Physics-informed neural networks in Cardiac mechanics

Cardiac mechanics is traditionally modeled using partial differential equations (PDEs) which are solved with the finite element method. In this traditional approach one selects a discrete mesh that represents the geometry of the heart, and approximate the solution in the nodes of this mesh. Physics-informed neural networks (PINNs) is an alternative and relatively new method, which is based on deep learning and can be used as a surrogate to conventional finite element modeling. PINNs could be a promising technique to combine machine learning with traditional physics-based modeling.
Master

We aim to compare the two approaches for a series of cardiac mechanics models, starting from very simple elasticity models on idealised geometries to fairly realistic models of the human heart. The finite element solvers will be implemented in Fenics, and the PINNS will be based on PyTorch. By gradually increasing the model complexity and realism we want to explore the potential of PINNs in cardiac mechanics modeling, and investigate its advantages and limitations compared with conventional approaches.

Goal

The goal of the project will be to compare finite element methods to the physics informed neural networks for modeling cardiac mechanics. The approaches will be compared in terms of their accuracy, computational cost, and their suitability for data-driven parameter estimation.

Learning outcome

The candidate will learn about biomechanics and cardiac modeling, as well as solution methods for PDEs based on the finite element method and on deep neural networks.

Qualifications

The candidate should have a solid background in partial differential equations and python programming. Background in machine learning is also preferred.

Supervisors

  • Joakim Sundnes
  • Henrik Nicolay Finsberg

References

Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural net-
works: A deep learning framework for solving forward and inverse problems involving non-
linear partial differential equations
. Journal of Computational physics, 378:686–707, 2019.

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