本研究探討深度學習技術在空間填充設計最佳化中的應用，旨在生成高品質的空間填充設計矩陣，以提高實驗數據的準確性和可靠性。首先，我們回顧了實驗設計和深度學習的基本概念，並介紹三種主要的實驗設計方法：最大最小距離設計、最大投影設計和均勻投影設計。隨後，我們構建了兩種深度學習模型——前饋神經網路和卷積神經網路，並將其應用於不同的實驗設計方法中，以評估其效果和優勢。研究結果表明，深度學習模型在最大最小距離設計和均勻投影設計中的表現優異，生成的空間填充設計矩陣在品質標準和電腦實驗中優於傳統方法。雖然在最大投影設計中，深度學習模型的表現未能超越傳統方法，但仍顯示出良好的潛力。此外，我們還探討了不同超參數設置對模型性能的影響，發現因子數和執行數是影響結果的主要因素。本研究的創新之處在於首次將深度學習技術應用於空間填充設計的最佳化，並證明其在提升實驗設計效率和效果方面的潛力。未來的研究可以進一步改進深度學習模型，並探索其在更多實驗設計領域中的應用，以期實現更高效和更準確的實驗設計。

This study explores the application of deep learning techniques in the optimization of space-filling design, aiming to generate high-quality space-filling design matrices to enhance the accuracy and reliability of experimental data. Firstly, we review the basic concepts of experimental design and deep learning, and introduce three main experimental design methods: maximin distance design, maximum projection design, and uniform projection design. Subsequently, we constructed two deep learning models, feedforward neural networks and convolutional neural networks, and applied them to different experimental design methods to evaluate their performance and advantages. The results indicate that the deep learning models perform excellently in maximin distance design and uniform projection design, with the generated space-filling design matrices outperforming traditional methods in terms of quality standards and computer experiments. Although the performance of the deep learning models did not surpass traditional methods in maximum projection design, they still demonstrate significant potential. Additionally, we investigated the impact of different hyperparameter settings on model performance, finding that the number of factors and levels are the main factors influencing the results. The innovation of this study lies in the first application of deep learning techniques to the optimization of space-filling design, demonstrating its potential in improving the efficiency and effectiveness of experimental design. Future research can further refine deep learning models and explore their applications in more areas of experimental design to achieve more efficient and accurate experimental designs.

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