Low-dimensional Descriptor Research Articles

A Gram-Charlier Analysis of Scattering to Describe Nonideal Polymer Conformations.

Theories of interpreting polymer physics and rheology at the molecular level from experiments, including small-angle scattering, typically rely on the assumption that polymer chains possess a Gaussian configuration distribution. This assumption frequently fails to describe features of real polymer molecules both at equilibrium (when polymers have nonlinear topology or heterogeneous chemistry) and out of equilibrium (when they are subjected to nonlinear deformations). To better describe non-Gaussian polymer conformation distributions, we propose a moments analysis based on the Gram-Charlier expansion as a natural framework for describing structure and scattering from non-Gaussian polymers. The expansion describes the conformation distribution in terms of cumulants (equivalent to moments of the distribution) of the underlying segment density distribution function, providing low-dimensional descriptors that can be inferred directly from measured scattering in a way that is agnostic to a polymer's topology, chemistry, or state of deformation. We use this framework to show that cumulants can be used to "fingerprint" non-Gaussian conformation distributions of polymers either at equilibrium (applied to sequence-defined heteropolymers) or out of equilibrium (applied to polymers experiencing nonlinear deformation due to flow). We anticipate that this new analysis method will provide a general framework for examining nonideal polymer configurations and the properties that arise from them.

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. The method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

An objective identification technique for potential vorticity structures associated with African easterly waves

Abstract. Tropical Africa and the North Atlantic Ocean are significantly influenced by African easterly waves (AEWs), which play a fundamental role in tropical rainfall and cyclogenesis in that region. The dynamics of AEWs can be described in a potential vorticity (PV) framework. The important impact of latent heat release by cloud processes is captured in this framework by the diabatic generation of PV anomalies. This paper introduces an innovative approach for the identification and tracking of PV structures within AEWs. By employing AEW tracking and computing the wave phase of each point within the AEW domain using a Hilbert transform, we are able to effectively identify and collect 3-D PV structures associated with specific AEWs. To facilitate a climatological analysis, performed here over the months of June to October from 2002 to 2022, these structures are subsequently characterized by low-dimensional descriptors, including their location, intensity, and orientation. Our climatological analysis reveals the seasonal evolution and the structural attributes of PV anomalies within AEWs over the study domain. PV feature locations closely align with the African easterly jet's latitudinal shift during the summer season. Analysis of the mean pressure level of the 3-D PV structures shows a remarkable shift during their life cycle, indicating deep moist convection characteristics over land and more shallow convection characteristics over the ocean. On average, PV features identified within AEW troughs tilt downshear over land and equatorward over the ocean. The trough-centered analysis reveals distinct differences between satellite-estimated and model-predicted rainfall. Agreement between the results of a more traditional composite analysis and our new feature analysis provides confidence in our feature approach as a novel diagnostic tool. The feature framework provides a low-dimensional representation of the PV structure of AEWs, which facilitates future statistical analyses of the relation of this structure to, for example, tropical cyclogenesis or the predictability of tropical rainfall.

Efficient interpolation of molecular properties across chemical compound space with low-dimensional descriptors

We demonstrate accurate data-starved models of molecular properties for interpolation in chemical compound spaces with low-dimensional descriptors. Our starting point is based on three-dimensional, universal, physical descriptors derived from the properties of the distributions of the eigenvalues of Coulomb matrices. To account for the shape and composition of molecules, we combine these descriptors with six-dimensional features informed by the Gershgorin circle theorem. We use the nine-dimensional descriptors thus obtained for Gaussian process regression based on kernels with variable functional form, leading to extremely efficient, low-dimensional interpolation models. The resulting models trained with 100 molecules are able to predict the product of entropy and temperature (S × T) and zero point vibrational energy (ZPVE) with the absolute error under 1 kcal mol−1 for >78 % and under 1.3 kcal mol−1 for >92 % of molecules in the test data. The test data comprises 20 000 molecules with complexity varying from three atoms to 29 atoms and the ranges of S × T and ZPVE covering 36 kcal mol−1 and 161 kcal mol−1, respectively. We also illustrate that the descriptors based on the Gershgorin circle theorem yield more accurate models of molecular entropy than those based on graph neural networks that explicitly account for the atomic connectivity of molecules.

Informative Training Data for Efficient Property Prediction in Metal-Organic Frameworks by Active Learning.

