The DOI matches its Crossref record; 112 of the 112 references it cites were found in a registry or an index; none of the 68 sources its claims cite is checked for support yet.
Unsupervised machine learning in atomistic simulations, between predictions and understanding
Open accessAbstract
Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods—that are geared toward classification and coarse-graining of molecular simulations—seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
This perspective reviews unsupervised machine-learning methods for atomistic simulations—clustering and dimensionality reduction—and argues they are powerful but strongly dependent on structural representations and hyperparameter choices. It recommends validating and optimizing unsupervised analyses through supervised learning tasks to reduce preconceived biases and improve understanding of structure–property relations.
Key findings
- Unsupervised schemes such as clustering and dimensionality reduction can identify structural motifs and coarse-grained states, but their outcome depends crucially on the feature space, metric, or kernel; non-linear transformations can split, merge, create, or destroy local maxima in the probability distribution.
- The paper states that for real data there is no “ground truth” for what partitioning or low-dimensional representation is best, and analyses often require human intervention in algorithm design and hyperparameter tuning, risking tuning until results match expectations.
- Supervised learning can provide objective metrics for unsupervised representations: checking how accurately a property can be predicted, analyzing learning curves, optimizing hyperparameters, and benchmarking order parameters against the committor in biomolecular simulations.
- The paper argues that combining supervised and unsupervised approaches side-by-side is key, with examples including Markov-state models, materials cartography, accelerated sampling, and structure searches; no original numerical results are reported.
Methods
- Perspective/review article; no new primary data, simulations, or experiments are reported.
- Reviews mathematical foundations of representations, distances/kernels, clustering, dimensionality reduction, and applications in atomistic modeling.
- Synthesizes literature and author opinion rather than performing a systematic quantitative meta-analysis.
Limitations
- The paper states that unsupervised learning lacks ground truth for real data and is sensitive to representation and hyperparameters; manual intervention can introduce preconceived biases.
- The paper states that supervised validation is proposed as a mitigation, but this is presented as the author’s opinion and not as a fully solved problem.
- Evident from the text: as a perspective, it provides no new numerical benchmarks or empirical validation, and its conclusions are based on literature synthesis and the author’s viewpoint.
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In the paper
“In all honesty, most of the time the analyses did require a significant amount of human intervention, first in the design of the details of the classification/dimensionality reduction algorithm, and later in the choice of the hyperparameters that define the structural representation and tune the functioning of the machine learning scheme.”
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“When considering the nitrogen-substituted analogues of pentacene, however, we found that the most clear-cut clustering was associated with in-plane H-bonding rather than with the stacking.”
What the sources say
- Not checked yetcites [84] 2018, Chem. Sci. source
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“we have recently developed a generalized convex hull (GCH) construction 113 that uses (kernel) principal component analysis to determine the structural parameters that capture the highest degree of diversity in a collection of (meta)stable structures.”
What the sources say
- Not checked yetcites [113] A. Wieczorek , M.Wieser, D.Murezzan, and V.Roth, “Learning sparse latent representations with the deep copula information bottleneck,” e-print arXiv:1804.06216 (2018).
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In the paper
“Supervised machine-learning techniques, that explicitly attempt to predict the properties of a material given its structure, are less susceptible to such biases.”
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In the paper
“A second reason - that is particularly relevant for unsupervised-learning applications geared towards simplifying the description of complex systems - is that the choice of representation provides ample leeway to incorporate prior knowledge or to otherwise restrict the scope of the analysis.”
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In the paper
“The main downside with using raw atomic coordinates as an input representation is precisely the fact that they discriminate between structures that are physically indistinguishable.”
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In the paper
“In closing this brief overview, it should be stressed that all of these techniques depend crucially on the choice of the feature space, and/or the metric that is used to estimate the similarity between inputs.”
