Aokun Wang

Aokun Wang, Anjali Nair, Zhongjian Wang et al.

This work develops machine learning approaches to classify structured light wave beams developing random speckle disturbances as they propagate through turbulent atmospheres. Beam propagation is modeled by the numerical simulation of a stochastic paraxial equation. We design convolutional neural networks tailored for this specific application and use them for a classification model with one-hot encoding. To address the challenge of potentially limited available data, we develop a prediction-based generative diffusion model to provide additional data during classifier training. We show that a Bregman distance minimization during the learning step improves the quality of the generation of high-frequency modes.

Yingyuan Li, Aokun Wang, Zhongjian Wang

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min optimization during training and does not impose any restriction on the network structure. Theoretically we establish a weak convergence guarantee and a quantitative error bound between the learned map and the optimal transport map. Our numerical experiments validate the theoretical results and the effectiveness of the new approach, particularly on real-world tasks.