Fast and accurate quasi-atom method for simultaneous atomistic and continuum simulation of solids

Artem Chuprov; Egor E. Nuzhin; Alexey A. Tsukanov; Nikolay V. Brilliantov

cond-mat.mtrl-sciFeb 16, 2026

Fast and accurate quasi-atom method for simultaneous atomistic and continuum simulation of solids

Authors: Artem Chuprov, Egor E. Nuzhin, Alexey A. Tsukanov, Nikolay V. Brilliantov

Organizations: Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russia · Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences B. Gruzinskaya str., 10, bld. 1, Moscow, 123242, Russia · School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK

Abstract

We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of different size, comprising composite medium. The parameters of interaction potential between the quasi-atoms are optimized to match elastic properties of the composite medium to those of the atomic one. The optimization method coincides conceptually with the online Machine Learning (ML) methods, making it computationally very efficient. Such an approach allows a straightforward application of standard software packages for molecular dynamics (MD), supplemented by the ML-based optimizer. The new method is applied to model systems with a simple, pairwise Lennard-Jones potential, as well with multi-body Tersoff potential, describing covalent bonds. Using LAMMPS software we simulate collision of particles of different size. Comparing simulation results, obtained by the novel method, with full-atomic simulations, we demonstrate its accuracy, validity and overwhelming superiority in computational speed. Furthermore, we compare our method with other hybrid methods, specifically, with the closest one -- AtC (Atomic to Continuum) method. We demonstrate a significant superiority of our approach in computational speed and implementation convenience. Finally, we discuss a possible extension of the method for modeling other phenomena.

Figures & tables

Figure 1: Illustration of two colliding multi-scale particles comprised of real atoms (black) in the critical region - the area of their contact and three different types of quasi-atoms, blue, yellow and rose, which are twice, four and eight times larger than the real atoms.

Figure 2: Main panel: The computation time dependence for inter-particle collisions, on the particle size for the original atomistic particles (blue line) and multi-scale particles: with $N=2$ types of atoms/quasi-atoms (lilac line), $N=3$ types (orange line) and $N=4$ types (green line). The original atomistic particles interact via standard Lennard-Jones potential corresponding to copper, while the potential parameters for the quasi-atoms are found by the optimization procedure. Inset: The dependence of the relative error for the target parameters, associated with the elastic constants of copper, on the iteration step of the optimization procedure for $N=4$ (see the main text).

Panel of Figure 3 — Figure 3: Comparative analysis of the collision dynamics of composite particles, comprised of atoms and quasi-atoms of three types and completely atomistic particles (full-scale MD simulations). The inter-particle force is plotted as the function of the overlap, $\xi=R_{1}+R_{2}-r_{12}$ . The radii of the particles are $R_{1}=R_{2}=75\,\text{\AA}$ , the impact velocity is $V=100\,m/s.$ The simulation time step is $\Delta t=0.1\,\mathrm{fs}$ and cutoff distance for LJ potential is $r_{cut}=2.5\,\sigma$ .

Panel of Figure 4 — Figure 4: Comparison of the collision dynamics of mesoscopic composite particles of radius $R=0.1\ \mu m$ with four types of atoms/quasi-atoms, with the prediction of theoretical models – the Hertz theory for non-adhesive contact (left) and JKR theory for the adhesive contact (right). Two types of the inter-atomic potentials are demonstrated – the pairwise Lennard-Jones potential (upper panels) and multi-atomic Tersoff potential (bottom panels). The inter-particle force is plotted as the function of the overlap (see the text for detail).

Figure 5: Computation time for equilibrium copper system at T=300 K, as a function of the system size. See the text for details.

Method	Atomistic simulation	Main phase	Open-source impl.	Comp. speed
This work (Hybrid)	✓	Solids	✓	High
Quasi-Continuum (QC)	✓	Solids	$\circ$	Med.
AtC (LAMMPS)	✓	Solids	✓	Med.
Coarse-Grained / AdResS	$\circ$	Liq./Gas	$\circ$	High
HMM	$\circ$	All (macro)	$\circ$	Case-dep.
Peridynamics	✗	Solids	✓	Med.

Table 1: Compact comparison of hybrid and mesoscale methods. Symbols: ✓ = yes; ✗ = no;

\circ

= partial/limited.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 6 — Figure 6: (a) The dependence of the loss function, $L$ , for a fixed number of points, $n=24$ , at the beginning of the optimization procedure on the number of processors (see Sec. 2.4 for more detail) and (b) relative mass deficiency $\Delta m$ as a function of particle radius $R$ for composite particles.

Computational Materials Science

Computational materials science uses computation and data-driven models to predict, explain, and design materials and their properties.

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A strategic roadmap for an atomistic machine-learning ecosystem

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Data-driven machine learning (ML) techniques have become an essential tool in many domains of science. Their application to atomistic simulations of matter is particularly widespread and impactful. This success is due largely to the existence of a well-developed and established physics-based modeling framework, ranging from first-principles electronic-structure calculations to molecular dynamics and statistical sampling, into which ML was integrated naturally to reshape long-standing trade-offs between accuracy, efficiency, and scale. Nevertheless, this integration raises both conceptual and practical challenges, from choosing between data-centric and physics-based modeling approaches to adapting established software stacks to modern hardware accelerators and ML libraries. As the field evolves rapidly, fueled in part by widespread enthusiasm but also by tangible impact, it seems appropriate to take a moment to consider the current state of the art and open challenges, and reflect on what can be done to better coordinate efforts across the community. With this goal in mind, several members of this community met in Lausanne in January 2026 at CECAM to discuss algorithms, models, software and hardware infrastructure, and the most promising scientific applications that have become possible thanks to the use of artificial intelligence in atomic-scale simulations. This strategic roadmap paper summarizes the outcomes of these discussions, suggesting some long-term goals, and some concrete actions, to establish a healthy, sustainable and impactful atomistic ML ecosystem.

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