An application of machine learning to statistical physics: from the phases of quantum control to satisfiability problems

This dissertation presents a study of machine learning methods with a focus on applications to statistical and condensed matter physics, in particular the problem of quantum state preparation, spin-glass and constraint satisfiability. We will start by introducing the core principles of machine learning such as overfitting, bias-variance tradeoff and the disciplines of supervised, unsupervised and reinforcement learning. This discussion will be set in the context of recent applications of machine learning to statistical physics and condensed matter physics. We then present the problem of quantum state preparation and show how reinforcement learning along with stochastic optimization methods can be applied to identify and define phases of quantum control. Reminiscent of condensed matter physics, the underlying phases of quantum control are identified via a set of order parameters and further detailed in terms of their universal implications for optimal quantum control. In particular, casting the optimal quantum control problem as an optimization problem, we show that it exhibits a generic glassy phase and establish a connection with the fields of spin-glass physics and constraint satisfiability problems. We then demonstrate how unsupervised learning methods can be used to obtain important information about the complexity of the phases described. We end by presenting a novel clustering framework, termed HAL for hierarchical agglomerative learning, which exploits out-of-sample accuracy estimates of machine learning classifiers to perform robust clustering of high-dimensional data. We show applications of HAL to various clustering problems

Balanced Order Batching with Task-Oriented Graph Clustering

Balanced order batching problem (BOBP) arises from the process of warehouse picking in Cainiao, the largest logistics platform in China. Batching orders together in the picking process to form a single picking route, reduces travel distance. The reason for its importance is that order picking is a labor intensive process and, by using good batching methods, substantial savings can be obtained. The BOBP is a NP-hard combinational optimization problem and designing a good problem-specific heuristic under the quasi-real-time system response requirement is non-trivial. In this paper, rather than designing heuristics, we propose an end-to-end learning and optimization framework named Balanced Task-orientated Graph Clustering Network (BTOGCN) to solve the BOBP by reducing it to balanced graph clustering optimization problem. In BTOGCN, a task-oriented estimator network is introduced to guide the type-aware heterogeneous graph clustering networks to find a better clustering result related to the BOBP objective. Through comprehensive experiments on single-graph and multi-graphs, we show: 1) our balanced task-oriented graph clustering network can directly utilize the guidance of target signal and outperforms the two-stage deep embedding and deep clustering method; 2) our method obtains an average 4.57m and 0.13m picking distance ("m" is the abbreviation of the meter (the SI base unit of length)) reduction than the expert-designed algorithm on single and multi-graph set and has a good generalization ability to apply in practical scenario.Comment: 10 pages, 6 figure

