Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression

Modeling a system's temporal behaviour in reaction to external stimuli is a fundamental problem in many areas. Pure Machine Learning (ML) approaches often fail in the small sample regime and cannot provide actionable insights beyond predictions. A promising modification has been to incorporate expert domain knowledge into ML models. The application we consider is predicting the patient health status and disease progression over time, where a wealth of domain knowledge is available from pharmacology. Pharmacological models describe the dynamics of carefully-chosen medically meaningful variables in terms of systems of Ordinary Differential Equations (ODEs). However, these models only describe a limited collection of variables, and these variables are often not observable in clinical environments. To close this gap, we propose the latent hybridisation model (LHM) that integrates a system of expert-designed ODEs with machine-learned Neural ODEs to fully describe the dynamics of the system and to link the expert and latent variables to observable quantities. We evaluated LHM on synthetic data as well as real-world intensive care data of COVID-19 patients. LHM consistently outperforms previous works, especially when few training samples are available such as at the beginning of the pandemic. © 2021 Neural information processing systems foundation. All rights reserved.

On the COVID-19 Temporal Evolution in Brazil

This paper has two main objectives. The first one is to present a new dynamic model that describes, with adequate precision, the temporal behavior of the coronavirus epidemic that currently occurs in Brazil. Every day, the number of new infections provided by the Brazilian Ministry of Health is taken into account. Thus, an assessment of the impact of social behavior on the evolution of the epidemic can also be made. The second objective is to analyze the need to develop a computational system, capable of simulating—with the Monte Carlo method—the dynamic behavior of epidemics allowing each individual to move through locations with different population densities. © 2022, Springer Nature Switzerland AG.