Unsupervised machine learning for detection of phase transitions in off-lattice systems. II. Applications

Calculating a Phase Diagram of a Simple Water Model Using Unsupervised Machine Learning on Simulation Data

We use unsupervised machine learning to construct a phase diagram of a simple 2D rose water model. The machine learning method that we use is a combination of dimensionality reduction methods and clustering algorithms. Two different data sets from the same simulations are used as input data for machine learning. These are angular distribution functions and a set of different thermodynamic, dynamic, and structural properties. To evaluate the efficiency of the method, the machine learning results are compared to manually determined phase diagrams. We show that the methods successfully predict the phase diagram of the rose water model. Furthermore, the phase diagrams obtained from the two data sets are in semiquantitative agreement with each other. Four different solid phases, one liquid phase, and one gaseous phase were determined. The method we have presented is straightforward and easy to implement. It requires almost no prior knowledge of the system to obtain a phase diagram. The method can also be used to distinguish between the different parts of the same phase that have different properties or a sufficiently different structure, and in this way find local differences and anomalies.

Machine learning in molecular biophysics: Protein allostery, multi-level free energy simulations, and lipid phase transitions

Machine learning (ML) techniques have been making major impacts on all areas of science and engineering, including biophysics. In this review, we discuss several applications of ML to biophysical problems based on our recent research. The topics include the use of ML techniques to identify hotspot residues in allosteric proteins using deep mutational scanning data and to analyze how mutations of these hotspots perturb co-operativity in the framework of a statistical thermodynamic model, to improve the accuracy of free energy simulations by integrating data from different levels of potential energy functions, and to determine the phase transition temperature of lipid membranes. Through these examples, we illustrate the unique value of ML in extracting patterns or parameters from complex data sets, as well as the remaining limitations. By implementing the ML approaches in the context of physically motivated models or computational frameworks, we are able to gain a deeper mechanistic understanding or better convergence in numerical simulations. We conclude by briefly discussing how the introduced models can be further expanded to tackle more complex problems.

Unsupervised Machine Learning Method for the Phase Behavior of the Constant Magnetization Ising Model in Two and Three Dimensions

Machine learning methods have been important in the study of phase transitions. Unsupervised methods are particularly attractive because they do not require prior knowledge of the existence of a phase transition. In this work we focus on the constant magnetization Ising model in two (2D) and three (3D) dimensions. While there have been many studies using machine learning for the critical behavior of these systems, we are not aware of any studies for the phase diagram at off-critical magnetizations below the critical temperature. Previous work has used the raw spins as the input feature. We show that a more robust input feature is the local affinity, where the value of the feature at each site is determined by the spin and its neighbors. When coupled with a variational autoencoder, the method is able to predict the phase behavior of the 2D and 3D Ising models (including the critical exponent β) in quantitative agreement with conventional simulations. The choice of activation functions in the autoencoder is crucial, and this requires physical insight into the nature of the phase transition. The method is general and can be applied to any lattice or off-lattice system.

Machine learning assisted sorting of active microswimmers

Active matter systems, being in a non-equilibrium state, exhibit complex behaviors, such as self-organization, giving rise to emergent phenomena. There are many examples of active particles with biological origins, including bacteria and spermatozoa, or with artificial origins, such as self-propelled swimmers and Janus particles. The ability to manipulate active particles is vital for their effective application, e.g., separating motile spermatozoa from nonmotile and dead ones, to increase fertilization chance. In this study, we proposed a mechanism-an apparatus-to sort and demix active particles based on their motility values (Péclet number). Initially, using Brownian simulations, we demonstrated the feasibility of sorting self-propelled particles. Following this, we employed machine learning methods, supplemented with data from comprehensive simulations that we conducted for this study, to model the complex behavior of active particles. This enabled us to sort them based on their Péclet number. Finally, we evaluated the performance of the developed models and showed their effectiveness in demixing and sorting the active particles. Our findings can find applications in various fields, including physics, biology, and biomedical science, where the sorting and manipulation of active particles play a pivotal role.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

Characterizing different motility-induced regimes in active matter with machine learning and noise

We examine motility-induced phase separation (MIPS) in two-dimensional run-and-tumble disk systems using both machine learning and noise fluctuation analysis. Our measures suggest that within the MIPS state there are several distinct regimes as a function of density and run time, so that systems with MIPS transitions exhibit an active fluid, an active crystal, and a critical regime. The different regimes can be detected by combining an order parameter extracted from principal component analysis with a cluster stability measurement. The principal component-derived order parameter is maximized in the critical regime, remains low in the active fluid, and has an intermediate value in the active crystal regime. We demonstrate that machine learning can better capture dynamical properties of the MIPS regimes compared to more standard structural measures such as the maximum cluster size. The different regimes can also be characterized via changes in the noise power of the fluctuations in the average speed. In the critical regime, the noise power passes through a maximum and has a broad spectrum with a 1/f^{1.6} signature, similar to the noise observed near depinning transitions or for solids undergoing plastic deformation.

