Neural-PDE modeling of reaction-diffusion using time-series imaging for sub-diffraction-limit 3D lithography

Two-color projection micro-stereolithography (PμSL) is an advanced additive manufacturing technique that enables rapid and continuous 3D printing. This method uses two distinct wavelengths of light to independently control photoinitiation and photoinhibition of polymerization in a photocurable resin, achieved by selecting a photoinitiator and photoinhibitor with complementary absorption spectra, enabling high-precision, continuous printing compatible with viscous resins. PμSL has significant potential in applications such as the fabrication of optical diffractive neural networks (D2NNs), which require sophisticated three-dimensional photonic structures capable of optical computation. However, achieving high-precision 3D printing with PμSL remains challenging due to limitations in current inspection and modeling techniques. The photochemical processes involved in photopolymerization are highly complex, with unknown local interactions among different species and non-local diffusion effects arising from spatial concentration differences in the reaction region. Accurate modeling of this lithography process is necessary for inverse design to fabricate precise sub-diffraction-limit polymer features. In this study, we develop a dynamic model for the polymerization process during 3D printing. We first establish a local generalized Lotka-Volterra system with parameters estimated from Fourier Transform Infrared Spectroscopy (FT-IR) measurements. We then extend this system to a reaction-diffusion model with unknown diffusion coefficients. To address residuals not captured by the symbolic models, we incorporate a neural network as a universal function approximator. Simulation results align closely with imaging measurements, and further analysis demonstrates improved generalization when additional physical priors are applied to the diffusion coefficients.