Bayesian optimal design accelerates discovery of material properties from bubble dynamics

TL;DR

This paper introduces a Bayesian optimal experimental design method to efficiently determine soft material properties from bubble cavitation data, significantly reducing the number of experiments needed for accurate characterization.

Contribution

It develops a novel Bayesian optimal design framework combined with hybrid inference to rapidly identify material properties and discriminate between constitutive models from minimal experimental data.

Findings

Achieves 1% relative error in property estimation within 10 experiments

Successfully discriminates between two constitutive models with over 99% confidence

Reduces experimental effort compared to traditional methods

Abstract

An optimal sequential experimental design approach is developed to computationally characterize soft material properties at the high strain rates associated with bubble cavitation. The approach involves optimal design and model inference. The optimal design strategy maximizes the expected information gain in a Bayesian statistical setting to design experiments that provide the most informative cavitation data about unknown soft material properties. We infer constitutive models by characterizing the associated viscoelastic properties from measurements via a hybrid ensemble-based 4D-Var method (En4D-Var). The inertial microcavitation-based high strain-rate rheometry (IMR) method ([1]) simulates the bubble dynamics under laser-induced cavitation. We use experimental measurements to create synthetic data representing the viscoelastic behavior of stiff and soft polyacrylamide hydrogels under realistic uncertainties. The synthetic data are seeded with larger errors than state-of-the-art measurements yet match known material properties, reaching 1% relative error within 10 sequential designs (experiments). We discern between two seemingly equally plausible constitutive models, Neo-Hookean Kelvin--Voigt and quadratic Kelvin--Voigt, with a probability of correctness larger than 99% in the same number of experiments. This strategy discovers soft material properties, including discriminating between constitutive models and discerning their parameters, using only a few experiments.