심층학습을 이용한 액체계의 성질 예측

학위논문(박사)--서울대학교 대학원 :자연과학대학 화학부,2020. 2. 정연준.최근 기계학습 기술의 급격한 발전과 이의 화학 분야에 대한 적용은 다양한 화학적 성질에 대한 구조-성질 정량 관계를 기반으로 한 예측 모형의 개발을 가속하고 있다. 용매화 자유 에너지는 그러한 기계학습의 적용 예중 하나이며 다양한 용매 내의 화학반응에서 중요한 역할을 하는 근본적 성질 중 하나이다. 본 연구에서 우리는 목표로 하는 용매화 자유 에너지를 원자간의 상호작용으로부터 구할 수 있는 새로운 심층학습 기반 용매화 모형을 소개한다. 제안된 심층학습 모형의 계산 과정은 용매와 용질 분자에 대한 부호화 함수가 각 원자와 분자들의 구조적 성질에 대한 벡터 표현을 추출하며, 이를 토대로 원자간 상호작용을 복잡한 퍼셉트론 신경망 대신 벡터간의 간단한 내적으로 구할 수 있다. 952가지의 유기용질과 147가지의 유기용매를 포함하는 6,493가지의 실험치를 토대로 기계학습 모형의 교차 검증 시험을 실시한 결과, 평균 절대 오차 기준 0.2 kcal/mol 수준으로 매우 높은 정확도를 가진다. 스캐폴드-기반 교차 검증의 결과 역시 0.6 kcal/mol 수준으로, 외삽으로 분류할 수 있는 비교적 새로운 분자 구조에 대한 예측에 대해서도 우수한 정확도를 보인다. 또한, 제안된 특정 기계학습 모형은 그 구조 상 특정 용매에 특화되지 않았기 때문에 높은 양도성을 가지며 학습에 이용할 데이터의 수를 늘이는 데 용이하다. 원자간 상호작용에 대한 분석을 통해 제안된 심층학습 모형 용매화 자유 에너지에 대한 그룹-기여도를 잘 재현할 수 있음을 알 수 있으며, 기계학습을 통해 단순히 목표로 하는 성질만을 예측하는 것을 넘어 더욱 상세한 물리화학적 이해를 하는 것이 가능할 것이라 기대할 수 있다.Recent advances in machine learning technologies and their chemical applications lead to the developments of diverse structure-property relationship based prediction models for various chemical properties; the free energy of solvation is one of them and plays a dominant role as a fundamental measure of solvation chemistry. Here, we introduce a novel machine learning-based solvation model, which calculates the target solvation free energy from pairwise atomistic interactions. The novelty of our proposed solvation model involves rather simple architecture: two encoding function extracts vector representations of the atomic and the molecular features from the given chemical structure, while the inner product between two atomistic features calculates their interactions, instead of black-boxed perceptron networks. The cross-validation result on 6,493 experimental measurements for 952 organic solutes and 147 organic solvents achieves an outstanding performance, which is 0.2 kcal/mol in MUE. The scaffold-based split method exhibits 0.6 kcal/mol, which shows that the proposed model guarantees reasonable accuracy even for extrapolated cases. Moreover, the proposed model shows an excellent transferability for enlarging training data due to its solvent-non-specific nature. Analysis of the atomistic interaction map shows there is a great potential that our proposed model reproduces group contributions on the solvation energy, which makes us believe that the proposed model not only provides the predicted target property, but also gives us more detailed physicochemical insights.1. Introduction 1 2. Delfos: Deep Learning Model for Prediction of Solvation Free Energies in Generic Organic Solvents 7 2.1. Methods 7 2.1.1. Embedding of Chemical Contexts 7 2.1.2. Encoder-Predictor Network 9 2.2. Results and Discussions 13 2.2.1. Computational Setup and Results 13 2.2.2. Transferability of the Model for New Compounds 17 2.2.3. Visualization of Attention Mechanism 26 3. Group Contribution Method for the Solvation Energy Estimation with Vector Representations of Atom 29 3.1. Model Description 29 3.1.1. Word Embedding 29 3.1.2. Network Architecture 33 3.2. Results and Discussions 39 3.2.1. Computational Details 39 3.2.2. Prediction Accuracy 42 3.2.3. Model Transferability 44 3.2.4. Group Contributions of Solvation Energy 49 4. Empirical Structure-Property Relationship Model for Liquid Transport Properties 55 5. Concluding Remarks 61 A. Analyzing Kinetic Trapping as a First-Order Dynamical Phase Transition in the Ensemble of Stochastic Trajectories 65 A1. Introduction 65 A2. Theory 68 A3. Lattice Gas Model 70 A4. Mathematical Model 73 A5. Dynamical Phase Transitions 75 A6. Conclusion 82 B. Reaction-Path Thermodynamics of the Michaelis-Menten Kinetics 85 B1. Introduction 85 B2. Reaction Path Thermodynamics 88 B3. Fixed Observation Time 94 B4. Conclusions 101Docto

