(433c) Implicit Neural Representations for Accurately Modeling State Transition Dynamics of a Distillation Column

This study explores the potential of implicit neural representations for accurately learning the state transition dynamics of a distillation column. Recently, implicit neural representations with periodic activation functions have shown promising results in modeling signals and its derivatives [1]. Due to its inherent properties, implicit neural representations have been widely used in various fields including image synthesis, robotics, physics-based simulations, and control systems. However, in the field of chemical engineering, relatively few studies have been conducted on the potentials and limitations of employing implicit neural representations.

Distillation is naturally a complex system with nonlinear dynamics because it involves the transport and separation of multiple chemical components with different volatilities. Optimal control of distillation systems has been widely studied in perspectives of model predictive control, dynamic optimization, and recently reinforcement learning. Considering its importance and established deep understanding of its system, it is a good starting-point for studying and evaluating a new algorithm.

This works presents the development of an accurate state transition dynamic model of a distillation column. A rigorous dynamic distillation column simulation is utilized as a simulator. We define a partially observable Markov decision process where internal hidden states are not observable. The input actions are reflux ratio, condenser duty, reboiler duty, flow rates of the distillate and bottoms. The observed outputs are temperatures of top and bottom of the column, liquid levels in the condenser and reboiler, and pressure at the top of column. Other process state variables are assumed to be not provided when learning state transition dynamics.

First, we compared the state transition dynamics of scenarios of when only outputs are learned, when only derivatives of outputs are learned, and when both outputs and their derivatives are learned. While all scenarios successfully learned the state transition dynamics, the scenario when both outputs and their gradients are learned showed the best performance.

Furthermore, we compared different sample strategies in the input action space. Specifically, random sampling, uniform sampling, and Latin hypercube sampling methods were compared with different sampling sizes. Each sampling method showed benefit in either sampling efficiency or accuracy.

Lastly, we explore the robustness of implicit neural representations to disturbances in observed output signals. Different scale in the variance of disturbance were tested and the capability and limitation of denoising effect by utilizing implicit neural representation will be presented.

Our work suggests that implicit neural representations are a promising approach for accurately modeling complex systems with nonlinear dynamics. The property of well-maintaining derivatives will be valuable when the state transition dynamics is utilized in means of application of control, optimization, and fault diagnosis. It is our future work to extend this work to optimal control via nonlinear model predictive control and Hamilton-Jacobi-Bellman-based neural optimal control [2].

Reference

[1] Sitzmann, V., Martel, J., Bergman, A., Lindell, D., and Wetzstein, G. (2020). Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33, 7462-7473.

[2] Engin, S. and Isler, V. (2023). Neural Optimal Control using Learned System Dynamics. arXiv preprint arXiv:2302.09846.