The unique orthogonal shapes of structured light beams have attracted researchers to use as information carriers. Structured light-based free space optical communication is subject to atmospheric propagation effects such as rain, fog, and rain, which complicate the mode demultiplexing process using conventional technology. In this context, we experimentally investigate the detection of Laguerre Gaussian and Hermite Gaussian beams under dust storm conditions using machine learning algorithms. Different algorithms are employed to detect various structured light encoding schemes including the use of a convolutional neural network (CNN), support vector machine, and k-nearest neighbor. We report an identification accuracy of 99% under a visibility level of 9 m. The CNN approach is further used to estimate the visibility range of a dusty communication channel.