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SUMMARY:Generative hyperplasticity with physics-informed probabilistic dif
 fusion fields - Adrian Buganza Tepole (Purdue University)
DTSTART:20230731T101500Z
DTEND:20230731T111500Z
UID:TALK202321@talks.cam.ac.uk
DESCRIPTION:Complex materials such as soft tissues exhibit nonlinear aniso
 tropic response and hetergeneous mechanical properties. Data-driven method
 s have been recently developed to capture the rich mechanical behavior of 
 these materials under extreme deformations. In particular\, we have contri
 buted to the field by leveraging neural ordinary differential equations (N
 ODEs) as the building blocks of strain energy density functions that autom
 atically satisfy polyconvexity\, objectivity\, material symmetry and posit
 ive energy dissipation requirements for realistic and physically plausible
  material models. However\, these data-driven models have lacked considera
 tion of uncertainty. This is particularly problematic for soft tissues whi
 ch exhibit a large variation in mechanical properties from one individual 
 to another. Here we establish a generative modeling framework based on sta
 ble diffusion to model distributions of materials while satisfying physics
  constraints. We use NODEs to describe the material response. Because the 
 NODE framework automatically satisfies the desired physics\, any samples o
 f parameters of the NODE produces feasible &nbsp\;materials. For a given m
 aterial of interest e.g. skin\, we assume that stress-strain curves from t
 he population are available. Fitting a subset of the NODE parameters to th
 e stress-strain data yields samples over the parameter space of the NODEs.
  Diffusion probabilistic models are then employed to learn that distributi
 on over these NODE parameters and\, inplicitly\, over the constitutive mod
 els. We showcase the ability of the framework to learn the distribution of
  material behavior for both syntethic examples and murine skin data\, outp
 erforming standard density estimation techniques. We anticipate that this 
 work will further establish the use of data-driven methods for materials t
 hat exhibit large variation across a population for which uncertainty quan
 tification is essential. &nbsp\;&nbsp\;\n&nbsp\;\nCo-authors: Vahidullah T
 ac\, Manuel Rausch\, Ilias Bilionis\, Francisco Sahli Costabal
LOCATION:Seminar Room 1\, Newton Institute
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