DeepPumas for Viral Dynamics

Introduction - Combining Mechanism and Machine Learning

Niklas Korsbo

2025-10-12

Welcome

Workshop Overview

Time	Session
09:00 - 09:20	Welcome and Introduction
09:20 - 10:30	NLME modeling in Pumas
10:30 - 10:45	☕ Coffee Break
10:45 - 11:15	DeepNLME
	Neural networks, SciML, UDEs and NeuralODEs
11:15 - 12:30	DeepNLME (hands-on)
12:30 - 13:30	🍽️ Lunch Break
13:30 - 13:55	Random effects, fitting NLME, and Generative AI
13:55 - 14:40	DeepNLME with Complex Covariates
14:40 - 15:00	NLME and Generative AI
15:00 - 15:30	Embeddings
15:30 - 15:45	☕ Coffee Break
15:45 - 16:15	Epidemiology Demo
16:15 - 17:00	Discussions and Conclusions

 

Machine learning

• Data-driven model discovery
• Finds unintuitive relationships
• Handles complex data

• Lacks scientific understanding
• Requires big data

Scientific modelling

• Encodes scientific understanding
• Data-efficient
• Interpretable
• Simple counterfactuals

• Labor intensive
• Misses unintuitive relationships
• Hard to utilize complex data

Data + Knowledge

Vision Spanning Pharma

Traditional NLME

Nonlinear Mixed Effects

Typical values \[ tvKa, \; tvCL, \; tvVc, \; Ω, \; σ \]

Covariates \[ Age, \; Weight \]

Random effects \[ η \sim MvNormal(Ω) \]

Individual parameters \[\begin{align*} Ka_i &= tvKa \cdot e^{η_{i,1}} \\ CL_i &= tvCL \cdot e^{η_{i,2}} \\ Vc_i &= tvVc \cdot e^{η_{i,3}} \end{align*}\]

Dynamics \[ \begin{align*} \frac{dDepot(t)}{dt} =& - Ka \cdot Depot(t) \\ \frac{dCentral(t)}{dt} =& Ka \cdot Depot(t) - \frac{CL}{Vc} \cdot Central(t) \end{align*} \]

Error model \[ dv(t) \sim Normal\left(\frac{Central(t)}{Vc}, \frac{Central(t)}{Vc} \cdot σ\right) \]

Let’s Get Started!

Next up: Hands-on NLME modeling with Pumas

• Synthetic viral dynamics data mimicking HIV
• Model building and fitting
  
• Understanding the foundations before we add neural networks