BIOMOLECULAR FUNCTION FROM STRUCTURAL SNAPSHOTS

Biological molecules can assume a continuous range of conformations during function. Near equilibrium, the Boltzmann relation connects a particular conformation\u27s free energy to the conformation\u27s occupation probability, thus giving rise to one or more energy landscapes. Biomolecular function proceeds along minimum-energy pathways on such landscapes. Consequently, a comprehensive understanding of biomolecular function often involves the determination of the free-energy landscapes and the identification of functionally relevant minimum-energy conformational paths on these landscapes. Specific techniques are necessary to determine continuous conformational spectra and identify functionally relevant conformational trajectories from a collection of raw single-particle snapshots from, e.g. cryogenic electron microscopy (cryo-EM) or X-ray diffraction. To assess the capability of different algorithms to recover conformational landscapes, we:• Measure, compare, and benchmark the performance of four leading data-analytical approaches to determine the accuracy with which energy landscapes are recovered from simulated cryo-EM data. Our simulated data are derived from projection directions along the great circle, emanating from a known energy landscape. • Demonstrate the ability to recover a biomolecule\u27s energy landscapes and functional pathways of biomolecules extracted from collections of cryo-EM snapshots. Structural biology applications in drug discovery and molecular medicine highlight the importance of the free-energy landscapes of the biomolecules more crucial than ever. Recently several data-driven machine learning algorithms have emerged to extract energy landscapes and functionally relevant continuous conformational pathways from single-particle data (Dashti et al., 2014; Dashti et al., 2020; Mashayekhi,et al., 2022). In a benchmarking study, the performance of several advanced data-analytical algorithms was critically assessed (Dsouza et al., 2023). In this dissertation, we have benchmarked the performance of four leading algorithms in extracting energy landscapes and functional pathways from single-particle cryo-EM snapshots. In addition, we have significantly improved the performance of the ManifoldEM algorithm, which has demonstrated the highest performance. Our contributions can be summarized as follows.: • Expert user supervision is required in one of the main steps of the ManifoldEM framework wherein the algorithm needs to propagate the conformational information through all angular space. We have succeeded in introducing an automated approach, which eliminates the need for user involvement. • The quality of the energy landscapes extracted by ManifoldEM from cryo-EM data has been improved, as the accuracy scores demonstrate this improvement. These measures have substantially enhanced ManifoldEM’s ability to recover the conformational motions of biomolecules by extracting the energy landscape from cryo-EM data.In line with the primary goal of our research, we aimed to extend the automated method across the entire angular sphere rather than a great circle. During this endeavor, we encountered challenges, particularly with some projection directions not following the proposed model. Through methodological adjustments and sampling optimization, we improved the projection direction\u27s conformity to the model. However, a small subset of Projection directions (5 %) remained challenging. We also recommended the use of specific methodologies, namely feature extraction and edge detection algorithms, to enhance the precision in quantifying image differentiation, a crucial component of our automated model. we also suggested that integrating different techniques might potentially resolve challenges associated with certain projection directions. We also applied ManifoldEM to experimental cryo-EM images of the SARS-CoV-2 spike protein in complex with the ACE2 receptor. By introducing several improvements, such as the incorporation of an adaptive mask and cosine curve fitting, we enhanced the framework\u27s output quality. This enhancement can be quantified by observing the removal of the artifact from the energy landscape, especially if the post-enhancement landscape differs from the artifact-affected one. These modifications, specifically aimed at addressing challenges from Nonlinear Laplacian Spectral Analysis (NLSA) (Giannakis et al., 2012), are intended for application in upcoming cryo-EM studies utilizing ManifoldEM. In the closing sections of this dissertation, a summary and a projection of future research directions are provided. While initial automated methods have been explored, there remains room for refinement. We have offered numerous methodological suggestions oriented toward addressing solutions to the challenge of conformational information propagation. Key methodologies discussed include Manifold Alignment, Canonical Correlation Analysis, and Multi-View Diffusion Maps. These recommendations are aimed to inform and guide subsequent developments in the ManifoldEM suite

Unsupervised Discovery and Representation of Subspace Trends in Massive Biomedical Datasets

The goal of this dissertation is to develop unsupervised algorithms for discovering previously unknown subspace trends in massive multivariate biomedical data sets without the benefit of prior information. A subspace trend is a sustained pattern of gradual/progressive changes within an unknown subset of feature dimensions. A fundamental challenge to subspace trend discovery is the presence of irrelevant data dimensions, noise, outliers, and confusion from multiple subspace trends driven by independent factors that are mixed in with each other. These factors can obscure the trends in traditional dimension reduction and projection based data visualizations. To overcome these limitations, we propose a novel graph-theoretic neighborhood similarity measure for sensing concordant progressive changes across data dimensions. Using this measure, we present an unsupervised algorithm for trend-relevant feature selection and visualization. Additionally, we propose to use an efficient online density-based representation to make the algorithm scalable for massive datasets. The representation not only assists in trend discovery, but also in cluster detection including rare populations. Our method has been successfully applied to diverse synthetic and real-world biomedical datasets, such as gene expression microarray and arbor morphology of neurons and microglia in brain tissue. Derived representations revealed biologically meaningful hidden subspace trend(s) that were obscured by irrelevant features and noise. Although our applications are mostly from the biomedical domain, the proposed algorithm is broadly applicable to exploratory analysis of high-dimensional data including visualization, hypothesis generation, knowledge discovery, and prediction in diverse other applications.Electrical and Computer Engineering, Department o

Core Formation, Coherence and Collapse: A New Core Evolution Paradigm Revealed by Machine Learning