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In the paper
“Machinelearning representations that are based on the description of local motifs, rather than on a conventional characterization of the system in terms of its lattice parameters and minimal unit cell, are very convenient, because they simplify the task of recognizing structures that correspond to alternative descriptions of the same periodic configuration (e.g. a conventional versus a primitive f”
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“While the cost and effectiveness of different representations may vary, one can demonstrate that most of these schemes can be seen as a specific implementation of a very abstract density-based scheme, in which a ket |A〉 is associated to each configuration 37 ,”
What the sources say
- Not checked yetcites [37] 2019, J. Chem. Phys. source
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In the paper
“The connection between density peaks and minima in the free energy makes density-based clustering methods (Fig. 3b) particularly well-suited to the analysis of finitetemperature atomistic simulations.”
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- It may state two separate claims as one. 14
- Probably not a substantial claim. 30
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In other terms Eq. (1) reproduces exactly the value of the kernel for each structure in the reference set, and provides a practical approximation of the vector |X〉 associated with the kernel for any other structure.”
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In the paper
“Obviously, opting for a specialized description of a system introduces some biases in the procedure.”
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In the paper
“From a formal point of view, the representer theorem guarantees that each positive-definite kernel 14 is associated with a Hilbert space whose scalar product 〈X|X ′ 〉 equals the kernel, and it is always possible to convert a kernel into a metric, e.g. by the relation d ( X , X ′ ) 2 = k ( X , X ) + k ( X ′ , X ′ ) -2 k ( X , X ′ ).”
What the sources say
- Not checked yetcites [14] M. Cuturi , e-print arXiv:0911.5367 (2009).
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In the paper
“It is worth stressing that the representation of a structure can take the form of a vector of features |X〉 (e.g. all the backbone dihedrals in a protein, the coordination number of atoms in a cluster, etc.), a measure of similarity between pairs of structures that can be implemented as a distance d ( X , X ′ ), or the form of a kernel k ( X , X ′ ). In fact, these three ways of representing a data”
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In the paper
“Given a representation in terms of a finite set of features x j ( X ) = 〈 j |X〉 , it is always possible to use it as the starting point to define a distance or a kernel.”
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In the paper
“Such a unifying view of input representations helps to understand the limits and strengths of each particular representation - for instance how SOAP power spectra components are systematic but overdetermined, and how Behler-Parrinello symmetry functions are highly correlated with each other.”
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In the paper
“It is however hard if not impossible to comprehend - not to mention visualize - the meaning or the relative positions of vectors in a high (or infinite) dimensional space.”
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In the paper
“The problem of obtaining a complete yet concise description of a molecular or condensed-phase structure is central to many modelling techniques, including the sampling of rare events 15 and the search for stable structures 2,16,17 .”
What the sources say
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In the paper
“One may argue that given sufficient amounts of training data a good ML scheme should be able to recognize these invariances, but why bother: most of the state-ofthe-art representations incorporate symmetries and by using them you can let your 20-layer convolutional neural network focus on learning correlations that are not as obvious.”
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In the paper
“Clustering techniques identify agglomeration of data in the most significant regions of feature space, but do not offer an overall picture of the relations between different structures.”
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In the paper
“In the context of unsupervised learning it is often performed manually, by trial and error, and constitutes one of the critical points to consider to keep the procedure truly unbiased.”
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In the paper
“This is a problem that obviously transcends the specific application to chemistry, physics or materials science, and dimensionality-reduction methods have long been sought after for all sorts of data analysis applications.”
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In the paper
“Obviously, the separation is far from clear-cut, and it is often possible to construct a local version of a global representation 25 , and vice versa to assemble local kernels and feature vectors into a representation of entire structures 32 .”
What the sources say
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In the paper
“The use of local, atom/fragment-based representations is also convenient to find recurring patterns in the building blocks of a structure, rather than in the overall configuration.”
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In the paper
“As we will discuss below, the risk of introducing spurious features can be mitigated by using general-purpose, relatively simple functions of the atomic coordinates as the input representation, and by checking that clustering is insensitive to the choice feature space, kernel or metric.”
