To detect differences in the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. The observations lying in each sub-area are assumed from the same population, and hypothesis test or multiple tests are used to detect the significance in each area. In my talk I will discuss a newly proposed method by using a large-scale multiple testing to find the significant sub-areas automatically in a general functional data analysis framework. A nonparametric Gaussian process regression model is introduced for simultaneous two-sided tests. The proposed procedure is asymptotically valid by controlling directional false discovery rates at any specified level. And it is computationally inexpensive and can accommodate different sampling schemes across the samples. I will also show some numerical examples including an application in an executive function research in children with Hemiplegic Cerebral Palsy.