Ordered ground state configurations of the asymmetric Wigner bilayer system-Revisited with unsupervised learning

We have reanalyzed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [Antlanger et al., Phys. Rev. Lett. 117, 118002 (2016)], comprising roughly 60 000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out "by hand," we have used for the present contribution machine learning concepts, notably based on a principal component analysis and a k-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters), we were able to reanalyze these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed, we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, thereby identifying a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.

Convolutional neural network-based colloidal self-assembly state classification

Colloidal self-assembly is a viable solution to making advanced metamaterials. While the physicochemical properties of the particles affect the properties of the assembled structures, particle configuration is also a critical determinant factor. Colloidal self-assembly state classification is typically achieved with order parameters, which are aggregate variables normally defined with nontrivial exploration and validation. Here, we present an image-based framework to classify the state of a 2-D colloidal self-assembly system. The framework leverages deep learning algorithms with unsupervised learning for state classification and a supervised learning-based convolutional neural network for state prediction. The neural network models are developed using data from an experimentally validated Brownian dynamics simulation. Our results demonstrate that the proposed approach gives a satisfying performance, comparable and even outperforming the commonly used order parameters in distinguishing void defective states from ordered states. Given the data-based nature of the approach, we anticipate its general applicability and potential automatability to different and complex systems where image or particle coordination acquisition is feasible.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Importance of feature construction in machine learning for phase transitions

Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom-Rowlinson (WR) mixture. We find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and -1 otherwise (affinity-based feature). We use principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) methods to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is key to the success of unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight in choice of input features is an important aspect of implementing machine learning methods.

Machine Learning-Assisted Design of Material Properties

Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical, inverse methods that frame design as a constrained optimization problem present an attractive alternative. However, even efficient algorithms require time- and resource-intensive characterization of material properties many times during optimization, imposing a design bottleneck. Approaches that incorporate machine learning can help address this limitation and accelerate the discovery of materials with targeted properties. In this article, we review how to leverage machine learning to reduce dimensionality in order to effectively explore design space, accelerate property evaluation, and generate unconventional material structures with optimal properties. We also discuss promising future directions, including integration of machine learning into multiple stages of a design algorithm and interpretation of machine learning models to understand how design parameters relate to material properties. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

From predictive modelling to machine learning and reverse engineering of colloidal self-assembly

An overwhelming diversity of colloidal building blocks with distinct sizes, materials and tunable interaction potentials are now available for colloidal self-assembly. The application space for materials composed of these building blocks is vast. To make progress in the rational design of new self-assembled materials, it is desirable to guide the experimental synthesis efforts by computational modelling. Here, we discuss computer simulation methods and strategies used for the design of soft materials created through bottom-up self-assembly of colloids and nanoparticles. We describe simulation techniques for investigating the self-assembly behaviour of colloidal suspensions, including crystal structure prediction methods, phase diagram calculations and enhanced sampling techniques, as well as their limitations. We also discuss the recent surge of interest in machine learning and reverse-engineering methods. Although their implementation in the colloidal realm is still in its infancy, we anticipate that these data-science tools offer new paradigms in understanding, predicting and (inverse) design of novel colloidal materials.

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems' stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. We first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

Machine learning for condensed matter physics

Condensed matter physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as chemistry, materials science, statistical physics, and high-performance computing. With the advancements in modern machine learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments.

Detecting depinning and nonequilibrium transitions with unsupervised machine learning

Using numerical simulations of a model disk system, we demonstrate that a machine learning generated order-parameter-like measure can detect depinning transitions and different dynamic flow phases in systems driven far from equilibrium. We specifically consider monodisperse passive disks with short range interactions undergoing a depinning phase transition when driven over quenched disorder. The machine learning derived order-parameter-like measure identifies the depinning transition as well as different dynamical regimes, such as the transition from a flowing liquid to a phase separated liquid-solid state that is not readily distinguished with traditional measures such as velocity-force curves or Voronoi tessellation. The order-parameter-like measure also shows markedly distinct behavior in the limit of high density where jamming effects occur. Our results should be general to the broad class of particle-based systems that exhibit depinning transitions and nonequilibrium phase transitions.