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In the paper
“In principle, the information on the absolute position of each input in space, and the relations between any given pair of inputs, are encoded fully in the feature vectors.”
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In the paper
“Non-linear transformations of the input space, or of the measure of similarity, introduce distortions that can easily split, merge, create and destroy local maxima in the probability distribution associated with the input set.”
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In the paper
“dimensionality reduction lies at the heart of the vast majority of accelerated sampling methods, which try to beat the time scale problem of molecular simulations”
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In the paper
“The idea that the data may lie on a manifold that is only low-dimensional on a local basis is also behind methods such as locally-linear embedding (LLE) 76”
What the sources say
- Not checked yetcites [76] 2000, Science source
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In the paper
“The time-lagged independent component analysis method (TICA) 80,81 identifies linear combinations of features from a time-dependent trajectory that not only have the largest variance, but that also have the longest autocorrelation time”
What the sources say
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- Rests on an assumption: The most relevant degrees of freedom for a system are those in which the dynamics are slower.
In the paper
“the spectral gap optimization of order parameters (SGOOP) method to single out the linear combination of input features that correspond to the direction that is most relevant for the long-time dynamics of the system being studied 82”
What the sources say
- Not checked yetcites [82] 2016, Proc. Natl. Acad. Sci. U. S. A. source
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- Rests on an assumption: The most relevant degrees of freedom for a system are those in which the dynamics are slower.
None of the sources cited for this claim have been checked yet.
In the paper
“'Materials cartography', as it has been referred to 57 , strives to obtain a low-dimensional (typically 2D) representation of a set of materials, or of different phases of the same material, that reflects the 'structureenergy-property' landscape 84,85 of that system.”
What the sources say
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In the paper
“Similar approaches have been applied to biomolecular simulations 86 , where the main application of dimensionality reduction has been in connection with accelerated sampling.”
What the sources say
- Not checked yetcites [86] 2012, J. Mol. Graphics Modell. source
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In the paper
“All of the methods discussed this far rely exclusively on the distribution of atoms in each structure.”
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In the paper
“ISOMAP 75 uses a neighborhood analysis to estimate geodesic distances between points, based on the assumption that the data lies on a curved, but locally low-dimensional, manifold.”
What the sources say
- Not checked yetcites [75] 2000, Science source
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In the paper
“The applications of dimensionality reduction schemes to atomistic simulations reflect the dual function of a coarse-grained representation, as a mean to simplify the description of a system to understand it better, and to explore more effectively its conformational space.”
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In the paper
“In order to observe a rare (activated) event without developing dedicated hardware 1 one needs to selectively increase the speed at which the pathways related to the transition are traversed 51,87,88 , to modify the probability distribution that is sampled during the simulation so that configurations that are close to the transition state occur more often 15,89 , or to generate adaptively ens”
What the sources say
- Not checked yetcites [1] 2009
- Not checked yetcites [51] 2002, Annu. Rev. Mater. Res. source
- Not checked yetcites [87] 2002, Annu. Rev. Phys. Chem. source
- Not checked yetcites [88] 2008, J. Phys. Chem. B source
- Not checked yetcites [15] 2002, Proc. Natl. Acad. Sci. U. S. A. source
- Not checked yetcites [89] 1977, J. Comput. Phys. source
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In the paper
“Take for instance the case of metadynamics, in which a repulsive bias is accumulated in locations that have already been visited during the trajectory, forcing the system out of free energy minima 93,94 . The volume of one of these minima grows exponentially with the dimensionality d of collective variable space, and so does the time to accumulate sufficient bias to escape the freeenergy basin.”
What the sources say
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In the paper
“Either way, the objective is to accelerate sampling while introducing a minimal disturbance to the natural behavior of the system 91”
What the sources say
- Not checked yetcites [91] 2013, Phys. Rev. Lett. source
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In the paper
“The accuracy of the regression model also provides an objective metric to optimize the hyperparameters that define the representation 107 , and even to determine the most effective non-linear function of features that reproduces the target properties 108 .”
