Bayesian optimization with kernel ensembles and disagreement-based acquisition for source localization and acoustic inversion

Gaussian processes with stationary kernels on bounded domains exhibit inflated posterior variance near the boundary. Despite being a long-recognized artifact in geostatistics and a source of over-exploration in Bayesian optimization, the causes and effects of boundary-induced acquisition bias are underexplored. We trace the root cause to a simple geometric mechanism: the truncation of the kernel correlation neighborhood at the domain boundary creates an observation-independent distortion that worsens with dimensionality. We show how this distortion manifests across three acquisition classes: variance maximization concentrates selections at the corners, whereas negative integrated posterior variance and expected predictive information gain move selections inward to axis-aligned interior shells. These patterns arise without reference to any objective function, meaning that acquisition behavior can be dominated by kernel geometry rather than the desired task-specific uncertainty. To quantify this, we introduce a function-free selection-profile diagnostic for arbitrary acquisitions, kernels, and bounded-domain geometries.

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

A learning-based physics-constrained neural kernel for sound field estimation is proposed. Sound field estimation aims to estimate the spatial distribution of an acoustic field from a discrete set of microphone measurements, which have a wide range of applications. Among existing sound field estimation methods, kernel-regression-based methods offer a flexible and principled framework for incorporating physical constraints and allow inference through linear operation. It is also possible to adapt the kernel function to the target acoustic environment by representing the directional weighting function as an implicit neural representation (INR) and optimizing hyperparameters using measurements. However, the kernel function is generally optimized for single snapshot measurements of the microphones, which can lead to strong overfitting and poor generalization. We propose a source-position-dependent INR for the directional weighting function, enabling the kernel function to capture common directional patterns and to generalize to unseen source positions in the target acoustic environment. Experimental results indicate that our proposed method outperforms the snapshot-based method by estimating a directional weighting function that matches the directivity of the target sound field.