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The image designed by Natalia Cano Murillo and colleagues shows the cross section of a ternary composite (boehmite/polycarbonate/epoxy, 80μm x 80μm). The surface was measured by AFM kelvin probe microscopy, yielding the surface potential which is shown as 3D‐surface and contour lines. The sample was further subjected to AFM force spectroscopy with a lateral resolution of 1μm², yielding the local Young's modulus, projected in false colors on the 3D surface. The ternary system, containing boehmite nanoparticles, shows a broad distribution of modulus, desirable for optimized macroscopic mechanical properties, such as high stiffness as well as toughness.
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems.