Fahime Seyedheydari

Fahime Seyedheydari, Kevin Conley, Simo Särkkä

We present a probabilistic, data-driven surrogate model for predicting the radiative properties of nanoparticle embedded scattering media. The model uses conditional normalizing flows, which learn the conditional distribution of optical outputs, including reflectance, absorbance, and transmittance, given input parameters such as the absorption coefficient, scattering coefficient, anisotropy factor, and particle size distribution. We generate training data using Monte Carlo radiative transfer simulations, with optical properties derived from Mie theory. Unlike conventional neural networks, the conditional normalizing flow model yields full posterior predictive distributions, enabling both accurate forecasts and principled uncertainty quantification. Our results demonstrate that this model achieves high predictive accuracy and reliable uncertainty estimates, establishing it as a powerful and efficient surrogate for radiative transfer simulations.

Fahime Seyedheydari, Mahdi Nasiri, Marcin Mińkowski et al.

In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly formulated as a Fredholm integral equation of the first kind, an ill-posed inverse problem characterized by instability due to measurement noise and limited data. To address this, we use a Gaussian process prior to regularize the solution and integrate a normalization constraint into the Gaussian process via two approaches: by constraining the Gaussian process using a pseudo-measurement and by using Lagrange multipliers in the equivalent optimization problem. To improve computational efficiency, we employ a spectral expansion of the covariance kernel using eigenfunctions of the Laplace operator, resulting in a computationally tractable low-rank representation without sacrificing accuracy. Additionally, we investigate two complementary strategies for hyperparameter estimation: a data-driven approach based on maximizing the unconstrained log marginal likelihood, and an alternative approach where the physical constraints are taken into account. Numerical experiments demonstrate that the proposed constrained Gaussian process regression framework accurately reconstructs particle size distributions, producing numerically stable, smooth, and physically interpretable results. This methodology provides a principled and efficient solution for addressing inverse scattering problems and related ill-posed integral equations.