Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids

Kontolati, Katiana; Alix-Williams, Darius; Boffi, Nicholas M.; Falk, Michael L.; Rycroft, Chris H.; Shields, Michael D.

doi:10.1016/j.actamat.2021.117008

Cited by 14 publications

(5 citation statements)

References 68 publications

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“…Machine learning has found applications in molecular simulations , too. In designing CG models themselves, ML has been extensively used in recent times (see refs − for a nonexhaustive list of references and ref for a detailed review). Again, these CG models are mostly focused on the structural properties of the systems.…”

Section: Introductionmentioning

confidence: 99%

Toward a Mobility-Preserving Coarse-Grained Model: A Data-Driven Approach

Bag

Meinel

Müller‐Plathe

2022

J. Chem. Theory Comput.

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Coarse-grained molecular dynamics (MD) simulation is a promising alternative to all-atom MD simulation for the fast calculation of system properties, which is imperative in designing materials with a specific target property. There have been several coarse-graining strategies developed over the past few years that provide accurate structural properties of the system. However, these coarse-grained models share a major drawback in that they introduce an artificial acceleration in molecular mobility. In this paper, we report a data-driven approach to generate coarse-grained models that preserve the all-atom molecular mobility. We designed a machine learning model in the form of an artificial neural network, which directly predicts the simulation-ready mobility-preserving coarse-grained potential as an output given the all-atom force field (FF) parameters as inputs. As a proof of principle, we took 2,3,4-trimethylpentane as a model system and described the development of machine learning models in detail. We quantify the artificial acceleration in molecular mobility by defining the acceleration factor as the ratio of the coarse-grained and the all-atom diffusion coefficient. The predicted coarse-grained potential generated by the best machine learning model can bring down the acceleration factor to a value of ∼2, which could be otherwise as large as 7 for a typical value of 3 × 10–9 m2 s–1 for the all-atom diffusion coefficient. We believe our method will be of interest in the community as a route to generating coarse-grained potentials with accurate dynamics.

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Section: Introductionmentioning

confidence: 99%

Toward a Mobility-Preserving Coarse-Grained Model: A Data-Driven Approach

Bag

Meinel

Müller‐Plathe

2022

J. Chem. Theory Comput.

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show abstract

“…45 More detailed atomistic simulations of amorphous solids have been done in the past with success to get relevant parameters for continuum models based on shear transformation zones. 69,70 In the present context, it is not obvious a priori that any kind of continuum description is relevant for these very thin strands, which are only a few particles in diameter. Hence we focus on a simple illustrative model, which can capture the main features of necking and failure.…”

Section: Continuum-scale Descriptionmentioning

confidence: 96%

Necking and failure of a particulate gel strand: signatures of yielding on different length scales

Thijssen,

Liverpool,

Royall

et al. 2023

Soft Matter

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“…The value of

\chi

is determined through an affine transformation of the weighted average atomic potential energies. See References 68,69 for a detailed explanation and methods to obtain the parameters of this affine transformation. Despite these efforts, there remains significant uncertainty as to the appropriate range of

\chi

for these fields.…”

Section: Examplesmentioning

confidence: 99%

“…Observations further suggest that this field can be approximated as Gaussian 56,68,69 . To approximate the initial

\chi

field using the Gaussian assumption, a sample of a zero‐mean delta‐correlated Gaussian field is obtained using the Box‐Muller transform.…”

Section: Examplesmentioning

confidence: 99%

“…Observations further suggest that this field can be approximated as Gaussian. 56,68,69 To approximate the initial 𝜒 field using the Gaussian assumption, a sample of a zero-mean delta-correlated Gaussian field is obtained using the Box-Muller transform. This sample is then smoothed with a bi-variate Gaussian of length scale (l 𝜒 = 10Å) centered at the nodes of the grid, where in this example r c = 5.…”

mentioning

confidence: 99%

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Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Santos

Giovanis

Kontolati

et al. 2022

Numerical Meth Engineering

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A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low-dimensional representation of the underlying behavior of physical/ mathematical systems with respect to uncertain input parameters. Using this representation, GH, an out-of-sample extension technique, is employed to create a global map from the input parameter space to a Grassmannian diffusion manifold. GH is further employed to locally map points on the diffusion manifold onto the tangent space of a Grassmann manifold. The exponential map is then used to project the points in the tangent space onto the Grassmann manifold, where reconstruction of the full solution is performed. The performance of the proposed surrogate model is verified with three examples. The first problem is a toy example used to illustrate the technique. In the second example, errors associated with the various mappings are assessed by studying response predictions of the electric potential of a dielectric cylinder in a homogeneous electric field. The last example applies the method for uncertainty prediction in the strain field evolution in a model amorphous material using the shear transformation zone theory of plasticity.

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Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids

Cited by 14 publications

References 68 publications

Toward a Mobility-Preserving Coarse-Grained Model: A Data-Driven Approach

Toward a Mobility-Preserving Coarse-Grained Model: A Data-Driven Approach

Necking and failure of a particulate gel strand: signatures of yielding on different length scales

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

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