Deep learning and differential equations for modeling changes in individual-level latent dynamics between observation...

Area of Science:

• Biomedical data analysis
• Computational neuroscience
• Psychological modeling

Background:

• Longitudinal biomedical data analysis often requires dimensionality reduction and dynamic modeling.
• Existing methods using artificial neural networks and differential equations assume constant dynamic parameters.
• This limitation hinders accurate modeling of time-varying individual trajectories.

Purpose of the Study:

• To extend dynamic modeling by allowing differential equation parameters to vary across observation subperiods.
• To develop a method for predicting psychological resilience using individual dynamic models.
• To identify key predictors of resilience and inform future study designs.

Main Methods:

• Proposed a deep dynamic modeling approach integrating artificial neural networks and differential equations.
• Allowed for distinct sets of differential equation parameters for different observation subperiods.
• Coupled estimation for intra-individual subperiods to accommodate smaller datasets.
• Derived prediction targets from individual dynamic models for resilience.
• Utilized baseline and follow-up measurements for predictor selection.

Main Results:

• Successfully identified individual-level parameters of dynamic models.
• Enabled stable selection of predictors, specifically resilience factors.
• Identified individual characteristics most promising for follow-up updates.
• Demonstrated the model's ability to handle time-varying dynamics in biomedical data.

Conclusions:

• The proposed deep dynamic modeling approach effectively captures changes in parameters between observation subperiods.
• This method enhances the prediction of psychological resilience and the identification of influential factors.
• The findings provide valuable insights for designing future studies on individual resilience and dynamic processes.