For many decades, physics-based PDEs have been commonly employed for modelling the mechanical responses of biological tissues, then traditional numerical methods were employed to solve the PDEs and provide predictions. However, when governing laws are unknown or when high degrees of heterogeneity present, these classical models may become inaccurate. In this talk we propose to use data-driven modelling which directly utilizes experimental measurements to learn the hidden physics and provide further predictions. In particular, we develop PDE-inspired neural operator architectures, to learn the mapping between loading conditions and the corresponding mechanical responses. By parameterizing the increment between layers as an integral operator, our neural operator can be seen as the analogue of a time-dependent nonlocal equation, which captures the long-range dependencies in the feature space and is guaranteed to be resolution-independent. Moreover, when applying to (hidden) PDE solving tasks, our neural operator provides a universal approximator to a fixed point iterative procedure, and partial physical knowledge can be incorporated to further improve the model’s generalizability and transferability. As a real-world application, we learn the material models directly from digital image correlation (DIC) displacement tracking measurements on a porcine tricuspid valve leaflet tissue, and show that the learnt model substantially outperforms conventional constitutive models.
This video was produced by the Isaac Newton Institute, as part of the workshop Mathematical mechanical biology: old school and new school, methods and applications, forming part of the programme Uncertainty quantification and stochastic modelling of materials.
