Artificial Intelligence (AI) has emerged as a transformative tool for tackling complex engineering and scientific challenges, significantly impacting computational modeling, optimization, uncertainty quantification (UQ), and inverse problem-solving. Recent advancements in deep learning architectures [1] and Physics-Informed Neural Networks (PINNs) [2] have enabled powerful representations of complex physical systems, reducing reliance on extensive datasets through physics-driven regularization and constraints. Simultaneously, large language models (LLMs) have demonstrated unprecedented capabilities in reasoning, generalization, and automated knowledge integration [3], opening exciting opportunities for agent-based workflows, automated optimization strategies, and novel decision-making paradigms. The natural progression of AI now demands interdisciplinary strategies, combining the strengths of traditional deep learning models [4,5,6], physics-based approaches [7], and the versatility of LLMs. Such integrative methodologies promise to enhance our ability to solve computationally expensive inverse problems, navigate high-dimensional optimization landscapes, and rigorously quantify uncertainties. Furthermore, by orchestrating AI frameworks with high-performance computing (HPC) platforms, the engineering and scientific communities can achieve previously unattainable computational efficiency and scale [8,9,10]. This mini-symposium invites researchers to explore cutting-edge methods and applications that integrate physics-informed machine learning, deep learning, advanced LLMs, and HPC to address fundamental and applied challenges. We encourage presentations that propose innovative agentic workflows, demonstrate novel ways to embed physics knowledge within AI models, explore the use of LLMs in multi-agent coordination, or highlight impactful case studies across diverse scientific domains. We specifically welcome contributions that demonstrate: • Novel implementations and benchmarks of Physics-Informed AI and PINNs. • Application of LLMs in agent-driven design optimization workflows, simulation orchestration, and data-driven decision-making. • Integration of AI-driven workflows with state-of-the-art HPC environments. • Advanced optimization and uncertainty quantification methods empowered by integrated AI and physics-based approaches. • Solutions to computationally challenging inverse problems leveraging combined AI and physics-driven modeling.