Closed-Loop Multiscale Bayesian Design of Defect-Engineered Monolayer Graphene

  • Bo, Jingkai (Institute of Science Tokyo)
  • Lei, Xiao-Wen (Institute of Science Tokyo)
  • Lu, Tong (Institute of Science Tokyo)
  • Fujii, Toshiyuki (Institute of Science Tokyo)

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Defect engineering in monolayer graphene offers a route to tailor stiffness, bending rigidity, and toughness, yet rational design is hindered by costly atomistic sampling, limited time scales accessible to molecular dynamics, and the gap between atomistic and continuum descriptions. We develop a closed-loop multiscale workflow that couples (i) molecular dynamics-based defect insertion and relaxation, (ii) adaptive Voronoi mapping to an extended phase-field crystal model for long-time thermodynamic reconstruction of defect networks, and (iii) back-mapping for atomistically resolved property extraction—thus explicitly bridging atomistic defect physics and continuum-scale evolution (Figure 1). Compared with energy-minimised configurations, extended phase-field crystal reconstruction stabilises defect-network states that molecular dynamics alone cannot access, revealing migration and coalescence pathways that govern mechanical response. Bayesian multi-objective optimisation, using Gaussian-process surrogates and expected hypervolume improvement, explores a design space spanned by total defect density and the relative fractions of Stone–Wales, divacancy, and disclination-dipole defects, initialised via Latin hypercube sampling. Across a curated library of reconstructed monolayer graphene, the workflow spans broad regimes of stiffness, bending rigidity, and toughness with far fewer high-fidelity evaluations than brute-force screening. The resulting Pareto set indicates that Stone–Wales-rich designs maximise stiffness, mixed Stone–Wales/disclination-dipole populations enhance toughness, and controlled divacancy content tunes bending response. Hypervolume gains plateau early, providing a practical stopping rule for expensive multiscale evaluations. Overall, thermodynamic defect reconstruction—rather than static defect placement—sets achievable property trade-offs in defect-engineered graphene, providing a transferable atomistic-to-continuum strategy for scale bridging in two-dimensional solids.