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Master Thesis: Unsupervised Learning of a Dynamic Surrogate Model using DAE-PINNs applied to a dynamic flash model

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© Giannios Georgios

Introduction

In the process industry, a commonly used approach to control a system is model predictive control (MPC) due to several reasons [1]. It utilizes an underlying system model to predict the future behavior of the control system. The knowledge about the future can be used to compute optimal control sequences given the underlying system model. Furthermore, it can be used to deal with multivariable processes and can cope with constraints.
However, accurate system models are often computationally expensive due to the solution of the differential-algebraic equation system (DAE), hence preventing the computation of an optimal control sequence in real-time [2]. A common solution is to use a dynamic surrogate model in the optimization to reduce the computational load with the drawbacks that the model may be less precise and, in case of supervised learning, training data has to be generated in advance. One typical issue arising from conventional supervised learning of surrogate models is the fact that it can lack on generalization capabilities. In addition to that, while many methods exist to build surrogate models of static or simple ODE models, developing a surrogate model for a DAE-system still remains a challenging task.
One recent evolution counteracting this issue are physics-informed neural networks (PINNs). They utilize physically derived equations and solve them according to different solution schemes [3]–[5]. They show good generalization capabilities and can be completely trained in an unsupervised fashion, which avoids the need to compute the training samples in advance, potentially speeding up the training process. Furthermore, the training process may not rely on noisy data, which complicates the training process.
In this work, techniques of PINN-training are applied to the DAE system underlying a complex flash model simulation. The approach shall be compared to classical supervised learning with respect to generalization capabilities and tracking of model dynamics and steady state values.

Objectives

  • Literature research on established PINN training algorithms like DAE-PINNs mentioned in [3], [4], …
  • Implementation of unsupervised DAE-PINN training techniques applied to the dynamic flash model
  • Comparison of PINN with respect to conventional trained (supervised leaning) benchmark neural network (generalization capabilities, steady state tracking, tracking of system dynamics, …)

Prerequisites

  • Experience in optimization and programming
  • Experience in machine learning, deep learning
  • Sophisticated basics in numerical integration schemes
  • Python experience is beneficial

Literature

[1] L. Grüne and J. Pannek, Nonlinear model predictive control, Second Edition. Cham, Switzerland: Springer Berlin Heidelberg, 2017.

[2] P. Kumar, J. B. Rawlings, and S. J. Wright, “Industrial, large-scale model predictive control with structured neural networks,” Computers & Chemical Engineering, vol. 150, p. 107291, Jul. 2021, doi: 10.1016/j.compchemeng.2021.107291.

[3] C. Moya and G. Lin, “DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks.” arXiv, Sep. 09, 2021. Accessed: Jul. 20, 2022. [Online]. Available: http://arxiv.org/abs/2109.04304

[4] S. Wang, Y. Teng, and P. Perdikaris, “Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks,” SIAM J. Sci. Comput., vol. 43, no. 5, pp. A3055–A3081, Jan. 2021, doi: 10.1137/20M1318043.

[5] M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational Physics, vol. 378, pp. 686–707, Feb. 2019, doi: 10.1016/j.jcp.2018.10.045.

Other

Your work will mostly be in English and you can communicate with your supervisor in English or German.
Please contact us for any further questions. We can discuss all details in a personal consultation.

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Location & approach

The campus of TU Dort­mund University is located close to interstate junction Dort­mund West, where the Sauerlandlinie A 45 (Frankfurt-Dort­mund) crosses the Ruhrschnellweg B 1 / A 40. The best interstate exit to take from A 45 is “Dort­mund-Eichlinghofen” (closer to South Campus), and from B 1 / A 40 “Dort­mund-Dorstfeld” (closer to North Campus). Signs for the uni­ver­si­ty are located at both exits. Also, there is a new exit before you pass over the B 1-bridge leading into Dort­mund.

To get from North Campus to South Campus by car, there is the connection via Vogelpothsweg/Baroper Straße. We recommend you leave your car on one of the parking lots at North Campus and use the H-Bahn (suspended monorail system), which conveniently connects the two campuses.

The Laboratory of Process Automation Systems is located at Building G2 on the North Campus. Find more information here.

TU Dort­mund University has its own train station (“Dort­mund Uni­ver­si­tät”). From there, suburban trains (S-Bahn) leave for Dort­mund main station (“Dort­mund Hauptbahnhof”) and Düsseldorf main station via the “Düsseldorf Airport Train Station” (take S-Bahn number 1, which leaves every 15 or 30 minutes). The uni­ver­si­ty is easily reached from Bochum, Essen, Mülheim an der Ruhr and Duisburg.

You can also take the bus or subway train from Dort­mund city to the uni­ver­si­ty: From Dort­mund main station, you can take any train bound for the Station “Stadtgarten”, usually lines U41, U45, U 47 and U49. At “Stadtgarten” you switch trains and get on line U42 towards “Hombruch”. Look out for the Station “An der Palmweide”. From the bus stop just across the road, busses bound for TU Dort­mund University leave every ten minutes (445, 447 and 462). Another option is to take the subway routes U41, U45, U47 and U49 from Dort­mund main station to the stop “Dort­mund Kampstraße”. From there, take U43 or U44 to the stop “Dort­mund Wittener Straße”. Switch to bus line 447 and get off at “Dort­mund Uni­ver­si­tät S”.

The Laboratory of Process Automation Systems is located at Building G2 on the North Campus. Find more information here.

The H-Bahn is one of the hallmarks of TU Dort­mund University. There are two stations on North Campus. One (“Dort­mund Uni­ver­si­tät S”) is directly located at the suburban train stop, which connects the uni­ver­si­ty directly with the city of Dort­mund and the rest of the Ruhr Area. Also from this station, there are connections to the “Technologiepark” and (via South Campus) Eichlinghofen. The other station is located at the dining hall at North Campus and offers a direct connection to South Campus every five minutes.

The Laboratory of Process Automation Systems is located at Building G2 on the North Campus. Find more information here. The building is within 5min walking distance of the H-Bahn Station "Dining Hall at North Campus".

The facilities of TU Dortmund University are spread over two campuses, the larger Campus North and the smaller Campus South. Additionally, some areas of the university are located in the adjacent “Technologiepark”.

Site Map of TU Dortmund University (Second Page in English).

Interactive map

The facilities of TU Dortmund University are spread over two campuses, the larger Campus North and the smaller Campus South. Additionally, some areas of the university are located in the adjacent "Technologiepark".

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