Sustainable Development Goals
Abstract/Objectives
This article studies an important sequential decision making problem known as the multi-armed stochastic bandit problem with covariates. Under a linear bandit framework with high-dimensional covariates, we propose a general multi-stage arm allocation algorithm that integrates both arm elimination and randomized assignment strategies. By employing a class of high-dimensional regression methods for coefficient estimation, the proposed algorithm is shown to have near optimal finite-time regret performance under a new study scope that requires neither a margin condition nor a reward gap condition for competitive arms. Based on the synergistically verified benefit of the margin, our algorithm exhibits adaptive performance that automatically adapts to the margin and gap conditions, and attains optimal regret rates simultaneously for both study scopes, without or with the margin, up to a logarithmic factor. Besides the desirable regret performance, the proposed algorithm simultaneously generates useful coefficient estimation output for competitive arms and is shown to achieve both estimation consistency and variable selection consistency. Promising empirical performance is demonstrated through extensive simulation and two real data evaluation examples. Supplementary materials for this article are available online. © 2023 American Statistical Association.
Results/Contributions

Research on Tidal Glacier Dynamics and Iceberg Collapse Mechanisms Under Climate Change: Numerical Analysis Based on the Galerkin Least Squares Finite Element Method

In recent years, global climate anomalies have led to a continuous rise in average temperatures, making climate change and the greenhouse effect central issues of international concern. This issue not only involves in-depth research in the natural sciences but also profoundly affects the sustainable development of human economic activities and future survival. As part of the United Nations Sustainable Development Goals (SDGs), specifically Goal 13: Climate Action (SDG 13: Climate Action), scientifically understanding and addressing the impact of climate change on polar environments is a crucial step in mitigating global warming, predicting climate disasters, and formulating effective response strategies. In exploring the processes of the greenhouse effect and sea-level rise, changes in the Arctic ice sheet have become an important focus of research affecting global climate stability.

This study employs the Galerkin Least Squares Finite Element Method to conduct numerical analysis on a two-dimensional nonlinear Tuckers ice sheet model to investigate the iceberg collapse mechanisms at the terminus of tidal glaciers. We have established a model for the generation of basal crevasses due to tidal action and used numerical simulation methods to thoroughly study its dynamical behavior. Through the least squares finite element method, we have analyzed the pressure distribution in the simulation results and its corresponding changes in the grounding line in detail. The results indicate that water pressure plays a crucial role in the process of crevice formation. Furthermore, there are significant differences in stress distribution within floating ice tidal glaciers compared to fully supported glaciers, which may further influence iceberg collapse behavior.

Within the framework of climate action (SDG 13), glacier collapse is directly linked to sea-level rise, having profound implications for coastal ecosystems, polar species, and human societies. To comprehensively assess the key factors influencing iceberg collapse, we conducted a series of comprehensive numerical experiments, focusing on the effects of parameters such as sliding length, crevice length, and surface slope, validating the applicability and accuracy of the Galerkin Least Squares method in addressing such numerical problems. The research results not only provide a deeper understanding of glacier dynamics but also offer important theoretical foundations for predicting changes in tidal glaciers and iceberg collapse behaviors.

The findings of this study help enhance the understanding of how climate change impacts polar environments and support the formulation of global climate policies and adaptation measures, aligning with the goal of strengthening scientific understanding and predictive capabilities regarding the effects of climate change as outlined in SDG 13. By reinforcing research on glacier and iceberg collapse behavior, this will aid in establishing more accurate climate models, provide scientific support for global climate action, and encourage countries to develop adaptive policies to mitigate the risks posed by climate change.

Keywords
Grounding lineIceberg calvingNonlinear Stokes equationTidewater glacierFinite element methodGalerkin least-squares
References
Contact Information
朱家杰老師
ccchu@math.nthu.edu.tw