pith. sign in

arxiv: 2605.30822 · v1 · pith:FMCFKMB2new · submitted 2026-05-29 · ❄️ cond-mat.dis-nn · cond-mat.soft

Using graph neural networks to predict many-body interactions in amorphous materials

Mehryar Jannesari Ghomsheh , Donald L. Koch , Sarah Hormozi This is my paper

Pith reviewed 2026-06-28 20:22 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.soft
keywords graph neural networksmany-body interactionsamorphous materialspolymer-grafted nanoparticlesdensity functional theoryMonte Carlo simulationsequivariant networkssoft glasses
0
0 comments X

The pith

Graph neural network trained only on high-energy configurations reproduces DFT energies and recovers experimental equilibrium structures in polymer-grafted nanoparticle glasses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that an equivariant graph neural network can capture the many-body interactions arising when grafted polymer chains fill the space between nanoparticle cores in a solvent-free soft glass. Training occurs exclusively on classical density functional theory calculations of high-energy, out-of-equilibrium particle arrangements, yet the network reproduces those energies across varied design parameters at four orders of magnitude lower cost. Monte Carlo simulations driven by the network then locate equilibrium configurations that contain locally favored icosahedral arrangements and match experimental observations. A sympathetic reader would care because many amorphous materials are governed by these angular-dependent interactions, which pairwise models routinely omit for computational reasons.

Core claim

NequIP, an equivariant message-passing graph neural network, learns the high-dimensional, rugged potential energy landscape of solvent-free polymer-grafted nanoparticles and reproduces classical DFT energies across a range of PGN design parameters at four orders of magnitude lower cost. GNN-driven Monte Carlo simulations reveal locally favored icosahedral-like structures at equilibrium and recover equilibrium structures in agreement with experiments, despite the network being trained only on high-energy, out-of-equilibrium configurations.

What carries the argument

NequIP, an equivariant message-passing graph neural network that maps atomic configurations to many-body interaction energies.

If this is right

  • The network reproduces DFT energies across a range of PGN design parameters at four orders of magnitude lower cost.
  • Systematic hyperparameter analysis yields physical insights into the range, anisotropy, and effective body order of the interactions.
  • GNN-driven Monte Carlo simulations recover equilibrium structures containing locally favored icosahedral-like arrangements.
  • These simulated equilibrium structures agree with experimental observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the approach holds, similar networks could be trained on limited high-energy data to explore equilibrium properties in other solvent-free or crowded soft-matter systems where direct equilibrium sampling is expensive.
  • The learned effective interactions might be inspected to test whether they recover known angular forms predicted by polymer physics for chain-mediated forces.
  • One could check whether the same network architecture, without retraining, transfers to related amorphous systems such as metallic glasses mentioned in the introduction.

Load-bearing premise

A graph neural network trained exclusively on high-energy out-of-equilibrium configurations will generalize to predict the lower-energy equilibrium structures and dynamics that match experiments.

What would settle it

If Monte Carlo simulations driven by the trained network produced pair-correlation functions or coordination statistics that differed measurably from experimental data on the same polymer-grafted nanoparticle systems, the generalization claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.30822 by Donald L. Koch, Mehryar Jannesari Ghomsheh, Sarah Hormozi.

Figure 1
Figure 1. Figure 1: Overview of the computational framework. Out-of-equilibrium particle configurations, 𝒟(R), are sampled via hard-sphere dynamics and their many-body potential energies are evaluated with classical DFT, producing a dataset 𝒟(R, 𝐸) that spans the high-energy region of the PEL (top left). The GNN is trained on this dataset. Each particle is represented as a node connected to its neighbors within a cutoff radiu… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of solvent-free PGNs. (a) Polymers uniformly fill the void space for a given configuration of particles. (b) Same configuration as (a) but with an arbitrary displacement of a random particle (shown in red). (c) Displacement of a single particle creates a cascade of polymer rearrangements to minimize the free energy by reaching a uniform number density. The equilibrium polymer number density profi… view at source ↗
Figure 3
Figure 3. Figure 3: Classical DFT results for 100 PGNs with a core volume fraction of 𝜙𝑐 = 0.1, polymer molecular weight of 𝑀𝑤 = 5 𝑘𝐷𝑎, and a grafting density of 𝜎𝑔 = 1.8 chains/𝑛𝑚2 . The normalized number density of the grafted polymers is shown across multiple planes for (a) the system with excess implicit solvent, displaying significant density fluctuations, and (b) the solvent-free system, showing a uniform density distri… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Parity plot comparing GNN predictions to classical DFT energies for solvent-free PGNs across varying design parameters. The energies are shifted by the mean value, 𝜇, and scaled by the standard deviation, 𝜎𝐸, for each sample. All samples have a polymer molecular weight of 𝑀𝑤 = 5 𝑘𝐷𝑎, except for the sample with a grafting density of 𝜎𝑔 = 1.0 chains/𝑛𝑚2 which has 𝑀𝑤 = 9 𝑘𝐷𝑎. (b) The energy MAE as a funct… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Per particle energy distribution for out-of-equilibrium configurations (sampled by hard-sphere dynamics and used for training GNN) and equilibrium configurations evaluated by GNN and classical DFT for the sample with 𝜙𝑐 = 0.1 and 𝜎𝑔 = 1.8 chains/𝑛𝑚2 . (b) Equilibrium pair distribution function and (c) static structure factor for solvent-free PGNs with different design parameters. (d) Nearest neighbors … view at source ↗
Figure 6
Figure 6. Figure 6: Distribution of BOO parameters characterizing local particle configurations in solvent-free PGNs with 𝜙𝑐 = 0.1, 𝜎𝑔 = 1.8 chains/𝑛𝑚2 , and 𝑀𝑤 = 5 𝑘𝐷𝑎. The characteristic BOO values associated with perfect reference structures are marked on each map. (a) The (𝑞¯4, 𝑞¯6) plane and (b) the (𝑤6, 𝑞¯6) plane. (c) Distribution of normalized 𝑤ˆ 6 and the Voronoi volumes of the structures in each 𝑤ˆ 6 bin normalized … view at source ↗
read the original abstract

