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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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