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Cited by 173Machine Learning in Materials ScienceAdvanced Physical and Chemical Molecular InteractionsModel Reduction and Neural Networks

Unsupervised machine learning in atomistic simulations, between predictions and understanding

Open access
Ceriotti, Michele·2019·The Journal of Chemical Physics
DOI 10.1063/1.5091842
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Abstract

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.

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.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1063/1.5091842

Cites

112 of 112 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 68 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning
    § VIII. THE PROBLEMS WITH UNSUPERVISED LEARNING · p. 8

    Most of the time, analyses using unsupervised learning required 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.

    “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.”
    Quote in the paperNot a substantial claim
  • Findingcitation
    § VIII. THE PROBLEMS WITH UNSUPERVISED LEARNING · p. 9

    In Ref. 84, when considering nitrogen-substituted analogues of pentacene, the most clear-cut clustering was associated with in-plane H-bonding rather than with the stacking.

    “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.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [84] 2018, Chem. Sci. source

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  • Findingcitation
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    A generalized convex hull (GCH) construction uses (kernel) principal component analysis to determine the structural parameters that capture the highest degree of diversity in a collection of (meta)stable structures.

    “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.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [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).

      Not checked in the free run.

  • Interpretationreasoning
    § Perspective: Unsupervised machine learning in atomistic simulations, between predictions and understanding · p. 1

    Supervised machine-learning techniques are less susceptible to preconceived biases than unsupervised techniques when used to rationalize 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.”
    Quote in the paperSubstantial claim
  • Premisereasoning
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 2

    The choice of representation provides leeway to incorporate prior knowledge or restrict the scope of the analysis.

    “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.”
    Quote in the paperNot a substantial claim
  • May combine two claims. 14
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    Findingnone given
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 2

    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.

    “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.”
    Quote in the paperNot a substantial claim

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    Interpretationnone given
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 2

    Opting for a specialized description of a system introduces biases in the procedure.

    “Obviously, opting for a specialized description of a system introduces some biases in the procedure.”
    Quote in the paperNot a substantial claim

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    Premisecitation
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 2

    Given a metric or a positive-definite kernel, it is possible to obtain an operative definition of a representation in terms of a set of features.

    “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 ′ ).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [14] M. Cuturi , e-print arXiv:0911.5367 (2009).

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    Premisereasoning
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 2

    The representation of a structure can take the form of a vector of features, a measure of similarity, or a kernel, and these three ways can be used interchangeably.

    “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”
    Quote in the paperNot a substantial claim

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    Premisenone given
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 2

    Given a representation in terms of a finite set of features, it is always possible to use it as the starting point to define a distance or a kernel.

    “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.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationreasoning
    § III. REPRESENTATIONS, DISTANCES AND KERNELS · p. 4

    SOAP power spectra components are systematic but overdetermined, and Behler-Parrinello symmetry functions are highly correlated with each other.

    “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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    Premisenone given
    § VI. DIMENSIONALITY REDUCTION · p. 6

    It is hard if not impossible to comprehend the meaning or the relative positions of vectors in a high (or infinite) dimensional space.

    “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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    Premisecitation
    § III. REPRESENTATIONS, DISTANCES AND KERNELS · p. 3

    The problem of obtaining a complete yet concise description of a molecular or condensed-phase structure is central to many modelling techniques.

    “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 .”
    Quote in the paperNot a substantial claim0 of 4 sources checked
    • cites [15] 2002, Proc. Natl. Acad. Sci. U. S. A. source

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    • cites [2] 2011, J. Phys.: Condens. Matter source

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    • cites [16] 2003

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    • cites [17] 2006, J. Chem. Phys. source

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    Premisenone given
    § III. REPRESENTATIONS, DISTANCES AND KERNELS · p. 4

    Most state-of-the-art representations incorporate symmetries.

    “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.”
    Quote in the paperNot a substantial claim

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    Premisenone given
    § VI. DIMENSIONALITY REDUCTION · p. 6

    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.

    “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.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given
    § II. MACHINE LEARNING FOR ATOMISTIC MODELING · p. 3

    In unsupervised learning, hyperparameter optimization is often performed manually, by trial and error, and constitutes one of the critical points to consider to keep the procedure truly unbiased.

    “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.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Premisereasoning
    § VI. DIMENSIONALITY REDUCTION · p. 6

    Dimensionality-reduction methods have long been sought after for all sorts of data analysis applications.

    “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.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § III. REPRESENTATIONS, DISTANCES AND KERNELS · p. 3

    The separation between global and local representations is far from clear-cut, and it is often possible to construct a local version of a global representation, and vice versa.

    “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 .”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [25] 2013, J. Chem. Phys. source

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    • cites [32] 2016, Phys. Chem. Chem. Phys. source

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    Interpretationnone given
    § V. APPLICATIONS OF CLUSTERING METHODS TO ATOMISTIC MODELING · p. 6

    The use of local, atom/fragment-based representations is convenient to find recurring patterns in the building blocks of a structure, rather than in the overall configuration.

    “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.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning
    § IV. CLUSTERING AND PATTERN RECOGNITION · p. 6

    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 of feature space, kernel or metric.

    “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.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Premisenone given
    § VI. DIMENSIONALITY REDUCTION · p. 6

    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.

    “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.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § IV. CLUSTERING AND PATTERN RECOGNITION · p. 6

    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.

    “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.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    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.

    “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”
    Quote in the paperNot a substantial claim

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    Premisecitation
    § VI. DIMENSIONALITY REDUCTION · p. 7

    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).

    “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”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [76] 2000, Science source

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    Premisecitation
    § VI. DIMENSIONALITY REDUCTION · p. 7

    TICA 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.

