In recent years, origin-destination (OD) demand prediction has gained significant attention for its profound implications in urban development. Existing data-driven deep learning methods primarily focus on the spatial or temporal dependency between regions yet neglecting regions' fundamental functional difference. Though knowledge-driven physical methods have characterised regions' functions by their radiation and attraction capacities, these functions are defined on numerical factors like population without considering regions' intrinsic nominal attributes, e.g., a region is a residential or industrial district. Moreover, the complicated relationships between two types of capacities, e.g., the radiation capacity of a residential district in the morning will be transformed into the attraction capacity in the evening, are totally missing from physical methods. In this paper, we not only generalize the physical radiation and attraction capacities into the deep learning framework with the extended capability to fulfil regions' functions, but also present a new model that captures the relationships between two types of capacities. Specifically, we first model regions' radiation and attraction capacities using a bilateral branch network, each equipped with regions' attribute representations. We then describe the transformation relationship of different capacities of the same region using a hypergraph-based parameter generation method. We finally unveil the competition relationship of different regions with the same attraction capacity through cluster-based adversarial learning. Extensive experiments on two datasets demonstrate the consistent improvements of our method over the state-of-the-art baselines, as well as the good explainability of regions' functions using their nominal attributes.