Séminaire virtuel: vendredi 3 mai 2024
Julien Martinelli

Lien Zoom

  • Meeting ID: 867 6409 6440
  • passcode: 149120

13h00 - 13h50 – Julien Martinelli

Inferring partially known mechanistic models using Gaussian Processes

Mechanistic modeling is the go-to framework in Systems Biology when quantitative data is available. As a blend of first principles and domain expertise, they possess generalization properties beyond the training data distribution, a property that more flexible models like Deep Neural Networks (DNN) lack when it comes to System Biology. The idea of combining a theory-driven component, like an ODE model involving biologically grounded parameters, with a data-driven component, such as a DNN, is better known as Grey-Box Modeling. The aim is to leverage the generalization properties of the imperfect theory-driven part jointly with the flexibility inherent to data-driven models. While the latter is usually captured by a DNN, this choice might not be suitable for health-related applications, where data measurements are often scarce and heterogeneous. As an alternative, Gaussian Processes (GPs) provide a natural way to encode prior beliefs over function spaces and can be seen as the probabilistic counterpart of the well-known kernel methods. As such, they are endowed with the universal approximation property and can aid in the inference of partially known mechanistic models. Such models could describe the dynamics of antibody response, whose behavior is typically not fully understood when considering newly discovered viruses, e.g., the latest SARS-CoV-2 variants. The principled uncertainty quantification provided by GPs coupled with their ability to cope with the low-data regime make them suitable candidates for health-related applications.

In this talk, I will give a detailed introduction of GPs and show how they can enhance partially known mechanistic models, effectively acting as a “model error” component that compensates for imperfect knowledge, while providing diagnostics about the well-specified nature of the mechanistic model. I will conclude by mentioning some open challenges in the field of Grey-Box Modeling.

Dernière modification le 03/05/2024