Transmittance prediction and inverse design of resin composite based on an optical model and deep learning

This study aimed to develop an integrated framework combining an optical model with deep learning to accurately predict the spectral transmittance of resin composite and inversely solve for the geometric parameters required to achieve a target color.

Experimental silica nanofiller resin composite was synthesized. An optical model integrating Mie scattering and the Beer-Lambert law was developed and validated against measured transmittance. Key parameters, including the spectral refractive indices of all components and the intrinsic filler geometry, were precisely characterized. Subsequently, a Bidirectional Neural Network (BNN) was constructed and trained on a large-scale dataset (11,781 samples) generated by the physical model to establish bidirectional mappings between geometric parameters (filler radius r, volume fraction f_v, thickness h) and CIE L^*a^*b^* color coordinates. The inverse design performance was evaluated using the color difference (∆E_ab^*) between the target and BNN-predicted colors.

The optical model demonstrated a strong predictive capability for transmittance, with R² > 0.7 and Pearson's r > 0.95 for all specimens. The BNN achieved remarkable inverse design performance, with a maximum ∆E_ab^* of less than 0.3 across all 1200 independent test samples, significantly below the human perceptibility threshold (∆E_ab^* < 1.0).

This integrated framework offers a data-driven approach that may assist in the future design of dental restorative materials by bridging physical optics with deep learning.

An optical model combining Mie scattering and the Beer-Lambert law was developed and validated, and a BNN was constructed to enable high‑precision color prediction and inverse parameter design from target color.