Centrala begrepp
Developing a novel neural network architecture enforcing constitutive constraints improves accuracy in multiscale modeling of biological tissues.
Sammanfattning
Introduction
Multiscale methodologies enable understanding of biological tissues.
Hierarchical approach homogenizes microscale behavior for macroscale analysis.
A Priori Homogenization
Simulations calibrate constitutive models like HGO or Fung model.
Analytical models may not capture behaviors from micromechanical fields.
Concurrent Hierarchical Method
FE2 method handles broader range of emergent behaviors but is computationally expensive.
Hierarchical Methods Requirements
Require strong scale separation and homogenization over a representative domain size.
Machine Learning Models
Increasingly important in engineering design, promising for predicting complex deformation fields and nonlinear materials.
Input Convex Neural Network (ICNN)
Ensures convexity by adhering to specific activation functions and non-negative weights.
Sobolev Training Protocol
Improves prediction accuracy for stress and stiffness by training on target output and derivatives concurrently.
Results and Discussions
ICNN-based model shows high predictive accuracy for strain energy density, stress, and stiffness components.
Statistik
Using our network and Sobolev minimization, we obtain a NMSE of 0.15% for the energy, 0.815% averaged across stress components, and 5.4% averaged across stiffness components.