Physics-based inverse modelling of dichroic glass: machine learning emulation of the lycurgus cup

The Lycurgus Cup is a fourth-century Roman cage cup that exhibits striking dichroism — appearing opaque green in reflected light and translucent red in transmission — arising from Au–Ag alloy nanoparticles embedded in soda-lime-silica glass matrix. Despite extensive analytical characterization, a quantitative computational framework linking microstructural parameters to the macroscopic dichroic appearance remains elusive. This work establishes a surrogate-assisted inverse design pipeline by integrating Mie electrodynamics, two-layer Monte Carlo photon transport, and CIEDE2000 perceptual color optimization to identify physically plausible glass compositions that reproduce the characteristic optical signature of the cup. A nine-parameter forward model incorporating nanoparticle plasmonic absorption, Fe2O3 ionic absorption, phase-separated silica droplet scattering, and heterogeneous layer structure was coupled with a Histogram-Based Gradient Boosting emulator (R2 = 0.955, spectral MAE = 0.004) trained on 2,000 Monte Carlo simulations with PCA-compressed spectral outputs. The trained emulator reduced per-evaluation cost from minutes to milliseconds, enabling exhaustive exploration of over 215,000 candidate compositions within a practical timeframe. The optimized composition (Au15Ag85 nanoparticles, diameter 83 nm, volume fraction ~ 10− 5, in 2.2 mm glass with 0.56 wt% Fe2O3) produced a red-to-green transmission ratio of 11.5 upon high-fidelity Monte Carlo validation (50,000 photons, 3 seeds averaged), with the reflected color matching the target olive-green within ΔE₀₀ = 12.0 under D65 illumination. The Pareto analysis revealed that only 0.05% of the sampled parameter space simultaneously achieved ΔE₀₀ < 15 for both transmission and reflection, quantifying the extremely narrow feasible composition window and offering insight into the historical rarity of successful dichroic glass production. The framework is applicable to the inverse design of engineered nanocomposite optical materials beyond the archaeological context.