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SUMMARY:Learning Neural Operators for Biological Tissue Modeling - Yue Yu 
 (Lehigh University)
DTSTART:20230803T090000Z
DTEND:20230803T100000Z
UID:TALK202432@talks.cam.ac.uk
DESCRIPTION:For many decades\, physics-based PDEs have been commonly emplo
 yed for modeling the mechanical responses of biological tissues\, then tra
 ditional numerical methods were employed to solve the PDEs and provide pre
 dictions. However\, when governing laws are unknown or when high degrees o
 f heterogeneity present\, these classical models may become inaccurate. In
  this talk we propose to use data-driven modeling which directly utilizes 
 experimental measurements to learn the hidden physics and provide further 
 predictions. In particular\, we develop PDE-inspired neural operator archi
 tectures\, to learn the mapping between loading conditions and the corresp
 onding mechanical responses. By parameterizing the increment between layer
 s as an integral operator\, our neural operator can be seen as the analog 
 of a time-dependent nonlocal equation\, which captures the long-range depe
 ndencies in the feature space and is guaranteed to be resolution-independe
 nt. Moreover\, when applying to (hidden) PDE solving tasks\, our neural op
 erator provides a universal approximator to a fixed point iterative proced
 ure\, and partial physical knowledge can be incorporated to further improv
 e the model&rsquo\;s generalizability and transferability. As a real-world
  application\, we learn the material models directly from digital image co
 rrelation (DIC) displacement tracking measurements on a porcine tricuspid 
 valve leaflet tissue\, and show that the learnt model substantially outper
 forms conventional constitutive models.
LOCATION:Seminar Room 1\, Newton Institute
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