We study the formation, evolution and collapse of dense cores by tracking density structures in a magnetohydrodynamic (MHD) simulation. We identify cores using the dendrogram algorithm and utilize machine learning techniques, including principal component analysis (PCA) and the k-means clustering algorithm to analyze the full density and velocity dispersion profiles of these cores. We find that there exists an evolutionary sequence consisting of three distinct phases: i) the formation of turbulent density structures (Phase I), ii) the dissipation of turbulence and the formation of coherent cores (Phase II), and iii) the transition to protostellar cores through gravitational collapse (Phase III). In dynamically evolving molecular clouds, the existence of these three phases corresponds to the coexistence of three populations of cores with distinct physical properties. The prestellar and protostellar cores frequently analyzed in previous studies of observations and simulations belong to the last phase in this evolutionary picture. We derive typical lifetimes of 1.4$\pm$1.0$\times$10$^5$ yr, 3.3$\pm$1.4$\times$10$^5$ yr and 3.3$\pm$1.4$\times$10$^5$ yr, respectively for Phase I, II and III. We find that cores can form from both converging flows and filament fragmentation and that cores may form both inside and outside the filaments. We then compare our results to previous observations of coherent cores and provide suggestions for future observations to study cores belonging to the three phases.Comment: Submitted to Astrophysical Journal in June, 202

Robust recognition and exploratory analysis of crystal structures using machine learning

In den Materialwissenschaften läuten Künstliche-Intelligenz Methoden einen Paradigmenwechsel in Richtung Big-data zentrierter Forschung ein. Datenbanken mit Millionen von Einträgen, sowie hochauflösende Experimente, z.B. Elektronenmikroskopie, enthalten eine Fülle wachsender Information. Um diese ungenützten, wertvollen Daten für die Entdeckung verborgener Muster und Physik zu nutzen, müssen automatische analytische Methoden entwickelt werden. Die Kristallstruktur-Klassifizierung ist essentiell für die Charakterisierung eines Materials. Vorhandene Daten bieten vielfältige atomare Strukturen, enthalten jedoch oft Defekte und sind unvollständig. Eine geeignete Methode sollte diesbezüglich robust sein und gleichzeitig viele Systeme klassifizieren können, was für verfügbare Methoden nicht zutrifft. In dieser Arbeit entwickeln wir ARISE, eine Methode, die auf Bayesian deep learning basiert und mehr als 100 Strukturklassen robust und ohne festzulegende Schwellwerte klassifiziert. Die einfach erweiterbare Strukturauswahl ist breit gefächert und umfasst nicht nur Bulk-, sondern auch zwei- und ein-dimensionale Systeme. Für die lokale Untersuchung von großen, polykristallinen Systemen, führen wir die strided pattern matching Methode ein. Obwohl nur auf perfekte Strukturen trainiert, kann ARISE stark gestörte mono- und polykristalline Systeme synthetischen als auch experimentellen Ursprungs charakterisieren. Das Model basiert auf Bayesian deep learning und ist somit probabilistisch, was die systematische Berechnung von Unsicherheiten erlaubt, welche mit der Kristallordnung von metallischen Nanopartikeln in Elektronentomographie-Experimenten korrelieren. Die Anwendung von unüberwachtem Lernen auf interne Darstellungen des neuronalen Netzes enthüllt Korngrenzen und nicht ersichtliche Regionen, die über interpretierbare geometrische Eigenschaften verknüpft sind. Diese Arbeit ermöglicht die Analyse atomarer Strukturen mit starken Rauschquellen auf bisher nicht mögliche Weise.In materials science, artificial-intelligence tools are driving a paradigm shift towards big data-centric research. Large computational databases with millions of entries and high-resolution experiments such as electron microscopy contain large and growing amount of information. To leverage this under-utilized - yet very valuable - data, automatic analytical methods need to be developed. The classification of the crystal structure of a material is essential for its characterization. The available data is structurally diverse but often defective and incomplete. A suitable method should therefore be robust with respect to sources of inaccuracy, while being able to treat multiple systems. Available methods do not fulfill both criteria at the same time. In this work, we introduce ARISE, a Bayesian-deep-learning based framework that can treat more than 100 structural classes in robust fashion, without any predefined threshold. The selection of structural classes, which can be easily extended on demand, encompasses a wide range of materials, in particular, not only bulk but also two- and one-dimensional systems. For the local study of large, polycrystalline samples, we extend ARISE by introducing so-called strided pattern matching. While being trained on ideal structures only, ARISE correctly characterizes strongly perturbed single- and polycrystalline systems, from both synthetic and experimental resources. The probabilistic nature of the Bayesian-deep-learning model allows to obtain principled uncertainty estimates which are found to be correlated with crystalline order of metallic nanoparticles in electron-tomography experiments. Applying unsupervised learning to the internal neural-network representations reveals grain boundaries and (unapparent) structural regions sharing easily interpretable geometrical properties. This work enables the hitherto hindered analysis of noisy atomic structural data