Many-body interactions govern the complex behavior of many amorphous materials, from metallic glasses to biological tissues, yet are often replaced by pairwise additive frameworks for computational efficiency. Here, we use classical density functional theory (DFT) to study a model soft glass of solvent-free polymer-grafted nanoparticles (PGNs), where the absence of solvent forces grafted chains to uniformly fill the interstitial space, generating strong angular-dependent many-body interactions between the cores. We show that NequIP, an equivariant message-passing graph neural network (GNN), learns the high-dimensional, rugged potential energy landscape of the system and reproduces classical DFT energies across a range of PGN design parameters at four orders of magnitude lower cost. Systematic analysis of GNN hyperparameters offers physical insights into the range, anisotropy, and effective body order of interactions. GNN-driven Monte Carlo simulations reveal locally favored icosahedral-like structures at equilibrium, and strikingly, recover equilibrium structures in agreement with experiments, despite the network being trained only on high-energy, out-of-equilibrium configurations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that an equivariant message-passing graph neural network (NequIP) trained on classical DFT calculations of high-energy, out-of-equilibrium configurations of solvent-free polymer-grafted nanoparticles (PGNs) can accurately reproduce the many-body potential energy landscape. This enables four-orders-of-magnitude faster energy evaluations across PGN design parameters, yields physical insights from hyperparameter analysis into interaction range and body order, and allows GNN-driven Monte Carlo simulations to recover equilibrium structures (including locally favored icosahedral motifs) that agree with experiments despite the training data being restricted to high-energy states.

Significance. If the central generalization result holds, the work would demonstrate a practical route to surrogate modeling of rugged many-body landscapes in amorphous materials, enabling larger-scale simulations that were previously limited by DFT cost. The systematic hyperparameter study and the reported success of extrapolation from out-of-equilibrium training data would be notable strengths for the field of machine-learned interatomic potentials in disordered systems.

major comments (2)
  1. [Abstract] Abstract: The claim that the GNN 'reproduces classical DFT energies' is presented without any quantitative error metrics (MAE, RMSE, or correlation coefficients), test-set details, or validation protocol. This information is load-bearing for the accuracy assertion and for the downstream claim that the learned potential supports reliable Monte Carlo sampling.
  2. [Abstract] Abstract (final sentence): The assertion that GNN-driven Monte Carlo recovers experimental equilibrium structures 'despite the network being trained only on high-energy, out-of-equilibrium configurations' is the central extrapolation result, yet the abstract supplies no hold-out comparison of GNN versus DFT energies on low-energy or equilibrated configurations, nor any structural metrics (e.g., g(r), structure factor) quantifying agreement with experiment. This gap directly affects the weakest assumption identified in the stress test.
minor comments (1)
  1. [Abstract] The abstract refers to 'systematic analysis of GNN hyperparameters' but does not indicate where in the manuscript the corresponding figures or tables appear; a forward reference would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for quantitative support in the abstract. We address each comment below and will revise the abstract to incorporate the requested details from the main text.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the GNN 'reproduces classical DFT energies' is presented without any quantitative error metrics (MAE, RMSE, or correlation coefficients), test-set details, or validation protocol. This information is load-bearing for the accuracy assertion and for the downstream claim that the learned potential supports reliable Monte Carlo sampling.

    Authors: We agree that the abstract would benefit from explicit quantitative metrics. The manuscript reports MAE, RMSE, and correlation coefficients on held-out test sets, together with the validation protocol, in the Results and Methods sections. We will revise the abstract to include a concise statement of these metrics and the test-set size. revision: yes

  2. Referee: [Abstract] Abstract (final sentence): The assertion that GNN-driven Monte Carlo recovers experimental equilibrium structures 'despite the network being trained only on high-energy, out-of-equilibrium configurations' is the central extrapolation result, yet the abstract supplies no hold-out comparison of GNN versus DFT energies on low-energy or equilibrated configurations, nor any structural metrics (e.g., g(r), structure factor) quantifying agreement with experiment. This gap directly affects the weakest assumption identified in the stress test.

    Authors: The main text presents GNN versus DFT energy comparisons across configurations and reports structural metrics (g(r) and structure factor) from the GNN-driven Monte Carlo runs that match experimental data. The structural agreement after equilibration provides indirect validation of the extrapolation to low-energy states. We will revise the abstract to reference these quantitative structural metrics and the reported energy accuracy on test sets. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external DFT and experiments

full rationale

The paper trains NequIP on classical DFT energies (external ground truth) and validates GNN-driven MC structures against independent experiments. No equations, fitted parameters, or self-citations are shown that reduce the reported reproduction of DFT energies or experimental agreement to a tautology or input by construction. The generalization from high-energy training data to equilibrium is presented as an empirical result, not a definitional or self-referential step. This is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach assumes classical DFT supplies an accurate many-body energy landscape for the PGN model, that the equivariant GNN architecture can represent angular-dependent interactions, and that the chosen PGN system exhibits the claimed strong many-body effects. No free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Equivariant message-passing graph neural networks can faithfully represent the potential energy surface of systems with angular many-body interactions.
    Invoked by the choice of NequIP architecture for the PGN system.
  • domain assumption Classical density functional theory provides a reliable reference for the many-body energies in solvent-free PGNs.
    Used as the training target throughout the abstract.

pith-pipeline@v0.9.1-grok · 5716 in / 1485 out tokens · 21779 ms · 2026-06-28T20:22:12.649409+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

86 extracted references · 3 canonical work pages

  1. [1]

    The physics of higher-order interactions in complex systems.Nature physics, 17(10):1093–1098, 2021

    Federico Battiston, Enrico Amico, Alain Barrat, Ginestra Bianconi, Guilherme Ferraz de Arruda, Benedetta Franceschiello, Iacopo Iacopini, Sonia Kéfi, Vito Latora, Yamir Moreno, et al. The physics of higher-order interactions in complex systems.Nature physics, 17(10):1093–1098, 2021

    2021

  2. [2]

    Simplicial models of social contagion.Nature communications, 10(1):2485, 2019

    Iacopo Iacopini, Giovanni Petri, Alain Barrat, and Vito Latora. Simplicial models of social contagion.Nature communications, 10(1):2485, 2019

    2019

  3. [3]

    Higher-order interactions stabilize dynamics in competitive network models.Nature, 548(7666):210–213, 2017

    Jacopo Grilli, György Barabás, Matthew J Michalska-Smith, and Stefano Allesina. Higher-order interactions stabilize dynamics in competitive network models.Nature, 548(7666):210–213, 2017

    2017

  4. [4]

    Beyond pairwise mechanisms of species coexistence in complex communities.Nature, 546(7656):56–64, 2017

    Jonathan M Levine, Jordi Bascompte, Peter B Adler, and Stefano Allesina. Beyond pairwise mechanisms of species coexistence in complex communities.Nature, 546(7656):56–64, 2017

    2017

  5. [5]

    Many-bodyelectrostaticforcesbetweencolloidalparticles at vanishing ionic strength.Phys

    JasonW.Merrill,SunilK.Sainis,andEricR.Dufresne. Many-bodyelectrostaticforcesbetweencolloidalparticles at vanishing ionic strength.Phys. Rev. Lett., 103:138301, Sep 2009

    2009

  6. [6]

    Many-body effects in nanocrystal superlattices: departure from sphere packing explains stability of binary phases.Journal of the American Chemical Society, 137(13):4494–4502, 2015

    Michael A Boles and Dmitri V Talapin. Many-body effects in nanocrystal superlattices: departure from sphere packing explains stability of binary phases.Journal of the American Chemical Society, 137(13):4494–4502, 2015

    2015

  7. [7]

    Free-standing nanoparticle superlattice sheets controlled by dna.Nature materials, 8(6):519–525, 2009

    Wenlong Cheng, Michael J Campolongo, Judy J Cha, Shawn J Tan, Christopher C Umbach, David A Muller, and Dan Luo. Free-standing nanoparticle superlattice sheets controlled by dna.Nature materials, 8(6):519–525, 2009

    2009

  8. [8]

    Atomic level structure in multicomponent bulk metallic glass.Physical review letters, 102(24):245501, 2009

    YQ Cheng, E Ma, and HW Sheng. Atomic level structure in multicomponent bulk metallic glass.Physical review letters, 102(24):245501, 2009

    2009

  9. [9]

    Many-body interactions in soft jammed materials.Soft matter, 13(7):1371–1383, 2017

    Reinhard Höhler and Sylvie Cohen-Addad. Many-body interactions in soft jammed materials.Soft matter, 13(7):1371–1383, 2017

    2017

  10. [10]

    A density-independent rigidity transition in biological tissues.Nature Physics, 11(12):1074–1079, 2015

    Dapeng Bi, JH Lopez, Jennifer M Schwarz, and M Lisa Manning. A density-independent rigidity transition in biological tissues.Nature Physics, 11(12):1074–1079, 2015

    2015

  11. [11]

