Improving System Identification of Kinetic Networks Using Neural Stochastic Differential Equations
Krystian Ganko, Massachusetts Institute of Technology
System structural identification is foundational to the application of the scientific method through model synthesis of natural processes. "Good" models both (1) explain the main trends observed in the system with good accuracy, and (2) produce falsifiable predictions which can be experimentally tested. In turn, many chemical and biological systems are experimentally observed to have both deterministic drift and noisy character. State-space stochastic differential equations (SDEs) model this noise, to more realistically describe the stochastic dynamics compared to ordinary differential equation (ODE) descriptions that employ the continuum approximation. Moreover, for physics that are poorly understood, neural networks may be embedded to increase model expressivity.
However, modelling noise terms requires additional parametric structures, which frequently introduces structural identifiability issues relative to ODE models. As such, the capacity of parameter-identified SDE models to predict system dynamics, as well as for any neural networks embedded in such models to learn distinguishable dynamics, is inherently limited. This work demonstrates that — under certain assumptions simplifying the Chemical Master Equation description of a kinetic network to an SDE in the form of the Chemical Langevin Equation (CLE) — structural identifiability and generalizability of any embedded neural networks are substantially improved for reacting chemical networks. The resulting model structure reduction leads to a decrease in the computational costs and an increase in the numerical accuracy compared to modelling the non-reduced SDE model and fitting the model to experimental kinetic data. As such, this approach enables the exploration of more expensive experimental spaces involving partially and completely unknown reaction network graphs. To illustrate these cases, mixed integer non-linear programs (MINLPs) were solved using Elastic Net regularization in the loss function to both (1) determine corresponding integer-valued stoichiometries of the reaction network, and (2) optimally fit the continuous-valued reaction network rate parameters to data.
Abstract Author(s): Krystian Ganko, Nathan M. Stover, Utkarsh, Richard D. Braatz, Christopher Rackauckas