利用條件去噪擴散機率模型生成具目標機械性質的結構

Abstract

自然界中，不同物種為適應各自所處的嚴苛環境，演化出多樣化且獨特的骨骼結構，展現出截然不同的機械性質。這些自然形成的結構為工程領域提供了豐富的靈感與設計參考。然而，現今大多數的工程設計仍採用前向設計方式，即設計者預先建立幾何結構，再透過模擬或實驗來評估其機械性質。在面對特定力學需求時，前向設計往往需要經過大量的反覆試誤才能找到合適結構，不僅耗時且效率低落。相對而言，逆向設計則是根據目標性能條件，直接生成對應的結構，能夠大幅縮短設計迭代時間，提升開發效率。 本研究以來自 11 種不同物種的骨骼微結構為基礎，探討其幾何與力學行為之間的關聯，並發展結合生成模型的逆向設計方法。首先，在力學行為模擬方面，研究採用二維三角晶格彈簧之複合材料模型，預測不同幾何結構下的楊氏係數與韌性表現。隨後進一步擴展至三維結構，透過貝茲曲線將骨骼微結構圖像轉換為三維離散顆粒的單一孔隙材料模型，用以預測三維結構下的楊氏係數與比能量吸收表現，為實現逆向設計，本研究訓練了一個去噪擴散機率模型。該模型基於馬可夫鏈程序，分為前向與反向傳播兩階段，在前向過程中，逐步向骨骼微結構圖像添加高斯噪聲；而在反向過程中，模型學習如何從純噪聲中逐步還原並生成結構。於訓練過程中，我們將目標機械性質嵌入條件向量，使模型能夠根據給定的力學條件生成對應的結構。 透過本模型，可針對特定目標機械性質生成對應結構，且觀察其幾何分布時，發現模型能在相同性能條件下產生多樣幾何狀，顯著拓展結構設計空間。此外，於相同孔隙率條件下改變輸入性，可觀察模型如何透過幾何配置進行調整，以實現高韌性結構的生成策略。在三維逆向設計方面，模型不僅可根據輸入的機械性質生成骨骼微結構，同時亦可輸出對應的貝茲曲線，進一步構建出三維結構。

In nature, different species have evolved diverse and unique bone microstructures to adapt to their harsh environments, showing distinct mechanical properties. These naturally formed structures provide rich inspiration and design references for engineering. However, most current engineering designs still use a forward design approach, where designers first build geometric structures and then evaluate their mechanical performance through simulations or experiments. When facing specific mechanical requirements, forward design often requires a lot of trial and error to find suitable structures, which is time-consuming and inefficient. In contrast, inverse design generates corresponding structures based on target performance conditions, which can significantly reduce design iteration time and improve development efficiency. This study is based on bone microstructures from 11 different species, aiming to explore the relationship between geometry and mechanical behavior, and to develop an inverse design method combined with a generative model. First, in mechanical behavior simulation, the study uses a 2D lattice spring composite model to predict Young’s modulus and toughness under different geometric structures. It is further extended to 3D by converting bone microstructure images into 3D particle-based models using Bezier curves, to predict Young’s modulus and specific energy absorption in 3D structures. To achieve inverse design, this study trains a denoising diffusion probabilistic model. This model is based on a Markov chain process, divided into forward and reverse propagation: in the forward process, Gaussian noise is gradually added to bone microstructures; in the reverse process, the model learns how to recover and generate structures from pure noise. During training, target mechanical properties are embedded into the condition vector, allowing the model to generate corresponding structures based on the given mechanical conditions. Through this model, structures can be generated for specific mechanical targets. When observing their geometric distribution, it is found that the model can produce various geometries under the same performance condition, greatly expanding the design space. Furthermore, when the porosity is kept constant, changing the input toughness allows observation of how the model adjusts the geometry to achieve higher toughness. In 3D inverse design, the model can not only generate bone microstructures according to mechanical inputs, but also output corresponding Bezier curves to build 3D structures.