    Relation between the dynamics of glassy clusters and characteristic features of their energy landscape.Physical Review Letters, 112(8):083401, 2014

    Sandip De, Bastian Schaefer, Ali Sadeghi, Michael Sicher, DG Kanhere, and Stefan Goedecker. Relation between the dynamics of glassy clusters and characteristic features of their energy landscape.Physical Review Letters, 112(8):083401, 2014

    2014

  12. [12]

    Revealing key structural features hidden in liquids and glasses.Nature Reviews Physics, 1(5):333–348, 2019

    Hajime Tanaka, Hua Tong, Rui Shi, and John Russo. Revealing key structural features hidden in liquids and glasses.Nature Reviews Physics, 1(5):333–348, 2019

    2019

  13. [13]

    Infinitely rugged intra-cage potential energy landscape in metallic glasses caused by many-body interaction.Materials Today Physics, 49:101582, 2024

    Haoyu Li, Hongyi Xiao, Takeshi Egami, and Yue Fan. Infinitely rugged intra-cage potential energy landscape in metallic glasses caused by many-body interaction.Materials Today Physics, 49:101582, 2024

    2024

  14. [14]

    Generalized neural-network representation of high-dimensional potential- energy surfaces.Physical review letters, 98(14):146401, 2007

    Jörg Behler and Michele Parrinello. Generalized neural-network representation of high-dimensional potential- energy surfaces.Physical review letters, 98(14):146401, 2007

    2007

  15. [15]

    On representing chemical environments.Physical Review B—Condensed Matter and Materials Physics, 87(18):184115, 2013

    Albert P Bartók, Risi Kondor, and Gábor Csányi. On representing chemical environments.Physical Review B—Condensed Matter and Materials Physics, 87(18):184115, 2013

    2013

  16. [16]

    Atomic cluster expansion for accurate and transferable interatomic potentials.Physical Review B, 99(1):014104, 2019

    Ralf Drautz. Atomic cluster expansion for accurate and transferable interatomic potentials.Physical Review B, 99(1):014104, 2019. 21

    2019

  17. [17]

    Physics- inspired structural representations for molecules and materials.Chemical Reviews, 121(16):9759–9815, 2021

    Felix Musil, Andrea Grisafi, Albert P Bartók, Christoph Ortner, Gábor Csányi, and Michele Ceriotti. Physics- inspired structural representations for molecules and materials.Chemical Reviews, 121(16):9759–9815, 2021

    2021

  18. [18]

    Schnet–a deep learning architecture for molecules and materials.The Journal of chemical physics, 148(24), 2018

    Kristof T Schütt, Huziel E Sauceda, P-J Kindermans, Alexandre Tkatchenko, and K-R Müller. Schnet–a deep learning architecture for molecules and materials.The Journal of chemical physics, 148(24), 2018

    2018

  19. [19]

    Mace: Higherorderequivariant message passing neural networks for fast and accurate force fields.Advances in neural information processing systems, 35:11423–11436, 2022

    IlyesBatatia,DavidPKovacs,GregorSimm,ChristophOrtner,andGáborCsányi. Mace: Higherorderequivariant message passing neural networks for fast and accurate force fields.Advances in neural information processing systems, 35:11423–11436, 2022

    2022

  20. [20]

    E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.Nature communications, 13(1):2453, 2022

    Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E Smidt, and Boris Kozinsky. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.Nature communications, 13(1):2453, 2022

    2022

  21. [21]

    Learning local equivariant representations for large-scale atomistic dynamics.Nature Communications, 14(1):579, 2023

    Albert Musaelian, Simon Batzner, Anders Johansson, Lixin Sun, Cameron J Owen, Mordechai Kornbluth, and Boris Kozinsky. Learning local equivariant representations for large-scale atomistic dynamics.Nature Communications, 14(1):579, 2023

    2023

  22. [22]

    Viscous liquids and the glass transition: a potential energy barrier picture.The Journal of Chemical Physics, 51(9):3728–3739, 1969

    Martin Goldstein. Viscous liquids and the glass transition: a potential energy barrier picture.The Journal of Chemical Physics, 51(9):3728–3739, 1969

    1969

  23. [23]

    What does the potential energy landscape tell us about the dynamics<? format?> of supercooled liquids and glasses?Physical review letters, 91(23):235501, 2003

    Burkhard Doliwa and Andreas Heuer. What does the potential energy landscape tell us about the dynamics<? format?> of supercooled liquids and glasses?Physical review letters, 91(23):235501, 2003

    2003

  24. [24]

    Supercooled liquids and the glass transition.Nature, 410(6825):259– 267, 2001

    Pablo G Debenedetti and Frank H Stillinger. Supercooled liquids and the glass transition.Nature, 410(6825):259– 267, 2001

    2001

  25. [25]

    Relaxationdynamics in the energy landscape of glass-forming liquids.Physical Review X, 12(2):021001, 2022

    YoshihikoNishikawa,MisakiOzawa,AtsushiIkeda,PinakiChaudhuri,andLudovicBerthier. Relaxationdynamics in the energy landscape of glass-forming liquids.Physical Review X, 12(2):021001, 2022