In recent data-driven approaches to material discovery, scenarios where target quantities are expensive to compute and measure are often overlooked. In such cases, it becomes imperative to construct a training set that includes the most diverse, representative, and informative samples. Here, a novel regression tree-based active learning algorithm is employed for such a purpose. It is applied to predict the band gap and adsorption properties of metal-organic frameworks (MOFs), a novel class of materials that results from the virtually infinite combinations of their building units. Simpler and low dimensional descriptors, such as those based on stoichiometric and geometric properties, are used to compute the feature space for this model owing to their ability to better represent MOFs in the low data regime. The partitions given by a regression tree constructed on the labeled part of the data set are used to select new samples to be added to the training set, thereby limiting its size while maximizing the prediction quality. Tests on the QMOF, hMOF, and dMOF data sets reveal that our method constructs small training data sets to learn regression models that predict the target properties more efficiently than existing active learning approaches, and with lower variance. Specifically, our active learning approach is highly beneficial when labels are unevenly distributed in the descriptor space and when the label distribution is imbalanced, which is often the case for real world data. The regions defined by the tree help in revealing patterns in the data, thereby offering a unique tool to efficiently analyze complex structure-property relationships in materials and accelerate materials discovery.

Inverse design of dual-phase steel microstructures using generative machine learning model and Bayesian optimization

The design of optimal microstructures requires first, the identification of microstructural features that influence the material’s properties and, then, a search for a combination of these features that give rise to desired properties. For microstructures with complex morphologies, where the number of features is large, deriving these structure–property relationships is a challenging task. To address this challenge, we propose a generative machine learning model that can automatically identify low-dimensional descriptors of microstructural features that can be used to establish structure–property relationships. Based on this model, we present an integrated, data-driven framework for microstructure characterization, reconstruction, and design that is applicable to heterogeneous materials with polycrystalline microstructures. The proposed method is evaluated on a case study of designing dual-phase steel microstructures created with the multi-level Voronoi tessellation method. To this end, we train a variational autoencoder to identify the descriptors from these synthetic dual-phase steel microstructures. Subsequently, we employ Bayesian optimization to search for the optimal combination of the descriptors and generate microstructures with specific yield stress and low susceptibility for damage initiation. The presented results show how microstructure descriptors, determined by the variational autoencoder model, act as design variables for an optimization algorithm that identifies microstructures with desired properties.

Efficient Interrogation of the Kinetic Barriers Demarcating Catalytic States of a Tyrosine Kinase with Optimal Physical Descriptors and Mixture Models.

Computer simulations are increasingly used to access thermo-kinetic information underlying structural transformation of protein kinases. Such information are necessary to probe their roles in disease progression and interactions with drug targets. However, the investigations are frequently challenged by forbiddingly high computational expense, and by the lack of standard protocols for the design of low dimensional physical descriptors that encode system features important for transitions. Here, we consider the demarcating characteristics of the different states of Abelson tyrosine kinase associated with distinct catalytic activity to construct a set of physically meaningful, orthogonal collective variables that preserve the slow modes of the system. Independent sampling of each metastable state is followed by the estimation of global partition function along the appropriate physical descriptors using the modified Expectation Maximized Molecular Dynamics method. The resultant free energy barriers are in excellent agreement with experimentally known rate-limiting dynamics and activation energy computed with conventional enhanced sampling methods. We discuss possible directions for further development and applications.

Advancing descriptor search in materials science: feature engineering and selection strategies

A main goal of data-driven materials research is to find optimal low-dimensional descriptors, allowing us to predict a physical property, and to interpret them in a human-understandable way. In this work, we advance methods to identify descriptors out of a large pool of candidate features by means of compressed sensing. To this extent, we develop schemes for engineering appropriate candidate features that are based on simple basic properties of building blocks that constitute the materials and that are able to represent a multi-component system by scalar numbers. Cross-validation based feature-selection methods are developed for identifying the most relevant features, thereby focusing on high generalizability. We apply our approaches to an ab initio dataset of ternary group-IV compounds to obtain a set of descriptors for predicting lattice constants and energies of mixing. In particular, we introduce simple complexity measures in terms of involved algebraic operations as well as the amount of utilized basic properties.

Determining Exception Context in Assembly Operations from Multimodal Data.

