The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass functional deep neural network (mfDNN) classifier as an innovative data mining and classification tool. The architecture incorporates a sparse deep neural network with Rectified Linear Unit (ReLU) activation function, minimizing cross-entropy loss in a multiclass classification framework. This design enables the utilization of modern computational tools. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. The efficacy of mfDNN is demonstrated through simulations and several benchmark datasets from different application domains.

The impairment of neural crest cells (NCCs) plays a pivotal role in the pathogenesis of fetal alcohol spectrum disorders (FASD). Epigenetic regulators mediate ethanol-induced disruptions in NCC development and represent promising targets for nutritional interventions. Here, we developed a biologically informed machine learning framework to predict nutritional supplements that modulate five key epigenetic regulators (miR-34a, DNMT3a, HDAC, miR-125b, and miR-135a) and mitigate ethanol’s adverse effects on NCCs. The optimized models demonstrated robust predictive performance and identified a number of nutritional supplements that could attenuate ethanol-induced NCC impairment, including resveratrol, vitamin B12, emodin, quercetin, and broccoli sprout-derived compounds. Our optimized models also revealed structural features that are critical for mitigating ethanol-induced NCC impairment through specific epigenetic mechanisms. These findings support predictive modeling as a tool to prioritize nutritional supplements for further investigation and the development of dietary strategies to prevent or reduce the risk of FASD.