Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations.

Area of Science:

• Dynamical Systems Modeling
• Machine Learning
• Computational Biology

Background:

• Black-box models like neural Ordinary Differential Equations (ODEs) offer flexible learning of dynamical systems from data.
• However, understanding the impact of system inputs (e.g., treatments, sub-populations) on system dynamics remains challenging.
• Existing methods often struggle to disentangle these input effects within the learned latent representation.

Purpose of the Study:

• To develop a structured latent ODE model that explicitly separates the influence of system inputs on latent representations.
• To enable actionable modeling through controlled generation of time-series data for novel input combinations.
• To provide a flexible framework for quantifying prediction uncertainties.

Main Methods:

• Proposed a structured latent ODE model building on static latent variable specifications.
• Learned independent stochastic factors of variation for each system input.
• Integrated a quantile regression formulation for uncertainty quantification.

Main Results:

• Demonstrated consistent improvements over baseline methods on challenging biological datasets.
• Showcased enhanced controlled generation of observational time-series data.
• Successfully inferred biologically meaningful system inputs and their effects.

Conclusions:

• The structured latent ODE model effectively captures and separates system input variations in the latent space.
• This approach facilitates a deeper understanding of dynamical systems and enables actionable insights through controlled data generation.
• The model offers a robust framework for analyzing complex biological data with quantified uncertainties.