(177e) Deep Learning for Probabilistic Uncertainty Quantification of an Integrated Biomanufacturing System for Martian Colonization

The aim of the Center for Utilization of Biological Engineering in Space (CUBES) is efficient exploitation of Martian in-situ resources for integrated bio-manufacturing of the necessary products for Martian colonization, including biologically produced pharmaceuticals, cell-based treatments/therapeutics, and materials for on-demand diverse additive manufacturing applications [1]. For a nominal period of a human mission on Mars, a comprehensive theoretical framework is leveraged to design a reference mission architecture. The individual pieces that constitute this framework are first-principles models of several bioprocesses that produce the necessary materials to ensure a successful mission. Nonetheless, accounting for process uncertainties such as those associated with kinetic model parameters and structure is crucial for reliable system analysis and mission design [2].

The biomanufacturing system of interest consists of several bioprocesses whose dynamic models involve a large number of states and parameters and are generally expensive to evaluate. This talk will focus on forward uncertainty quantification (UQ) of the biomanufacturing system, with the goal of quantifying the effects of model parameter uncertainty on the performance of individual bioprocesses and pair-wise integration of different bioprocesses within the biomanufacturing system. Quantifying the effects of probabilistic parameter uncertainties on the mission design metrics relies on uncertainty propagation to characterize the probability distributions of quantities of interest (QoI) relevant to the mission design. The most widely used approaches to UQ are based on sample-based methods, e.g., Monte Carlo sampling, that require a large number of model evaluations, which can be prohibitive when the bioprocess models are expensive to evaluate.

In this work, we investigate deep learning to derive cheap-to-evaluate deep neural network (DNN) surrogates for high-fidelity bioprocess models. DNNs have the advantage of being universal function approximators whereby their predictive capability increases when more training data are used [3], which is not necessarily the case in other surrogate modeling methods such as Kriging or polynomial chaos [4]. In particular, we investigate the ResNet architecture [5] for approximating the dynamics of complex bioprocesses, where the central idea is to “learn” a flow map decomposition of system dynamics. In effect, the proposed DNN-based framework for UQ attempts to predict future states of the system as a function of uncertain parameters and past system states [6]. The hyperparameters of the DNN are optimally chosen via a Bayesian optimization approach [7]. Furthermore, active learning techniques are employed to reduce the number of training samples, generated through costly simulations of high-fidelity models, while achieving the desired approximation accuracy of the DNN surrogate. To this end, we use a stochastic dropout-based uncertainty method that iteratively refines a DNN surrogate through enriching the training dataset by targeted sampling of input regions that yield the most uncertain predictions [8].

The proposed DNN framework for UQ is applied to an integrated system of three batch bioprocesses within the biomanufacturing system. The integrated system consists of: (1) a microbial electrosynthesis reactor (MER) [9] for carbon fixation and acetate production by a bacterial biofilm grown on the surface of the cathode, (2) a downstream bioreactor that utilizes the acetate produced in the MER for cell growth with fixed nitrogen, used for hydroponic crop growth, and (3) a biopolymer production reactor for on-demand additive manufacturing of tools. We demonstrate that the proposed DNN framework enables fast and flexible uncertainty quantification of the integrated bioprocesses under probabilistic uncertainties, which is a crucial step toward robust model-based analysis and optimization of the biomanufacturing system.

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[2] Makrygiorgos G., Gupta S.S., Menezes A.A., Mesbah A., Fast probabilistic uncertainty quantification and sensitivity analysis of a Mars life support system model. In Proceedings of the IFAC World Congress, 2020.

[3] Liang S., Rayadurgam S., Why deep neural networks for function approximation? arXiv preprint, arXiv:1610.04161, 2016.

[4] Makrygiorgos G., Maggioni G.M., Mesbah A., Surrogate modeling for fast uncertainty quantification: Application to 2D population balance models. Computers & Chemical Engineering, 138, 106814, 2020.

[5] Qin T., Wu, K., & Xiu D. (2019). Data driven governing equations approximation using deep neural networks. Journal of Computational Physics, 395, 620-635, 2019.

[6] Qin T., Chen Z., Jakeman J., Xiu D., A neural network approach for uncertainty quantification for time-dependent problems with random parameters. arXiv preprint, arXiv:1910.07096, 2019.

[7] Tripathy R.K., Bilionis I., Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification. Journal of Computational Physics, 375, 565-588, 2018.

[8] Evgenii T., Panov M., Shapeev A., Dropout-based active learning for regression. International Conference on Analysis of Images, Social Networks and Texts, Springer, 2018.

[9] Kazemi M., Biria D., Rismani-Yazdi H., Modelling bio-electrosynthesis in a reverse microbial fuel cell to produce acetate from CO₂ and H₂O. Physical Chemistry Chemical Physics, 17, 12561, 2015.