    2022

  26. [26]

    Modern computational studies of the glass transition.Nature Reviews Physics, 5(2):102–116, 2023

    Ludovic Berthier and David R Reichman. Modern computational studies of the glass transition.Nature Reviews Physics, 5(2):102–116, 2023

    2023

  27. [27]

    Local vs

    Massimo Pica Ciamarra, Wencheng Ji, and Matthieu Wyart. Local vs. cooperative: Unraveling glass transition mechanisms with seer.Proceedings of the National Academy of Sciences, 121(22):e2400611121, 2024

    2024

  28. [28]

    How thermally activated deformation starts in metallic glass

    Yue Fan, Takuya Iwashita, and Takeshi Egami. How thermally activated deformation starts in metallic glass. Nature communications, 5(1):5083, 2014

    2014

  29. [29]

    KumpeiShiraishi,HideyukiMizuno,andAtsushiIkeda.Johari–goldstein 𝛽relaxationinglassydynamicsoriginates from two-scale energy landscape.Proceedings of the National Academy of Sciences, 120(14):e2215153120, 2023

    2023

  30. [30]

    Theroleofexcitationsinsupercooledliquids: Density, geometry, and relaxation dynamics.Proceedings of the National Academy of Sciences, 122(11):e2416800122, 2025

    WenchengJi,MassimoPicaCiamarra,andMatthieuWyart. Theroleofexcitationsinsupercooledliquids: Density, geometry, and relaxation dynamics.Proceedings of the National Academy of Sciences, 122(11):e2416800122, 2025

    2025

  31. [31]

    Development of a neuroevolution machine learning potential of pd-cu-ni-p alloys.Materials & Design, 231:112012, 2023

    Rui Zhao, Shucheng Wang, Zhuangzhuang Kong, Yunlei Xu, Kuan Fu, Ping Peng, and Cuilan Wu. Development of a neuroevolution machine learning potential of pd-cu-ni-p alloys.Materials & Design, 231:112012, 2023. 22

    2023

  32. [32]

    Recent advances in metallic glasses.arXiv preprint arXiv:2512.16590, 2025

    Silvia Bonfanti, Ralf Busch, Jesper Byggmästar, Jeppe C Dyre, Jürgen Eckert, Spencer Fajardo, Michael L Falk, Isabella Gallino, Jamie J Kruzic, Jiayin Lu, et al. Recent advances in metallic glasses.arXiv preprint arXiv:2512.16590, 2025

    work page arXiv 2025

  33. [33]

    Anisotropic self-assembly of spherical polymer-grafted nanoparticles.Nature materials, 8(4):354–359, 2009

    Pinar Akcora, Hongjun Liu, Sanat K Kumar, Joseph Moll, Yu Li, Brian C Benicewicz, Linda S Schadler, Devrim Acehan, Athanassios Z Panagiotopoulos, Victor Pryamitsyn, et al. Anisotropic self-assembly of spherical polymer-grafted nanoparticles.Nature materials, 8(4):354–359, 2009

    2009

  34. [34]

    Nanocomposites with polymer grafted nanoparticles.Macromolecules, 46(9):3199–3214, 2013

    Sanat K Kumar, Nicolas Jouault, Brian Benicewicz, and Tony Neely. Nanocomposites with polymer grafted nanoparticles.Macromolecules, 46(9):3199–3214, 2013

    2013

  35. [35]

    A generalized machine- learning framework for developing alchemical many-body interaction models for polymer-grafted nanoparticles

    Melody Yiyuan Zhang, Shih-Kuang Alex Lee, Sharon C Glotzer, and Rebecca K Lindsey. A generalized machine- learning framework for developing alchemical many-body interaction models for polymer-grafted nanoparticles. Journal of Chemical Theory and Computation, 21(19):9853–9867, 2025

    2025

  36. [36]

    Modeling theanisotropicself-assemblyofsphericalpolymer-graftednanoparticles.TheJournalofchemicalphysics,131(22), 2009

    VictorPryamtisyn, VenkatGanesan, AthanassiosZPanagiotopoulos, HongjunLiu, andSanatKKumar. Modeling theanisotropicself-assemblyofsphericalpolymer-graftednanoparticles.TheJournalofchemicalphysics,131(22), 2009

    2009

  37. [37]

    Anisotropic three-particle interactions between spherical polymer-grafted nanoparticles in a polymer matrix.Macromolecules, 50(3):1167–1183, 2017

    Tsung-Yeh Tang and Gaurav Arya. Anisotropic three-particle interactions between spherical polymer-grafted nanoparticles in a polymer matrix.Macromolecules, 50(3):1167–1183, 2017

    2017

  38. [38]

    Many-bodypotentialfor simulating the self-assembly of polymer-grafted nanoparticles in a polymer matrix.npj Computational Materials, 9(1):224, 2023

    YilongZhou,SigbjørnLølandBore,AndreaRTao,FrancescoPaesani,andGauravArya. Many-bodypotentialfor simulating the self-assembly of polymer-grafted nanoparticles in a polymer matrix.npj Computational Materials, 9(1):224, 2023

