A nonlinear sparse neural ordinary differential equation model for multiple functional processes.

Area of Science:

• Computational Biology
• Machine Learning
• Dynamical Systems

Background:

• Understanding complex relationships between multiple functional processes is crucial in various scientific domains.
• Existing models may struggle to capture both nonlinear dynamics and sparse dependencies simultaneously.

Purpose of the Study:

• To propose a novel sparse neural ordinary differential equation (ODE) model for characterizing flexible and sparse relations among multivariate functions.
• To develop a method capable of modeling dynamic changes in latent states with both nonlinear and sparse dependent characteristics.

Main Methods:

• Utilizing ordinary differential equations to characterize latent states of functions.
• Employing a deep neural network (DNN) with a specialized architecture and sparsity-inducing regularization to model dynamic changes.
• Developing an efficient optimization algorithm for estimating DNN weights under sparsity constraints.

Main Results:

• The proposed sparse neural ODE model effectively captures nonlinear and sparse dependent relations among multivariate functions.
• Algorithmic convergence and selection consistency were established, providing theoretical guarantees.
• The method's efficacy was demonstrated through simulations and a gene regulatory network analysis.

Conclusions:

• The developed sparse neural ODE model offers a powerful tool for analyzing complex functional processes with dynamic and sparse interdependencies.
• The method provides a theoretically sound and computationally efficient approach for uncovering hidden relationships in multivariate data.
• This work has significant implications for fields requiring the modeling of dynamic systems, such as systems biology and neuroscience.