為瞭解材料中多變的物理現象，對於「結構-性質」關係的瞭解是不可或缺的。在材料科學中一項重大挑戰即為透過在微觀尺度下控制材料表現，使其具有全新性質與功能。相較於晶體材料的高度對稱性，無序材料內額外的熱力學與結構自由度為其提供了許多優勢。無序系統內固有的隨機性使得其行為無法如同晶體一般簡單的透過其組成粒子於空間中排列的對稱性描述。然而，然而「無序」一詞不代表其結構缺乏特徵。由於存在不可忽視的粒子間交互作用，在無序系統中每個粒子的排列或多或少的與其周遭環境關聯。而此類微妙的關聯性只能透過統計學變數描述，其總結了足夠大量粒子行為的的集體行為。在此觀點下討論任意單獨粒子的性質是無意義的。

散射是常見於研究無序系統塊材特性的技術。藉由分析中子束與材料互動後發生的動能與方向變化，散射頻譜可供研究者一窺其中組成成分的排列形式。相反的，給定材料於微觀尺度下之互動，可透過電腦模擬取樣得出其於巨觀下之結構、行為。傳統上分析散射頻譜的方法為藉由遞迴地更新已知解析形式的數學函數中參數以比對測量所得數據，並以最終取得最佳化之參數組合描述材料特性。然而發展具解析形式的散射函數以精確地捕捉散射頻譜中特徵並連結材料性質通常是一項極為艱鉅的挑戰，我們因而尋求資料探勘技術協助，比對自散射實驗與電腦模擬中得到的粒子分布關聯函數，透過機率性的描述連結散射函數與其關聯之材料物理特性。

於本論文中我們提出一種泛用的策略，藉由基於高斯過程回歸算法的機器學習模型協助定量的由散射頻譜推測控制軟物質材料構象之參數。其中由分子動力學模擬產生的數據將作為基準訓練集用於訓練回歸模型。另外，為解決散射數據中粒子間與粒子內關聯難以分離的棘手問題，訓練集中的粒子間關聯函數將透過變分自動編碼器算法生成低維度代表，用於協助形塑人造散射函數以擬合與材料構象直接相關的粒子間關聯函數。

我們選擇兩個具代表性的無序系統：1. 軟物質，包含帶電膠體懸浮液與二元長鏈共聚物，以及2. 一類具成分無序性的晶體材料：高熵合金，作為研究對象，以測試本研究中提出用於結構鑑定之非參數性算法的可行性與泛用性。最後，我們成功展示了這些新發展的算法相較傳統方法具有更高的精準度以及更優良的運算效率。

One of the grand challenges and opportunities in materials science is to harness the new phenomena, properties, and function that emerge by de novo design of materials at the nanoscale. In this pursuit, materials characterized by inherent structural disorder offer many advantages due to their additional thermodynamic degrees of freedom in comparison to the crystalline materials.

The signature feature shared by numerous disordered systems is their inherent disorderliness. As a result, their structure and behavior cannot be simply characterized by the periodicity in spatial arrangement of particles as crystalline materials. Nevertheless, the term disorder does not necessarily mean that the structure in such systems are entirely random as in gas. Due to the presence of interaction at the atomic and molecular level, the constituent particles in disordered systems are highly correlated in position and momentum. Such coherence can only be described in terms of statistical variables that portray the behavior of a collection of sufficiently large amount of particles. Attribute of any single particle is not relevant in this descriptive framework.

Prominent among the tools for addressing the structure-property relationships of disordered systems are computer simulation and elastic scattering. In both techniques, the quantity of interest is the two-point static correlation function in reciprocal Q space, which manifests the spatial arrangement of particles in real space.

In this mathematical setting, the routine approach for obtaining the microstructural insights, from either computational trajectories or experimental spectra, is to first identify the relevant structural parameters, establish the theoretical model of two-point correlator accordingly, and use it as a basis of regression analysis in order to obtain the optimized parameters for structural description.

However, more than often the structure of disordered systems cannot be satisfactorily modelled analytically due to the complexity in structural collectivity. As a result, the disordered structure cannot be reconstructed in an unbiased manner. To circumvent this inherent deficiency of the existing deterministic methods, in this thesis we establish a non-parametric strategy, based on the principle of machine learning, to address the structural inversion problem in a probabilistic manner. Specifically, we deliberately select two representative soft condensed systems, colloidal suspension and copolymer solutions, and one hard matter system, the high entropy alloy, which is treated as heated solids with frozen atomic configurations in our study, to demonstrate the feasibility and usefulness of this new non-parametric method for investigating the structure of disordered systems.

In this thesis we have successfully demonstrated the superior performance of this method in numerical accuracy, computational efficiency, and general applicability over the existing parametric approaches. We are therefore optimistic to abut the prospect of our method and hope it will render a new window of opportunity for facilitating the structural inversion problems commonly encountered in the various topics of materials study.

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