/aihpc/128
M. Lazar, E. Zuazua (2024) Eigenvalue bounds for the Gramian operator of the heat equation, Automatica, Vol. 164, pp. 111-653, https://doi.org/10.1016/j.automatica.2024.111653
E. Zuazua (2024) Fourier series and sidewise control of 1-d waves, Volume in honor of Yves Meyer, Documents Mathématiques of the French Mathematical Society (SMF), Vol. 22, p. 341-365, arXiv:2308.04906
GM. Coclite, N. De Nitti, F. Maddalena, G. Orlando, E. Zuazua. (2024) Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings, M3AS
F. Della Pietra, G. Fantuzzi, L. Ignat, A.L. Masiello, E. Zuazua (2024) Finite element approximation of the Hardy constant. J. Convex Anal. – Special Issue Giuseppe Buttazzo 70
D. Ruiz-Balet, E. Zuazua (2024) Control of neural transport for normalising flows. J. Math. Pures Appl., Vol. 181, pp. 58-90, ISSN 0021-7824. https://doi.org/10.1016/j.matpur.2023.10.005
U. Biccari, Y. Song, X. Yuan, E. Zuazua (2024) A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation, Inverse Problems, IP-103963, https://arxiv.org/abs/2202.01589
M. Hernandez, R. Lecaros, S. Zamorano (2023) Averaged turnpike property for differential equations with random constant coefficients, Mathematical Control and Related Fields, Vol. 13, No. 2, pp. 808-832, https://doi.org/10.3934/mcrf.2022016

No publications found.

Our Publications at TRR154