Dennis Meier

Radu Ioan Bot, Ernö Robert Csetnek, Dennis Meier

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve strong convergence, one usually needs to impose more restrictive properties for the involved operators, like strong monotonicity (respectively, strong convexity for optimization problems). In this paper, we propose a modified Krasnosel'ski\uı--Mann algorithm in connection with the determination of a fixed point of a nonexpansive mapping and show strong convergence of the iteratively generated sequence to the minimal norm solution of the problem. Relying on this, we derive a forward-backward and a Douglas-Rachford algorithm, both endowed with Tikhonov regularization terms, which generate iterates that strongly converge to the minimal norm solution of the set of zeros of the sum of two maximally monotone operators. Furthermore, we formulate strong convergent primal-dual algorithms of forward-backward and Douglas-Rachford-type for highly structured monotone inclusion problems involving parallel-sums and compositions with linear operators. The resulting iterative schemes are particularized to the solving of convex minimization problems.

Ralph Bulanadi, Jefferey Baxter, Arpan Biswas et al.

Self-driving laboratories or autonomous experimentation are emerging as transformative platforms for accelerating scientific discovery. Bayesian optimization (BO) is among the most widely used machine learning frameworks for these purposes, but these BO-based frameworks rely on predefined scalar descriptors to guide experimentation. In many situations, the determination of an appropriate scalar descriptor can be challenging, and may fail to capture subtle yet scientifically important phenomena apparent to experts with interdisciplinary insight. To overcome this limitation, here we develop deep-kernel pairwise learning (DKPL), an approach for autonomous microscopy experiments which incorporates human expertise and interdisciplinary scientific knowledge into an active learning loop. Instead of relying on explicit scalar objectives, DKPL enables experts to directly evaluate which experimental output is more promising using interdisciplinary knowledge. DKPL then learns a latent utility function from these expert judgements to guide subsequent autonomous microscopy experiments. We demonstrate DKPL's performance in learning physically meaningful nanoscale structures while effectively prioritizing high-information measurement regions using an experimental model dataset with known ground truth. We further apply DKPL to analyze the character of ferroelectric domain walls, where we find DKPL capable of distinguishing between high and low characteristic domain-wall angles in bismuth ferrite, and able to discover both head-to-head and tail-to-tail domain-wall character in erbium manganite. This development establishes an approach to integrate expert knowledge into autonomous microscopy experiments and demonstrates a pathway toward expert-guided self-driving laboratories capable of addressing scientific problems beyond the limits of scalar-metrics-driven learning.