Linearized Bayesian inference for Young's modulus parameter field in an elastic model of slender structures.

Area of Science:

• Computational physics
• Materials science
• Nanotechnology

Background:

• Nano-scale slender structures exhibit deformations sensitive to non-homogenous elasticity.
• Experimental determination of elasticity fields at the nano-scale is challenging.
• Molecular dynamics simulations offer potential data but require efficient inverse problem solutions.

Purpose of the Study:

• To formulate an inverse problem for inferring elasticity parameter fields in nano-scale structures.
• To develop a computationally efficient and robust Bayesian inference framework.
• To validate the framework using simulations of cantilever bending and helical rod stretching.

Main Methods:

• Formulation of an inverse problem using a linear elastic model.
• Application of Bayesian inference with Gaussian approximation of the posterior distribution.
• Reconstruction of Young's modulus fields from simulated deformation data.

Main Results:

• Successful reconstruction of smoothly varying parameter fields from noisy data.
• Demonstration of the framework's performance in cantilever bending and helical rod stretching scenarios.
• Quantification of uncertainty in inferred elasticity parameters.

Conclusions:

• The developed Bayesian framework enables accurate inference of nano-scale elasticity fields.
• The method is robust and performs well even with noisy experimental or simulation data.
• Data quality significantly impacts the accuracy of parameter field reconstructions.