    2023

  39. [39]

    Structural transitions of solvent-free oligomer-grafted nanoparticles.Physical review letters, 107(10):105503, 2011

    Alexandros Chremos and Athanassios Z Panagiotopoulos. Structural transitions of solvent-free oligomer-grafted nanoparticles.Physical review letters, 107(10):105503, 2011

    2011

  40. [40]

    Self-assembly of polymer-grafted nanoparticles in solvent-free conditions.Soft Matter, 12(47):9527–9537, 2016

    Alexandros Chremos and Jack F Douglas. Self-assembly of polymer-grafted nanoparticles in solvent-free conditions.Soft Matter, 12(47):9527–9537, 2016

    2016

  41. [41]

    Linking the rheology of thermal amorphous materials to molecular-scale physics.Journal of Fluid Mechanics, 1027:A32, 2026

    Mehryar Jannesari Ghomsheh, Anubhab Roy, Donald L Koch, and Sarah Hormozi. Linking the rheology of thermal amorphous materials to molecular-scale physics.Journal of Fluid Mechanics, 1027:A32, 2026

    2026

  42. [42]

    Strain-accelerated dynamics of soft colloidal glasses.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 83(4):041402, 2011

    Praveen Agarwal and Lynden A Archer. Strain-accelerated dynamics of soft colloidal glasses.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 83(4):041402, 2011

    2011

  43. [43]

    Microscopic origins of caging and equilibration of self-suspended hairy nanoparticles.Macromolecules, 52(21):8187–8196, 2019

    Xiaotun Liu, Brooks A Abel, Qing Zhao, Shuke Li, Snehashis Choudhury, Jingxu Zheng, and Lynden A Archer. Microscopic origins of caging and equilibration of self-suspended hairy nanoparticles.Macromolecules, 52(21):8187–8196, 2019

    2019

  44. [44]

    The ages in a self-suspended nanoparticle liquid.Nano letters, 10(1):111–115, 2010

    Praveen Agarwal, Haibo Qi, and Lynden A Archer. The ages in a self-suspended nanoparticle liquid.Nano letters, 10(1):111–115, 2010

    2010

  45. [45]

    Crowded, confined, and frustrated: dynamics of molecules tethered to nanoparticles.Physical review letters, 109(25):258301, 2012

    Praveen Agarwal, Sung A Kim, and Lynden A Archer. Crowded, confined, and frustrated: dynamics of molecules tethered to nanoparticles.Physical review letters, 109(25):258301, 2012

    2012

  46. [46]

    Self-suspended suspensions of covalently grafted hairy nanoparticles.Langmuir, 31(10):3222–3231, 2015

    Snehashis Choudhury, Akanksha Agrawal, Sung A Kim, and Lynden A Archer. Self-suspended suspensions of covalently grafted hairy nanoparticles.Langmuir, 31(10):3222–3231, 2015. 23

    2015

  47. [47]

    Hyperdiffusive dynamics in newtonian nanoparticle fluids.ACS Macro Letters, 4(10):1149–1153, 2015

    SamanvayaSrivastava,PraveenAgarwal,RahulMangal,DonaldLKoch,SureshNarayanan,andLyndenAArcher. Hyperdiffusive dynamics in newtonian nanoparticle fluids.ACS Macro Letters, 4(10):1149–1153, 2015

    2015

  48. [48]

    Dynamics and rheology of soft colloidal glasses.ACS Macro Letters, 4(1):119–123, 2015

    Yu Ho Wen, Jennifer L Schaefer, and Lynden A Archer. Dynamics and rheology of soft colloidal glasses.ACS Macro Letters, 4(1):119–123, 2015

    2015

  49. [49]

    Universal polymeric-to-colloidal transition in melts of hairy nanoparticles.ACS nano, 15(10):16697–16708, 2021

    Daniele Parisi, Eileen Buenning, Nikolaos Kalafatakis, Leo Gury, Brian C Benicewicz, Mario Gauthier, Michel Cloitre, Michael Rubinstein, Sanat K Kumar, and Dimitris Vlassopoulos. Universal polymeric-to-colloidal transition in melts of hairy nanoparticles.ACS nano, 15(10):16697–16708, 2021

    2021

  50. [50]

    Structure of solvent-free nanoparticle- organic hybrid materials.Langmuir, 26(22):16801–16811, 2010

    Hsiu-Yu Yu and Donald L Koch. Structure of solvent-free nanoparticle- organic hybrid materials.Langmuir, 26(22):16801–16811, 2010

    2010

  51. [51]

    Structurefactorofblendsofsolvent-free nanoparticle–organic hybrid materials: density-functional theory and small angle x-ray scattering.Soft Matter, 10(45):9120–9135, 2014

    Hsiu-YuYu,SamanvayaSrivastava,LyndenAArcher,andDonaldLKoch. Structurefactorofblendsofsolvent-free nanoparticle–organic hybrid materials: density-functional theory and small angle x-ray scattering.Soft Matter, 10(45):9120–9135, 2014