Robot assembly tasks can fail due to unpredictable errors and can only continue with the manual intervention of a human operator. Recently, we proposed an exception strategy learning framework based on statistical learning and context determination, which can successfully resolve such situations. This paper deals with context determination from multimodal data, which is the key component of our framework. We propose a novel approach to generate unified low-dimensional context descriptions based on image and force-torque data. For this purpose, we combine a state-of-the-art neural network model for image segmentation and contact point estimation using force-torque measurements. An ensemble of decision trees is used to combine features from the two modalities. To validate the proposed approach, we have collected datasets of deliberately induced insertion failures both for the classic peg-in-hole insertion task and for an industrially relevant task of car starter assembly. We demonstrate that the proposed approach generates reliable low-dimensional descriptors, suitable as queries necessary in statistical learning.

Simple machine-learned interatomic potentials for complex alloys

Developing data-driven machine-learning interatomic potential for materials containing many elements becomes increasingly challenging due to the vast configuration space that must be sampled by the training data. We study the learning rates and achievable accuracy of machine-learning interatomic potentials for many-element alloys with different combinations of descriptors for the local atomic environments. We show that for a five-element alloy system, potentials using simple low-dimensional descriptors can reach meV/atom-accuracy with modestly sized training datasets, significantly outperforming the high-dimensional SOAP descriptor in data efficiency, accuracy, and speed. In particular, we develop a computationally fast machine-learned and tabulated Gaussian approximation potential (tabGAP) for Mo--Nb--Ta--V--W alloys with a combination of two-body, three-body, and a new simple scalar many-body density descriptor based on the embedded atom method.

Spectral Representation of Behaviour Primitives for Depression Analysis

Depression is a serious mental disorder affecting millions of people all over the world. Traditional clinical diagnosis methods are subjective, complicated and require extensive participation of clinicians. Recent advances in automatic depression analysis systems promise a future where these shortcomings are addressed by objective, repeatable, and readily available diagnostic tools to aid health professionals in their work. Yet there remain a number of barriers to the development of such tools. One barrier is that existing automatic depression analysis algorithms base their predictions on very brief sequential segments, sometimes as little as one frame. Another barrier is that existing methods do not take into account what the context of the measured behaviour is. In this article, we extract multi-scale video-level features for video-based automatic depression analysis. We propose to use automatically detected human behaviour primitives as the low-dimensional descriptor for each frame. We also propose two novel spectral representations, i.e., spectral heatmaps and spectral vectors, to represent video-level multi-scale temporal dynamics of expressive behaviour. Constructed spectral representations are fed to Convolution Neural Networks (CNNs) and Artificial Neural Networks (ANNs) for depression analysis. We conducted experiments on the AVEC 2013 and AVEC 2014 benchmark datasets to investigate the influence of interview tasks on depression analysis. In addition to achieving state of the art accuracy in severity of depression estimation, we show that the task conducted by the user matters, that fusion of a combination of tasks reaches highest accuracy, and that longer tasks are more informative than shorter tasks, up to a point.

Appearance-Based Sequential Robot Localization Using a Patchwise Approximation of a Descriptor Manifold.

This paper addresses appearance-based robot localization in 2D with a sparse, lightweight map of the environment composed of descriptor–pose image pairs. Based on previous research in the field, we assume that image descriptors are samples of a low-dimensional Descriptor Manifold that is locally articulated by the camera pose. We propose a piecewise approximation of the geometry of such Descriptor Manifold through a tessellation of so-called Patches of Smooth Appearance Change (PSACs), which defines our appearance map. Upon this map, the presented robot localization method applies both a Gaussian Process Particle Filter (GPPF) to perform camera tracking and a Place Recognition (PR) technique for relocalization within the most likely PSACs according to the observed descriptor. A specific Gaussian Process (GP) is trained for each PSAC to regress a Gaussian distribution over the descriptor for any particle pose lying within that PSAC. The evaluation of the observed descriptor in this distribution gives us a likelihood, which is used as the weight for the particle. Besides, we model the impact of appearance variations on image descriptors as a white noise distribution within the GP formulation, ensuring adequate operation under lighting and scene appearance changes with respect to the conditions in which the map was constructed. A series of experiments with both real and synthetic images show that our method outperforms state-of-the-art appearance-based localization methods in terms of robustness and accuracy, with median errors below 0.3 m and 6°.

Learning Transformation-Invariant Local Descriptors With Low-Coupling Binary Codes.

