Data-Driven Flow-Map Models for Data-Efficient Discovery of Dynamics and
Fast Uncertainty Quantification of Biological and Biochemical Systems
Abstract
Computational models are increasingly used to investigate and predict
the complex dynamics of biological and biochemical systems.
Nevertheless, governing equations of a biochemical system may not be
(fully) known, which would necessitate learning the system dynamics
directly from, often limited and noisy, observed data. On the other
hand, when expensive models are available, systematic and efficient
quantification of the effects of model uncertainties on quantities of
interest can be an arduous task. This paper leverages the notion of
flow-map (de)compositions to present a framework that can address both
of these challenges via learning data-driven models useful for capturing
the dynamical behavior of biochemical systems. Data-driven flow-map
models seek to directly learn the integration operators of the governing
differential equations in a black-box manner, irrespective of structure
of the underlying equations. As such, they can serve as a flexible
approach for deriving fast-to-evaluate surrogates for expensive
computational models of system dynamics, or, alternatively, for
reconstructing the long-term system dynamics via experimental
observations. We present a data-efficient approach to data-driven
flow-map modeling based on polynomial chaos Kriging. The approach is
demonstrated for discovery of the dynamics of various benchmark systems
and a co-culture bioreactor subject to external forcing, as well as for
uncertainty quantification of a microbial electrosynthesis reactor. Such
data-driven models and analyses of dynamical systems can be paramount in
the design and optimization of bioprocesses and integrated
biomanufacturing systems.