    2014

  52. [52]

    Self-suspended polymer grafted nanoparticles.Current opinion in chemical engineering, 16:92–101, 2017

    Samanvaya Srivastava, Snehashis Choudhury, Akanksha Agrawal, and Lynden A Archer. Self-suspended polymer grafted nanoparticles.Current opinion in chemical engineering, 16:92–101, 2017

    2017

  53. [53]

    Structure of solvent-free grafted nanoparticles: Molecular dynamics and density-functional theory.The Journal of chemical physics, 135(11), 2011

    Alexandros Chremos, Athanassios Z Panagiotopoulos, Hsiu-Yu Yu, and Donald L Koch. Structure of solvent-free grafted nanoparticles: Molecular dynamics and density-functional theory.The Journal of chemical physics, 135(11), 2011

    2011

  54. [54]

    Cambridge university press, 2020

    Richard M Martin.Electronic structure: basic theory and practical methods. Cambridge university press, 2020

    2020

  55. [55]

    The design space of e (3)-equivariant atom-centred interatomic potentials.Nature Machine Intelligence, 7(1):56–67, 2025

    Ilyes Batatia, Simon Batzner, Dávid Péter Kovács, Albert Musaelian, Gregor NC Simm, Ralf Drautz, Christoph Ortner, Boris Kozinsky, and Gábor Csányi. The design space of e (3)-equivariant atom-centred interatomic potentials.Nature Machine Intelligence, 7(1):56–67, 2025

    2025

  56. [56]

    Particlelocalizationandhyperuniformityofpolymer-graftednanoparticle materials.Annalen der Physik, 529(5):1600342, 2017

    AlexandrosChremosandJackFDouglas. Particlelocalizationandhyperuniformityofpolymer-graftednanoparticle materials.Annalen der Physik, 529(5):1600342, 2017

    2017

  57. [57]

    Bond-orientational order inliquids andglasses.Physical Review B, 28(2):784, 1983

    PaulJ Steinhardt, David RNelson, and MarcoRonchetti. Bond-orientational order inliquids andglasses.Physical Review B, 28(2):784, 1983

    1983

  58. [58]

    Accurate determination of crystal structures based on averaged local bond order parameters.The Journal of chemical physics, 129(11), 2008

    Wolfgang Lechner and Christoph Dellago. Accurate determination of crystal structures based on averaged local bond order parameters.The Journal of chemical physics, 129(11), 2008

    2008

  59. [59]

    Real-space structure of colloidal hard-sphere glasses.Science, 270(5239):1177–1179, 1995

    Alfons Van Blaaderen and Pierre Wiltzius. Real-space structure of colloidal hard-sphere glasses.Science, 270(5239):1177–1179, 1995

    1995

  60. [60]

    Roles of icosahedral and crystal-like order in the hard spheres glass transition.Nature communications, 3(1):974, 2012

    Mathieu Leocmach and Hajime Tanaka. Roles of icosahedral and crystal-like order in the hard spheres glass transition.Nature communications, 3(1):974, 2012

    2012

  61. [61]

    Emergence and persistence of flow inhomogeneities in the yielding and fluidization of dense soft solids.Physical Review E, 102(1):010604, 2020

    Vishwas Venkatesh Vasisht, Gabrielle Roberts, and Emanuela Del Gado. Emergence and persistence of flow inhomogeneities in the yielding and fluidization of dense soft solids.Physical Review E, 102(1):010604, 2020

    2020

  62. [62]

    Memory of shear flow in soft jammed materials.PNAS nexus, 3(10):pgae441, 2024

    HA Vinutha, Manon Marchand, Marco Caggioni, Vishwas V Vasisht, Emanuela Del Gado, and Veronique Trappe. Memory of shear flow in soft jammed materials.PNAS nexus, 3(10):pgae441, 2024. 24

    2024

  63. [63]

    Observation of five-fold local symmetry in liquid lead.Nature, 408(6814):839–841, 2000

    H Reichert, O Klein, H Dosch, M Denk, V Honkimäki, T Lippmann, and G Reiter. Observation of five-fold local symmetry in liquid lead.Nature, 408(6814):839–841, 2000

    2000

  64. [64]

    Is there icosahedral ordering in liquid and undercooled metals?Physical review letters, 91(13):135505, 2003

    Andrea Di Cicco, Angela Trapananti, Silena Faggioni, and Adriano Filipponi. Is there icosahedral ordering in liquid and undercooled metals?Physical review letters, 91(13):135505, 2003

    2003

  65. [65]

    Supercooling of liquids.Proceedings of the Royal Society of London

    Frederick Charles Frank. Supercooling of liquids.Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 215(1120):43–46, 1952

    1952

  66. [66]

    Five-fold symmetry in liquids.Nature, 408(6814):781–782, 2000

    Frans Spaepen. Five-fold symmetry in liquids.Nature, 408(6814):781–782, 2000

    2000

  67. [67]

    Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement.Nature materials, 14(1):56–60, 2015