Despite the great success achieved by prevailing binary local descriptors, they are still suffering from two problems: 1) vulnerable to the geometric transformations; 2) lack of an effective treatment to the highly-correlated bits that are generated by directly applying the scheme of image hashing. To tackle both limitations, we propose an unsupervised Transformation-invariant Binary Local Descriptor learning method (TBLD). Specifically, the transformation invariance of binary local descriptors is ensured by projecting the original patches and their transformed counterparts into an identical high-dimensional feature space and an identical low-dimensional descriptor space simultaneously. Meanwhile, it enforces the dissimilar image patches to have distinctive binary local descriptors. Moreover, to reduce high correlations between bits, we propose a bottom-up learning strategy, termed Adversarial Constraint Module, where low-coupling binary codes are introduced externally to guide the learning of binary local descriptors. With the aid of the Wasserstein loss, the framework is optimized to encourage the distribution of the generated binary local descriptors to mimic that of the introduced low-coupling binary codes, eventually making the former more low-coupling. Experimental results on three benchmark datasets well demonstrate the superiority of the proposed method over the state-of-the-art methods. The project page is available at https://github.com/yoqim/TBLD.

Conditional out-of-distribution generation for unpaired data using transfer VAE.

While generative models have shown great success in sampling high-dimensional samples conditional on low-dimensional descriptors (stroke thickness in MNIST, hair color in CelebA, speaker identity in WaveNet), their generation out-of-distribution poses fundamental problems due to the difficulty of learning compact joint distribution across conditions. The canonical example of the conditional variational autoencoder (CVAE), for instance, does not explicitly relate conditions during training and, hence, has no explicit incentive of learning such a compact representation. We overcome the limitation of the CVAE by matching distributions across conditions using maximum mean discrepancy in the decoder layer that follows the bottleneck. This introduces a strong regularization both for reconstructing samples within the same condition and for transforming samples across conditions, resulting in much improved generalization. As this amount to solving a style-transfer problem, we refer to the model as transfer VAE (trVAE). Benchmarking trVAE on high-dimensional image and single-cell RNA-seq, we demonstrate higher robustness and higher accuracy than existing approaches. We also show qualitatively improved predictions by tackling previously problematic minority classes and multiple conditions in the context of cellular perturbation response to treatment and disease based on high-dimensional single-cell gene expression data. For generic tasks, we improve Pearson correlations of high-dimensional estimated means and variances with their ground truths from 0.89 to 0.97 and 0.75 to 0.87, respectively. We further demonstrate that trVAE learns cell-type-specific responses after perturbation and improves the prediction of most cell-type-specific genes by 65%. The trVAE implementation is available via github.com/theislab/trvae. The results of this article can be reproduced via github.com/theislab/trvae_reproducibility.

Topological data analysis: Concepts, computation, and applications in chemical engineering

A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g., convolutional neural nets, Fourier series). Topological Data Analysis (TDA) is a field of mathematics that analyzes data from a fundamentally different perspective. TDA represents datasets as geometric objects and provides dimensionality reduction techniques that project such objects onto low-dimensional descriptors. The key properties of these descriptors (also known as topological features) are that they provide multiscale information and that they are stable under perturbations (e.g., noise, translation, and rotation). In this work, we review the key mathematical concepts and methods of TDA and present different applications in chemical engineering.

Approach for 3D Cultural Relic Classification Based on a Low-Dimensional Descriptor and Unsupervised Learning

Computer-aided classification serves as the basis of virtual cultural relic management and display. The majority of the existing cultural relic classification methods require labelling of the samples of the dataset; however, in practical applications, there is often a lack of category labels of samples or an uneven distribution of samples of different categories. To solve this problem, we propose a 3D cultural relic classification method based on a low dimensional descriptor and unsupervised learning. First, the scale-invariant heat kernel signature (Si-HKS) was computed. The heat kernel signature denotes the heat flow of any two vertices across a 3D shape and the heat diffusion propagation is governed by the heat equation. Secondly, the Bag-of-Words (BoW) mechanism was utilized to transform the Si-HKS descriptor into a low-dimensional feature tensor, named a SiHKS-BoW descriptor that is related to entropy. Finally, we applied an unsupervised learning algorithm, called MKDSIF-FCM, to conduct the classification task. A dataset consisting of 3D models from 41 Tang tri-color Hu terracotta Eures was utilized to validate the effectiveness of the proposed method. A series of experiments demonstrated that the SiHKS-BoW descriptor along with the MKDSIF-FCM algorithm showed the best classification accuracy, up to 99.41%, which is a solution for an actual case with the absence of category labels and an uneven distribution of different categories of data. The present work promotes the application of virtual reality in digital projects and enriches the content of digital archaeology.

