  In this paper, we propose a robust estimator for the location function from
multi-dimensional functional data. The proposed estimators are based on the
deep neural networks with ReLU activation function. At the meanwhile, the
estimators are less susceptible to outlying observations and
model-misspecification. For any multi-dimensional functional data, we provide
the uniform convergence rates for the proposed robust deep neural networks
estimators. Simulation studies illustrate the competitive performance of the
robust deep neural network estimators on regular data and their superior
performance on data that contain anomalies. The proposed method is also applied
to analyze 2D and 3D images of patients with Alzheimer's disease obtained from
the Alzheimer Disease Neuroimaging Initiative database.