What the sources say
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is then tempting to pick one own's arbitrary perception of what an 'insightful' outcome of the analysis would be, and tune the representation and machine-learning scheme until the results reflect most clearly one's expectations.”
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In the paper
“For starters, it gives an idea of the limiting accuracy that can be expected when inferring structureproperty relations by application of unsupervised classification or coarse-graining schemes.”
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In the paper
“Clustering can be used to select the most relevant reference configurations from a database 109 , or to partition it into regions on which specialized models can be trained. 110”
What the sources say
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
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In the paper
“A low-dimensional representation of a dataset can help when it comes to identifying problematic regions, and understanding how a given representation 'sees' a set of structures 58,104,111 .”
What the sources say
Strength:plain· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
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In the paper
“Choosing to describe the inputs using a feature vector that is not problem specific, and validating and optimizing it through a relevant supervised learning exercise, reduces substantially the amount of human intervention and the possibility of introducing preconceived biases when applying clustering and dimensionality reduction schemes.”
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In the paper
“Unsupervised schemes can help shed light on the functioning of supervised algorithms that are often opaque, and supervised schemes can help to formulate quantitative metrics to assess the performance of unsupervised learning.”
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The paper relies on this without support.
In biomolecular simulations, entropically-stabilized states are the norm rather than the exception.
“particularly in the case of biomolecular simulations in which entropically-stabilized states are the norm rather than the exception.”
The paper relies on this without support.
In crystalline materials with few defects, local minima on the potential energy surface unequivocally identify the meta-stable states of the system.
“This is because in crystalline materials with few defects local minima on the potential energy surface unequivocally identify the meta-stable states of the system.”
The paper relies on this without support.
The most relevant degrees of freedom for a system are those in which the dynamics are slower.
“It is often the case, however, that the most relevant degrees of freedom for a system are those in which the dynamics are slower.”
The paper relies on this without support.
The complexity of simulations is increasing for materials, chemical and biomolecular applications.
“as the complexity of simulations is increasing for materials, chemical and biomolecular applications.”
Claims other papers make about this one
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The cited source says what the claim attributes to it.
In the citing paper
“ML models, analysis of their key features (32,52), and dimensionality reduction (i.e., unsupervised learning) (53-56) represent important tools for building structure-property relationships and mapping chemical space (57).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [56]
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Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
PCA input vectors are described as d-dimensional
MinorThe text defines x_i as a D-dimensional input vector and s_i as its d-dimensional principal-component representation. It later calls the x_i vectors d-dimensional.
“Another way to interpret PCA is to see { x i } as the set of d -dimensional points”
“Given a set of D -dimensional input vectors x i associated with N structures or local environments, PCA identifies the d linear combinations of the feature components that capture the largest possible fraction of the variability of the dataset (Fig. 4a).”
LLE discussion points to the wrong figure panel
MinorThe LLE discussion points to Fig. 4c, but the caption assigns local-relation-preserving embedding methods to Fig. 4d; Fig. 4c is assigned to multidimensional scaling.
“and then by imposing self-consistently that each point in low dimension should be a combination of its neighbors using the same weights (Fig. 4c)”
“(c) Multi-dimensional scaling and related approaches attempt to reproduce the similarity between high-dimensional data points in low dimension. (d) Embedding methods explicitly try to preserve local relations between points, under the assumption that they lie on a (locally) low-dimensional manifold.”
