glitterin: Towards Replacing the Role of Lorenz-Mie Theory in Astronomy Using Neural Networks Trained on Light Scattering of Irregularly Shaped Grains

TL;DR

This work tackles the mismatch between spherical grain modeling with Lorenz-Mie theory and the reality of irregular dust grains in astrophysical environments. It trains glitterin, a set of eight neural networks, on extensive DDA-based scattering data for irregular grains across a broad range of size parameters $x_{ ext{enc}}$ and complex refractive indices $m=n+ik$, to predict $C_{ ext{ext}}$, $C_{ ext{abs}}$, and scattering-matrix elements $Z_{ij}$ with millisecond speed. Glitterin consistently outperforms linear interpolation in accuracy and generalizes to unseen parameter regions, achieving substantial speedups (up to ~$10^{10}$) while maintaining ~5–10% level fidelity in many cases, and aligns well with laboratory measurements for feldspar and hematite. The model reveals meaningful morphology-driven differences in cross sections and polarization, particularly at millimeter wavelengths, with significant implications for debris-disk and protoplanetary-disk dust inferences. The authors provide public access to the training data and model, offering a practical path toward incorporating realistic grain morphologies into radiative transfer and emission analyses.

Abstract

Light scattering by dust particles is often modeled assuming the dust is spherical for numerical simplicity and speed. However, real dust particles have highly irregular morphologies that significantly affect their scattering properties. We have developed glitterin, a neural network trained to predict light scattering from irregularly shaped dust grains, offering a computationally efficient alternative to Lorenz-Mie theory. We computed scattering properties using the Discrete Dipole Approximation code ADDA for irregularly shaped particles across size parameters x from 0.1 to 65, covering a range in complex refractive index m that includes astrosilicates, pyroxene, enstatite, water-ice, etc. The neural network operates at millisecond timescales while maintaining superior accuracy compared to linear interpolation. Irregular grains exhibit x-dependent deviations from spherical predictions. At small x, cross-sections approach volume-equivalent spheres for low m. At large x, irregular grains show enhanced cross-sections due to greater geometric extension. Increasing m also enhances the absorption cross-section relative to the volume-equivalent spheres. This differential x and m dependence creates mid-IR solid-state features distinct from predictions from spherical grains. Validation against laboratory measurements of forsterite and hematite demonstrates that our neural network captures both qualitative and quantitative behaviors more accurately than spherical models. Millimeter-wavelength applications reveal that spherical grains produce opposite polarization signatures compared to irregular grains, potentially relaxing stringent ~100um grain size constraints in protoplanetary disks. glitterin is publicly available and alleviates the computational barriers to incorporating emission and scattering of realistic grain morphologies.

Figures (12)

• Figure 1: Visualization of six different irregular particles with $n_{\text{lat}}=256$ as a demonstration.
• Figure 2: Refractive indices for a few reference compositions in comparison to the coverage in $n$ (horizontal axis) and $k$ (vertical axis) for different datasets (see Table \ref{['tab:dataset_description']} for details). Each composition covers a different wavelength range. "Draine Silicates" refers to the astrosilicates from Draine2003ARAA..41..241D covering from 0.6 $\mu$m to 400 $\mu$m. "Olivine" refers to crystalline San Carlos olivine at 300 K along the $z$-axis covering 6.7 $\mu$m to 50 $\mu$m Zeidler2015ApJ...798..125Z. "Carbon" is the amorphous carbon from Zubko1996MNRAS.282.1321Z from 0.1 $\mu$m to 50 $\mu$m. "Water Ice" corresponds to water ice from Warren2008JGRD..11314220W. "DSHARP" is the composition from Birnstiel2018ApJ...869L..45B shown from 0.1 $\mu$m to 9 mm. The vertical and horizontal gray lines mark $n=1$ and $k=1$, respectively.
• Figure 3: Predictions of the neural network (green) and linear interpolation (orange) against the test data. The neural network clearly outperforms the linear interpolation in accuracy. The horizontal axes show the true value and the vertical axes are the corresponding predicted values. The dashed black lines show the ideal case of perfect prediction. The text in each panel shows the performance of the neural network and linear interpolation, where $R^{2}$, $L$, RMSE, and $N$ refer to the coefficient of determination, the value of the loss function (Eq. \ref{['eq:loss_function']}), the root mean squared error, and the number of points used for the assessment.
• Figure 4: Extinction and absorption efficiencies and the albedo as a function of $x_{\text{vol}}$ for irregularly shaped grains and spherical grains of the same volume and refractive index $m=1.7+0.01i$. Panels a and d: The exinction efficiencies $Q_{\text{ext}}^{\text{vol}}$ and $Q_{\text{ext}}^{\text{pja}}$ (see Eq. \ref{['eq:C_eq_Q_pi_r2']}). The values for spheres are the same in both panels. Panels b and e: The absorption efficiencies $Q_{\text{abs}}^{\text{vol}}$ and $Q_{\text{abs}}^{\text{pja}}$. We additionally show estimates from MANTA-Ray in panel b where $Q_{\text{abs}}^{\text{vol}}$ is available. The shaded region shows $20\%$ error. Panels c and f: The albedo $\omega$ and $\epsilon$. For each panel, the green solid lines are predictions from the neural network. The dotted points are independent DDA calculations that the neural network never trained on. The datapoint of the largest grain we could simulate has $x_{\text{enc}}=90$ ($x_{\text{vol}} \sim 56$). The orange lines are calculations from Lorenz-Mie theory. The top axes show $x_{\text{enc}}$ for the irregularly shaped grains. The left and right regions are shaded to show the minimum and maximum $x_{\text{enc}}$ of the training data for the neural network at $m=1.7+0.01i$. We show predictions of the neural network beyond this range to visualize how well it generalizes to size parameters beyond its training data.
• Figure 5: The extinction efficiency and absorption efficiencies, and the albedo as a function of $x_{\text{vol}}$ for $m=2.5+1i$. The figure is plotted in the same way as Fig. \ref{['fig:plot_x_2']}. Panel b shows that irregularly shaped grains have a larger absorption cross-section than a sphere having the same material volume in the small grain regime ($x_{\text{vol}}<1$) and large grain regime ($x_{\text{vol}}>10$).