Accelerating Bayesian Optimal Experimental Design via Local Radial Basis Functions: Application to Soft Material Characterization

TL;DR

This paper introduces a local RBF-based computational method to significantly accelerate Bayesian optimal experimental design, demonstrated on soft material characterization, reducing computational costs while maintaining accuracy.

Contribution

The paper presents a novel RBF--BOED approach that constructs deterministic surrogates for efficient Bayesian experimental design, reducing the need for extensive forward-model simulations.

Findings

EIG estimates achieved at 8% of full computational cost

Method effectively handles scattered parameter points

Demonstrated on soft material characterization with high accuracy

Abstract

We develop a computational approach that significantly improves the efficiency of Bayesian optimal experimental design (BOED) using local radial basis functions (RBFs). The presented RBF--BOED method uses the intrinsic ability of RBFs to handle scattered parameter points, a property that aligns naturally with the probabilistic sampling inherent in Bayesian methods. By constructing accurate deterministic surrogates from local neighborhood information, the method enables high-order approximations with reduced computational overhead. As a result, computing the expected information gain (EIG) requires evaluating only a small uniformly sampled subset of prior parameter values, greatly reducing the number of expensive forward-model simulations needed. For demonstration, we apply RBF--BOED to optimize a laser-induced cavitation (LIC) experimental setup, where forward simulations follow from inertial microcavitation rheometry (IMR) and characterize the viscoelastic properties of hydrogels. Two experimental design scenarios, single- and multi-constitutive-model problems, are explored. Results show that EIG estimates can be obtained at just 8% of the full computational cost in a five-model problem within a two-dimensional design space. This advance offers a scalable path toward optimal experimental design in soft and biological materials.