Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic...

Area of Science:

• Computational Biology
• Systems Physiology
• Biophysics

Background:

• Modeling complex biological systems is difficult due to interconnected components and incomplete knowledge.
• Existing methods struggle to mechanistically model physiological dynamics with unknown elements.

Purpose of the Study:

• To develop a hybrid approach combining neural networks (NNs) and physics-based models for biological dynamical systems.
• To approximate missing ordinary differential equations (ODEs) within physiological models.
• To simultaneously estimate dynamic state variables and train model parameters.

Main Methods:

• Utilized a recursive Bayesian state estimation (RBSE) framework.
• Integrated NNs to approximate unknown ODEs within a known ODE system.
• Applied the method to a human retinal blood circulation model, replacing a core ODE with an NN.
• Compared RBSE training with backpropagation through time (BPTT).

Main Results:

• The NN successfully approximated the dynamics of the missing ODEs.
• The RBSE framework enabled joint estimation of state variables and NN parameters.
• RBSE training of NN parameters resulted in superior state estimation accuracy compared to BPTT.

Conclusions:

• Hybrid NN-physics-based models can effectively capture dynamics of incompletely understood physiological systems.
• RBSE provides a robust framework for joint state and parameter estimation in such hybrid models.
• The proposed RBSE approach offers improved accuracy for modeling biological dynamical systems with unknown components.