(29a) Robust Artificial Neural Networks for Nonlinear Model Predictive Control of Multiscale Stochastic Systems

Multiscale stochastic systems are comprised of non-closed-form expressions that represent the discrete scale and continuum transport equations that describe macroscale phenomena. The discrete and continuum scales are coupled in order to provide the results of accurate microscale simulations to the domain sizes available to the macroscale simulations. However, the presence of non-closed-form expressions introduces noise into the observables and increases the total computational cost such that these multiscale models become too intensive for online model predictive control applications. This motivates the development of computationally efficient data-driven models to predict the responses of the full multiscale model to changes in the input parameters. Artificial Neural Networks (ANNs) are a machine learning technique that demonstrated the ability to accurately and efficiently predict the relationships between diverse input and output timeseries [1,2]. However, the ANN performance deteriorates when trained on noisy data [1] because the weights of the networks aim to capture the mean responses to the inputs. To reduce model-plant mismatch in the case of multiscale stochastic systems, it is necessary to predict the distribution of the response variables obtained from the ANNs rather than only their expectation values.

In our previous work [3], we used ANN models to predict the responses of a stochastic multiscale model of thin film formation by Chemical Vapour Deposition (CVD) [4]. The ANN models were subsequently incorporated into a shrinking horizon nonlinear model predictive control scheme. The predicted responses were roughness and growth rate while the manipulated variables were substrate temperature and bulk precursor mole fraction. It was demonstrated that the ANNs can efficiently provide accurate predictions of the system’s observables and reject disturbances not seen during training. However, uncertainty was not considered when generating the data from the stochastic multiscale model.

In this work, we propose training robust ANNs with distributed weights under parametric uncertainty to efficiently generate predictions that account for the variability in the observables. As a case study, we employ the aforementioned CVD system [4] to generate the training datasets under parametric uncertainty. We obtain the distributions and the statistical moments of the observables and subsequently incorporate the robust ANNs into a nonlinear model predictive control framework. The predicted trajectories are subsequently validated against the multiscale CVD model. Rather than obtaining only the mean response of the observables to the manipulated variables, we predict several possible time series of the observables and provide bounds, thereby enabling robust control of the multiscale stochastic system in the presence of parametric uncertainty.

References

[1] Svozil, D., Kvasnicka, V. and Pospichal, J. Introduction to Multi-Layer Feed-Forward Neural Networks, Chemometrics and Intelligent Laboratory Systems, vol. 39, no. 1, pp. 43–62, Nov. 1997.

[2] Venkatasubramanian, V. The promise of artificial intelligence in chemical engineering: Is it here, finally?, AIChE Journal, vol. 65, no. 2, pp. 466–478, 2019.

[3] Kimaev, G. and Ricardez-Sandoval, L. A. Nonlinear Model Predictive Control of a Multiscale Thin Film Deposition Process Using Artificial Neural Networks, Chemical Engineering Science, submitted on 2019-Apr-06.

[4] Vlachos, D. Multiscale Integration Hybrid Algorithms for Homogeneous-Heterogeneous Reactors, AIChE Journal, vol. 43, no. 11, 1997.