Citations
Cites
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Self-citationSymmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems
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Machine learning for the structure–energy–property landscapes of molecular crystals
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Accurate molecular polarizabilities with coupled cluster theory and machine learning
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Self-citationUsing sketch-map coordinates to analyze and bias molecular dynamics simulations
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Self-citationMode-finding for mixtures of Gaussian distributions
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Atom-density representations for machine learning
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Self-citationAccelerated materials property predictions and design using motif-based fingerprints
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Systematic determination of order parameters for chain dynamics using diffusion maps
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Efficient nonparametric n -body force fields from machine learning
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Self-citationStochastic Neural Network Approach for Learning High-Dimensional Free Energy Surfaces
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Demonstrating the Transferability and the Descriptive Power of Sketch-Map
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Self-citationIntrinsic map dynamics exploration for uncharted effective free-energy landscapes
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Predicting polymorphism in molecular crystals using orientational entropy
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Self-citationSolid-liquid interface free energy through metadynamics simulations
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Self-citationAlgorithms for clustering molecular dynamics configurations
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Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression
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Locating landmarks on high-dimensional free energy surfaces
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Network and graph analyses of folding free energy surfaces
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Gasparotto, P., & Ceriotti, M. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4900655 · Cited by 72
Self-citationNonlinear dimensionality reduction and mapping of compound libraries for drug discovery
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Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap
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Generalized Density-Functional Tight-Binding Repulsive Potentials from Unsupervised Machine Learning
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Free energy surface reconstruction from umbrella samples using Gaussian process regressionPreprint
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Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression
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Recognizing Local and Global Structural Motifs at the Atomic Scale
Gasparotto, P., Meißner, R. H., & Ceriotti, M. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00993 · Cited by 50
Self-citationGeneralized convex hull construction for materials discovery
Anelli, A., Engel, E. A., Pickard, C. J., & Ceriotti, M. (2018) · Physical Review Materials · doi:10.1103/physrevmaterials.2.103804 · Cited by 48
Self-citationModeling lithium-ion solid-state electrolytes with a pinball model
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The inefficiency of re-weighted sampling and the curse of system size in high-order path integration
Ceriotti, M., Brain, G. A. R., Riordan, O. M., & Manolopoulos, D. E. (2011) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2011.0413 · Cited by 44
Self-citationMapping and classifying molecules from a high-throughput structural database
De, S., Musil, F., Ingram, T., Baldauf, C., & Ceriotti, M. (2017) · Journal of Cheminformatics · doi:10.1186/s13321-017-0192-4 · Cited by 42
Self-citationMansbach, R. A., & Ferguson, A. L. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4914144 · Cited by 39
Delineation of Folding Pathways of a β-Sheet Miniprotein
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Automated crystal characterization with a fast neighborhood graph analysis method
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A chirality‐based metrics for free‐energy calculations in biomolecular systems
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Positive Definite Kernels in Machine LearningPreprint
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Learning Sparse Latent Representations with the Deep Copula Information BottleneckPreprint
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Preface: Special Topic on Materials Genome
Phillips, C. L., & Littlewood, P. B. (2016) · APL Materials · doi:10.1063/1.4952608 · Cited by 11
Flagged first, then by citations
Research works printed but not linked: 7
- 2016, The God Delusion
- 2011, Pattern Recognition and Machine Learning (Information Science and Statistics)
- 2006, Gaussian Processes for Machine Learning
- 2003, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses
- H. Huo and M.Rupp, e-print arxiv:1704.06439 (2017). · arXiv
- 2010, Multidimensional Scaling
- 2008, J. Mach. Learn. Res., 9, 2579
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Metadata
- Authors
- Ceriotti, M.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- Corresponding author
- Ceriotti, Michele
- ORCID
- Ceriotti, Michele
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2019-04-19
- Volume
- 150
- Issue
- 15
- Pages
- 150901-150901
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2924564326
- Semantic Scholar
- 1db247fc224065b15b85c26dcb31a91eb3b0b05f
- Cited by
- 173
- References
- 110
- Citations by year
- 2026: 8 · 2025: 24 · 2024: 18 · 2023: 24 · 2022: 32 · 2021: 25 · 2020: 28 · 2019: 14
- FWCI
- 8.93
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- The Journal of Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Funders
- H2020 European Research Council (677013-HBMAP)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Keywords
- unsupervised learning, atomistic simulation, molecular dynamics, clustering, dimensionality reduction, coarse-graining, structure-property relationships, machine learning bias, structure representation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-08, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-08 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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