(65a) Bayesian Transfer Learning to Improve Predictive Performance of an ODE-Based Kinetic Model

This work focuses on the hydrodenitrogenation reaction modelisation. The removal of nitrogen-containing molecules is part of the hydrotreating process which is required before
the catalytic conversion process. Impurities in the oil fraction are eliminated by mixing the feedstock with hydrogen and passing it through a fixed bed catalytic reactor at high
temperature and pressure. Hydrotreating is a common operation in every oil refinery and allows satisfying the environmental regulations for the final products.

Reactions take place in presence of catalyst and when supplying a catalyst, a vendor must guarantee its performance. The aim is to predict the nitrogen content (N) after the
hydrotreating stage based on information on the feedstock and operating conditions (x). In order to model the nitrogen content evolution during the reaction, kinetic models (1)
are used. The structure of f is fixed and it depends on parameters θ to be optimized.
dN/dt = fθ(N|x). (1)
The predictive model fitting is based on experimental data and experiments are very expensive. New catalysts are constantly being developed so that each new generation of a
catalyst requires a new model that is until now built from scratch from new experiments. The aim of this work is to build the best predictive model for a new catalyst from fewer
observations and using the observations of previous generation catalysts. This task is known as transfer learning (Pan and Yang 2010 and Tsung et al. 2018).

In order to adapt the past knowledge to the new catalyst, a Bayesian approach is considered. The Bayes Theorem gives the posterior distribution of the model parameters
θ (2), where N is the vector of the nitrogen content for the different observations, X the matrix of new observations, π(θ) the prior distribution of parameters, L(N|θ,X) the
likelihood and L(N|X) the marginal likelihood.
π(θ|N,X) = π(θ)L(N|θ,X)/L(N|X). (2)
The likelihood represents the knowledge about the new observations, thus the posterior distribution will be modified when adding observations. The idea of the approach is to
take as prior π(θ) a distribution centered on the previous model parameters, with variance large enough to allow parameter change and small enough to retain the information.
Previous work has shown the effectiveness of this Bayesian transfer approach for modelling using linear models and kriging models (Iapteff et al. 2021), and this current work
aims to adapt it on kinetic models. Results are good and show a reduction in the number of observations required to achieve good results.

References
Iapteff, L. et al. (2021). “Reducing the number of experiments required for modelling the hydrocracking process with kriging through Bayesian transfer learning”. In: J R Stat
Soc Series C, pp. 1–21.
Pan, S. and Q. Yang (2010). “A Survey on Transfer Learning”. In: IEEE Transactions on Knowledge and Data Engineering, pp. 1345–1359.
Tsung, F. et al. (2018). “Statistical transfer learning: A review and some extensions to statistical process control”. In: Quality Engineering, pp. 115–128.