Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations

TL;DR

This paper introduces a structured latent ODE model that explicitly captures input variations in dynamical systems, enabling better understanding and controlled generation of time-series data, especially in biological contexts.

Contribution

The paper presents a novel structured latent ODE framework that models input effects separately, improving interpretability and control in dynamical system modeling.

Findings

Improved controlled generation of biological time-series data.

Enhanced inference of system inputs from observational data.

Consistent performance gains over baseline models.

Abstract

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics. Unfortunately, this flexibility comes at the cost of understanding the dynamical system, for which ODEs are used ubiquitously. Further, experimental data are collected under various conditions (inputs), such as treatments, or grouped in some way, such as part of sub-populations. Understanding the effects of these system inputs on system outputs is crucial to have any meaningful model of a dynamical system. To that end, we propose a structured latent ODE model that explicitly captures system input variations within its latent representation. Building on a static latent variable specification, our model learns (independent) stochastic factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space. This approach provides actionable modeling through the controlled generation of time-series data for novel input combinations (or perturbations). Additionally, we propose a flexible approach for quantifying uncertainties, leveraging a quantile regression formulation. Results on challenging biological datasets show consistent improvements over competitive baselines in the controlled generation of observational data and inference of biologically meaningful system inputs.