    “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”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [80] 1994, Phys. Rev. Lett. source

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    • cites [81] 2013, J. Chem. Phys. 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.

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    Premisecitation
    § VI. DIMENSIONALITY REDUCTION · p. 7

    SGOOP singles 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.

    “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”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [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.

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    Premisecitation
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    Materials cartography 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 'structure-energy-property' landscape of that system.

    “'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.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [57] 2015, Chem. Mater. source

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    • cites [84] 2018, Chem. Sci. source

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    • cites [85] 2018, Chem. Mater. source

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    Premisecitation
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    Similar approaches have been applied to biomolecular simulations, where the main application of dimensionality reduction has been in connection with accelerated sampling.

    “Similar approaches have been applied to biomolecular simulations 86 , where the main application of dimensionality reduction has been in connection with accelerated sampling.”
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    • cites [86] 2012, J. Mol. Graphics Modell. source

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    Premisenone given
    § VI. DIMENSIONALITY REDUCTION · p. 7

    All of the dimensionality reduction methods discussed up to this point rely exclusively on the distribution of atoms in each structure.

    “All of the methods discussed this far rely exclusively on the distribution of atoms in each structure.”
    Quote in the paperNot a substantial claim

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    Premisecitation
    § VI. DIMENSIONALITY REDUCTION · p. 7

    ISOMAP 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.

    “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.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [75] 2000, Science source

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    Premisereasoning
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    The applications of dimensionality reduction schemes to atomistic simulations reflect the dual function of a coarse-grained representation: to simplify the description of a system to understand it better, and to explore more effectively its conformational space.

    “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.”
    Quote in the paperSubstantial claim

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    Premisecitation
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    In order to observe a rare (activated) event without developing dedicated hardware, one needs to selectively increase the speed at which the pathways related to the transition are traversed, to modify the probability distribution that is sampled during the simulation so that configurations close to the transition state occur more often, or to generate adaptively ensembles of trajectories that覆盖the

    “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”
    Quote in the paperNot a substantial claim0 of 6 sources checked
    • cites [1] 2009

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    • cites [51] 2002, Annu. Rev. Mater. Res. source

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    • cites [87] 2002, Annu. Rev. Phys. Chem. source

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    • cites [88] 2008, J. Phys. Chem. B source

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    • cites [15] 2002, Proc. Natl. Acad. Sci. U. S. A. source

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    • cites [89] 1977, J. Comput. Phys. source

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    Premisecitation
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    In metadynamics, the volume of a free energy minimum grows exponentially with the dimensionality d of collective variable space, and so does the time to accumulate sufficient bias to escape the free-energy basin.

    “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.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [93] 2005, J. Phys. Chem. B source

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    • cites [94] 2008, Rep. Prog. Phys. source

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    Premisecitation
    § VII. APPLICATIONS OF DIMENSIONALITY REDUCTION TO ATOMISTIC MODELING · p. 8

    The objective of accelerated sampling is to accelerate sampling while introducing a minimal disturbance to the natural behavior of the system.

    “Either way, the objective is to accelerate sampling while introducing a minimal disturbance to the natural behavior of the system 91”
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    • cites [91] 2013, Phys. Rev. Lett. source

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    Interpretationcitation
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    The accuracy of the regression model provides an objective metric to optimize the hyperparameters that define the representation, and even to determine the most effective non-linear function of features that reproduces the target properties.

    “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 .”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [107] 2018, Phys. Chem. Chem. Phys. source

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    • cites [108] 2018, Phys. Rev. Mater. source

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    Interpretationreasoning
    § VIII. THE PROBLEMS WITH UNSUPERVISED LEARNING · p. 8

    It is tempting to pick one's own 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.

    “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.”
    Quote in the paperNot a substantial claim

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    Interpretationreasoning
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    Checking how accurately one can machine-learn the property of interest based on the structural representation used as input for an unsupervised learning scheme gives an idea of the limiting accuracy that can be expected when inferring structure-property relations by application of unsupervised classification or coarse-graining schemes.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    Clustering can be used to select the most relevant reference configurations from a database, or to partition it into regions on which specialized models can be trained.

    “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”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [109] 2015, Int. J. Quantum Chem. source

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    • cites [110] 2018, J. Chem. Theory Comput. source

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    Premisecitation
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    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.

    “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 .”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [58] 2017, J. Cheminf. source

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    • cites [104] 2017, Sci. Adv. source

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    • cites [111] 2018, J. Chem. Phys. source

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    Interpretationnone given
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    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.

    “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.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given
    § IX. PUTTING SOME SUPERVISION INTO UNSUPERVISED LEARNING · p. 9

    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.

    “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.”
    Quote in the paperNot a substantial claim
36 of 36

  • 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.”
4 of 4

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • ML models, analysis of their key features, and dimensionality reduction represent important tools for building structure-property relationships and mapping chemical space.

    “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]

Self-check

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

    Minor

    The 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.

  • LLE discussion points to the wrong figure panel

    Minor

    The 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.

2 of 2

Cites

Flagged first, then by citations

Research works printed but not linked: 7

  1. 2016, The God Delusion
  2. 2011, Pattern Recognition and Machine Learning (Information Science and Statistics)
  3. 2006, Gaussian Processes for Machine Learning
  4. 2003, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses
  5. H. Huo and M.Rupp, e-print arxiv:1704.06439 (2017). · arXiv
  6. 2010, Multidimensional Scaling
  7. 2008, J. Mach. Learn. Res., 9, 2579

Cited by

Sorted by citations

Related

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
DOI
10.1063/1.5091842
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
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.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-08.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-08.

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.

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