Human Body Shape Reconstruction from Binary Image Using Convolutional Neural Network

Human body modeling is an important part of virtual try-on. In order to quickly reconstruct the three-dimensional(3D) human body based on the minimum input, we propose a new method for accurate reconstruction of the human body by inputting binary images from either single view or multiple views. We first encode the shape of the human body via Principal Component Analysis (PCA) to extract the low dimensional shape descriptor. Secondly, we design a novel Body Reconstruction Convolutional Neural Network (BRCNN) with two branches, which could capture deep correlated features from different views and merge them. Given the obtained statistical shape space of the human body, we jointly train the BRCNN to learn a global mapping from the input to the shape descriptor which can be then decoded to points cloud for the reconstruction of various body shapes under neutral poses. The experimental results show that compared with the existing human reconstruction technology, the accuracy has been improved by 1.07%, and the prediction results of the two views are better than those from the single view. Further investigation also reveals that the prediction results of the weight-sharing network are better than the network without weight-sharing.

Theory-Guided Machine Learning Finds Geometric Structure-Property Relationships for Chemisorption on Subsurface Alloys

Summary Developing physically transparent and quantitatively accurate models that relate the chemical interaction (chemisorption strength) between an adsorbate and a solid surface to the adsorption site's geometry is critical for our understanding of catalysis, corrosion, and electrochemistry. We develop a theory-guided machine-learning (ML) approach, which uses an interpretable class of ML models called generalized additive models (iGAM models), to discover predictive structure-property models that can quantify and explain the link between the geometric structure of an adsorption site and the chemisorption strength. We demonstrate the approach through several case studies, where we analyze the chemisorption strength of chemically distinct adsorbates (O, OH, S, and Cl) on subsurface metal alloy surfaces subjected to various strain- and ligand-induced changes in the local geometric structure. By comparing the ML-derived chemisorption models to previously established electronic-structure models, we clarify the critical physical parameters that control the chemisorption process on metal surfaces.

Chord-Length Shape Features for License Plate Character Recognition

Despite their recognized merits in terms of discrimination, compactness, and robustness, chord-length shape features have not received a great deal of attention in the literature on license plate recognition. In this paper, we present an innovative k nearest neighbors (kNN) approach for license plate detection and recognition, where a new low-dimensional descriptor that incorporates shape information of plate characters is formed from a finite set of established 1D chord-length signatures. When evaluated on a dataset incorporating a relatively large and diverse collection of plate image data, the proposed approach delivers promising results that compare favorably with those reported in the literature, without sacrificing computational efficiency or stability.

Functional form of the superconducting critical temperature from machine learning

Predicting the critical temperature $T_c$ of new superconductors is a notoriously difficult task, even for electron-phonon paired superconductors for which the theory is relatively well understood. Early attempts by McMillan and Allen and Dynes to improve on the weak-coupling BCS formula led to closed-form approximate relations between $T_c$ and various measures of the phonon spectrum and the electron-phonon interaction appearing in Eliashberg theory. Here we propose that these approaches can be improved with the use of machine learning algorithms. As an initial test, we train a model for identifying low-dimensional descriptors using the $T_c < 10$ K data tested by Allen and Dynes, and show that a simple analytical expression thus obtained improves upon the Allen-Dynes fit. Furthermore, the prediction for the recently discovered high $T_c$ material H$_3$S at high pressure is quite reasonable. Interestingly, $T_c$'s for more recently discovered superconducting systems with a more two-dimensional electron-phonon coupling, which do not follow Allen and Dynes' expression, also do not follow our analytic expression. Thus, this machine learning approach appears to be a powerful method for highlighting the need for a new descriptor beyond those used by Allen and Dynes to describe their set of isotropic electron-phonon coupled superconductors. We argue that this machine learning method, and its implied need for a descriptor characterizing Fermi surface properties, represents a promising new approach to superconductor materials discovery which may eventually replace the serendipitous discovery paradigm begun by Kamerlingh Onnes.