Understanding how interdisciplinary research teams converge on shared knowledge is a persistent challenge. This paper presents a novel, multi-layer, AI-driven analytical framework for mapping research convergence in interdisciplinary teams. The framework integrates large language models (LLMs), graph-based visualization and analytics, and human-in-the-loop evaluation to examine how research viewpoints are shared, influenced, and integrated over time. LLMs are used to extract structured viewpoints aligned with the \emph{Needs-Approach-Benefits-Competition (NABC)} framework and to infer potential viewpoint flows across presenters, forming a common semantic foundation for three complementary analyses: (1) similarity-based qualitative analysis to identify two key types of viewpoints, popular and unique, for building convergence, (2) quantitative cross-domain influence analysis using network centrality measures, and (3) temporal viewpoint flow analysis to capture convergence dynamics. To address uncertainty in LLM-based inference, the framework incorporates expert validation through structured surveys and cross-layer consistency checks. A case study on water insecurity in underserved communities as part of the Arizona Water Innovation Initiatives demonstrates increasing viewpoint convergence and domain-specific influence patterns, illustrating the value of the proposed AI-enabled approach for research convergence analysis.