Computer-aided engineering (CAE) is undergoing a paradigm shift from human-coded algorithms and traditional neural network-based systems to natural language interfaces powered by Large Language Models (LLMs) [1]. Beyond text generation, LLMs function as reasoning engines capable of automating scientific workflows. While recent applications streamline tasks such as computer-aided design (CAD) models and simulation scripting, they do not address the computational challenges of high-dimensional parametric PDEs [1]. Traditional Model Order Reduction (MOR) methods, like Proper Orthogonal Decomposition (POD), reduce cost but rely on expensive offline training. Intrusive MOR approaches offer greater efficiency but remain underutilized due to their complexity and implementation barriers [1]. Building on the previous demonstration of an LLM-driven CAE agent for Space-Parameter-Time (SPT) decomposition using Tensor-decomposition-based A Priori Surrogates (TAPS) [2] and a subspace iterative solver [1], we extend the framework to incorporate a Newton–Raphson scheme for fully coupled multi-dimensional solutions. We show that this approach significantly improves accuracy beyond initial subspace approximations. Leveraging LLM automation enables rapid expansion to higher dimensions by efficiently deriving complex governing equations and generating code. Following presentation of the methodologies, we demonstrate the application of TAPS to analysis of thermal and solid mechanics problems and how LLM is employed to establish new formulations with similar tensor structures derived from Galerkin weak form. We conclude that the Agentic CAE MOR approach delivers faster, more accurate, and scalable solutions compared to traditional approaches.