(575e) Hybrid Modeling Using Universal Differential Equations for Lab-Scale Batch Production of ?-Carotene Using Saccharomyces Cerevisiae

Carotenoids are a diverse group of yellow-orange pigments present in many biological systems, and are produced by bacteria, fungi, and plants. They have been extensively used as constituents in dietary and vitamin supplements, and food pigmentation because of their colored characteristics. Specifically, β-carotene plays an important role as a precursor to Vitamin A. Additionally, it has been shown that β-carotene has a positive impact on human health with its antioxidant and protective properties against cancer. Currently, the use of chemical technology for the production of carotenoids leads to byproducts with undesirable effects upon consumption due to which the use of microbial sources for their production has received lots of attention [1]. But modeling the production of β-carotene in a fermentation process using first-principles such as conservation of mass and energy, kinetic laws, thermodynamic laws, and transport laws, etc., leads to limited accuracy. This is because first-principles cannot fully account for all the complex phenomena that occur within the process unless multiple laws are used which can lead to high computational costs [2]. Alternatively, data-driven modeling can be used but it suffers from poor extrapolation properties. To overcome these limitations, hybrid modeling is utilized which combines the first-principles and data-driven modeling, specifically deep neural networks, approaches resulting in superior accuracy and extrapolation properties than first-principles models and data-driven models, respectively [3].

Recently, a new class of neural networks called Neural ODEs has been developed wherein instead of specifying a discrete sequence of hidden layers in the neural network structure, the progression of the input through the hidden layers becomes continuous and is represented using an ODE [4]. Solving this ODE using a black-box ODE solver gives the output of the Neural ODEs. These continuous-depth Neural ODE networks have a constant memory cost, are able to adapt their evaluation strategy to each input, and explicitly trade computational speed for accuracy. These Neural ODEs can be combined with a first-principles-based model to build a hybrid model called Universal Differential Equations (UDEs) [5]. In this work, we built a UDE-based hybrid model for batch production of β-carotene using Saccharomyces cerevisiae strain mutant SM14. This model was developed using multiple software packages in Julia programming language and trained using data obtained from experiments wherein the initial glucose concentration was 20 g/L. Subsequently, the trained UDE model was tested using another experimental dataset wherein the initial glucose concentration was 22.36 g/L. The UDE-based hybrid model shows accuracy superior to the existing first-principles model specifically in the case of biomass, acetic acid and β-carotene concentrations. This work illustrates that UDE-based hybrid models can be utilized to quantify the unknowns in the first-principles model thereby improving its overall accuracy.

Literature cited:

[1] Ordonez, M.C., Raftery, J.P., Jaladi, T., Chen, X., Kao, K., Karim, M.N. Modeling of batch kinetics of aerobic carotenoid production using Saccharomyces cerevisiae. Biochem. Eng. J., 114:226-236, 2016.

[2] Bangi, M.S.F., Kwon, J.S.I. Deep hybrid modeling of chemical process: application to hydraulic fracturing. Comput. Chem. Eng., 134:106696, 2020.

[3] Shah, P., Sheriff, M.Z., Bangi, M.S.F., Kravaris, C., Kwon, J.S.I., Botre, C., Hirota, J. Deep neural network-based hybrid modeling and experimental validation for an industry-scale fermentation process: Identification of time-varying dependencies among parameters. Chemical Engineering Journal, 135643, 2022.

[4] Chen, T.Q., Rubanova, Y., Bettencourt, J., Duvenaud, D.K. Neural ordinary differential equations. Advances in Neural Information Processing Systems 31, 6571-6583, 2018.

[5] Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A. Universal Differential Equations for Scientific Machine Learning. arXiv:2001.04385, 2020.