<p>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 (Estrada et al. J Mech Phys Solids 112:291–317, 2018) 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 matches known material properties, reaching <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="466_2025_2606_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$1\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="466_2025_2606_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$99\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>99</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

Bayesian optimal design accelerates discovery of soft material properties from bubble dynamics

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发表日期：

2025年2月11日

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Tianyi Chu,
Jonathan B. Estrada,
Spencer H. Bryngelson

摘要

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 (Estrada et al. J Mech Phys Solids 112:291–317, 2018) 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 matches known material properties, reaching $1\%$ $1 %$ 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 $99\%$ $99 %$ 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.