In-silico material discovery and design have traditionally relied on high-fidelity first-principles methods such as density functional theory (DFT) [1] and ab-initio molecular dynamics (AIMD) [2] to accurately model atomic interactions and predict material properties. Despite their effectiveness, these methods face significant challenges due to their prohibitive computational cost, limiting their scalability for highthroughput screening across vast chemical spaces and for simulations over large length and time scales. Moreover, many advanced materials remain beyond the reach of widespread predictive theories due to a fundamental lack of mechanistic understanding. These challenges stem from the inherent complexity of their chemical composition, phase stability, and the intricate interplay of multiple order parameters, compounded by the lack of self-consistent integration between theoretical models and multi-modal experimental findings. As a result, breakthroughs in functional materials, such as new classes of correlated oxides, nitrides, and low-dimensional quantum materials, have largely been serendipitous or guided by phenomenological intuition rather than systematic, theory-driven design. Attempts to predict new materials and functionalities have often led to mixed results, with theoretically proposed systems failing to exhibit the desired properties when synthesized and tested.

The Large Language Model (LLM) has gained significant popularity and is extensively utilized across various domains. Most LLM deployments occur within cloud data centers, where they encounter substantial response delays and incur high costs, thereby impacting the Quality of Services (QoS) at the network edge. Leveraging vector database caching to store LLM request results at the edge can substantially mitigate response delays and cost associated with similar requests, which has been overlooked by previous research. Addressing these gaps, this paper introduces a novel Vector database-assisted cloud-Edge collaborative LLM QoS Optimization (VELO) framework. Firstly, we propose the VELO framework, which ingeniously employs vector database to cache the results of some LLM requests at the edge to reduce the response time of subsequent similar requests. Diverging from direct optimization of the LLM, our VELO framework does not necessitate altering the internal structure of LLM and is broadly applicable to diverse LLMs. Subsequently, building upon the VELO framework, we formulate the QoS optimization problem as a Markov Decision Process (MDP) and devise an algorithm grounded in Multi-Agent Reinforcement Learning (MARL) to decide whether to request the LLM in the cloud or directly return the results from the vector database at the edge. Moreover, to enhance request feature extraction and expedite training, we refine the policy network of MARL and integrate expert demonstrations. Finally, we implement the proposed algorithm within a real edge system. Experimental findings confirm that our VELO framework substantially enhances user satisfaction by concurrently diminishing delay and resource consumption for edge users utilizing LLMs.