Generative Reliability-Based Design Optimization Using In-Context Learning Capabilities of Large Language Models

Large Language Models (LLMs) have demonstrated remarkable in-context learning capabilities, enabling flexible utilization of limited historical information to play pivotal roles in reasoning, problem-solving, and complex pattern recognition tasks. Inspired by the successful applications of LLMs in multiple domains, this paper proposes a generative design method by leveraging the in-context learning capabilities of LLMs with the iterative search mechanisms of metaheuristic algorithms for solving reliability-based design optimization problems. In detail, reliability analysis is performed by engaging the LLMs and Kriging surrogate modeling to overcome the computational burden. By dynamically providing critical information of design points to the LLMs with prompt engineering, the method enables rapid generation of high-quality design alternatives that satisfy reliability constraints while achieving performance optimization. With the Deepseek-V3 model, three case studies are used to demonstrated the performance of the proposed approach. Experimental results indicate that the proposed LLM-RBDO method successfully identifies feasible solutions that meet reliability constraints while achieving a comparable convergence rate compared to traditional genetic algorithms.

fastkqr: A Fast Algorithm for Kernel Quantile Regression

Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising from the non-smooth quantile loss function. In this paper, we introduce a novel algorithm named fastkqr, which significantly advances the computation of quantile regression in reproducing kernel Hilbert spaces. The core of fastkqr is a finite smoothing algorithm that magically produces exact regression quantiles, rather than approximations. To further accelerate the algorithm, we equip fastkqr with a novel spectral technique that carefully reutilizes matrix computations. In addition, we extend fastkqr to accommodate a flexible kernel quantile regression with a data-driven crossing penalty, addressing the interpretability challenges of crossing quantile curves at multiple levels. We have implemented fastkqr in a publicly available R package. Extensive simulations and real applications show that fastkqr matches the accuracy of state-of-the-art algorithms but can operate up to an order of magnitude faster.