    Bart De Nijs, Simone Dussi, Frank Smallenburg, Johannes D Meeldijk, Dirk J Groenendijk, Laura Filion, Arnout Imhof, Alfons Van Blaaderen, and Marjolein Dijkstra. Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement.Nature materials, 14(1):56–60, 2015

    2015

  68. [68]

    Clustersofpolyhedra in spherical confinement.Proceedings of the National Academy of Sciences, 113(6):E669–E678, 2016

    ErinGTeich,GregVanAnders,DaphneKlotsa,JuliaDshemuchadse,andSharonCGlotzer. Clustersofpolyhedra in spherical confinement.Proceedings of the National Academy of Sciences, 113(6):E669–E678, 2016

    2016

  69. [69]

    Dynamics and yielding of binary self-suspended nanoparticle fluids.Soft Matter, 11(26):5224–5234, 2015

    Akanksha Agrawal, Hsiu-Yu Yu, Samanvaya Srivastava, Snehashis Choudhury, Suresh Narayanan, and Lynden A Archer. Dynamics and yielding of binary self-suspended nanoparticle fluids.Soft Matter, 11(26):5224–5234, 2015

    2015

  70. [70]

    Unveiling the predictive power of static structure in glassy systems.Nature physics, 16(4):448–454, 2020

    Victor Bapst, Thomas Keck, A Grabska-Barwińska, Craig Donner, Ekin Dogus Cubuk, Samuel S Schoenholz, Annette Obika, Alexander WR Nelson, Trevor Back, Demis Hassabis, et al. Unveiling the predictive power of static structure in glassy systems.Nature physics, 16(4):448–454, 2020

    2020

  71. [71]

    Roadmap on machine learning glassy dynamics.Nature Reviews Physics, 7(2):91–104, 2025

    Gerhard Jung, Rinske M Alkemade, Victor Bapst, Daniele Coslovich, Laura Filion, François P Landes, Andrea J Liu, Francesco Saverio Pezzicoli, Hayato Shiba, Giovanni Volpe, et al. Roadmap on machine learning glassy dynamics.Nature Reviews Physics, 7(2):91–104, 2025

    2025

  72. [72]

    Machine learning many-body potentials for colloidal systems.The Journal of Chemical Physics, 155(17), 2021

    Gerardo Campos-Villalobos, Emanuele Boattini, Laura Filion, and Marjolein Dijkstra. Machine learning many-body potentials for colloidal systems.The Journal of Chemical Physics, 155(17), 2021

    2021

  73. [73]

    Coarse-grained many-body potentials of ligand-stabilized nanoparticles from machine-learned mean forces.ACS nano, 17(23):23391–23404, 2023

    Giuliana Giunta, Gerardo Campos-Villalobos, and Marjolein Dijkstra. Coarse-grained many-body potentials of ligand-stabilized nanoparticles from machine-learned mean forces.ACS nano, 17(23):23391–23404, 2023

    2023

  74. [74]

    Machine-learned coarse- grained potentials for particles with anisotropic shapes and interactions.npj Computational Materials, 10(1):228, 2024

    Gerardo Campos-Villalobos, Rodolfo Subert, Giuliana Giunta, and Marjolein Dijkstra. Machine-learned coarse- grained potentials for particles with anisotropic shapes and interactions.npj Computational Materials, 10(1):228, 2024

    2024

  75. [75]

    Machine learning short-ranged many-body interactions in colloidal systems using descriptors based on voronoi cells.The Journal of chemical physics, 162(23), 2025

    Rinske M Alkemade, Rastko Sknepnek, Frank Smallenburg, and Laura Filion. Machine learning short-ranged many-body interactions in colloidal systems using descriptors based on voronoi cells.The Journal of chemical physics, 162(23), 2025

    2025

  76. [76]

    From predictive modelling to machine learning and reverse engineering of colloidal self-assembly.Nature materials, 20(6):762–773, 2021

    Marjolein Dijkstra and Erik Luijten. From predictive modelling to machine learning and reverse engineering of colloidal self-assembly.Nature materials, 20(6):762–773, 2021

    2021

  77. [77]

    Equation of state for the lennard–jones fluid based on the perturbation theory.Fluid phase equilibria, 264(1-2):174–183, 2008

    FF Betancourt-Cárdenas, LA Galicia-Luna, and SI Sandler. Equation of state for the lennard–jones fluid based on the perturbation theory.Fluid phase equilibria, 264(1-2):174–183, 2008. 25

    2008

  78. [78]

    Adsorption of chain molecules with a polar head a scaling description.Journal De Physique, 38(8):983–987, 1977

    S Alexander. Adsorption of chain molecules with a polar head a scaling description.Journal De Physique, 38(8):983–987, 1977

    1977

  79. [79]

    Conformations of polymers attached to an interface.Macromolecules, 13(5):1069–1075, 1980

    PrG de Gennes. Conformations of polymers attached to an interface.Macromolecules, 13(5):1069–1075, 1980

    1980

  80. [80]

    Courier Corporation, 2003

    Thomas JR Hughes.The finite element method: linear static and dynamic finite element analysis. Courier Corporation, 2003

    2003

Showing first 80 references.