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Recent advances in applying Graph Neural Networks (GNNs) to molecular science have showcased the power of learning three-dimensional (3D) structure representations with GNNs. However, most existing GNNs suffer from the limitations of insufficient modeling of diverse interactions, computational expensive operations, and ignorance of vectorial values. Here, we tackle these limitations by proposing a novel GNN model, Physics-aware Multiplex Graph Neural Network (PaxNet), to efficiently and accurately learn the representations of 3D molecules for both small organic compounds and macromolecule complexes. PaxNet separates the modeling of local and non-local interactions inspired by molecular mechanics, and reduces the expensive angle-related computations. Besides scalar properties, PaxNet can also predict vectorial properties by learning an associated vector for each atom. To evaluate the performance of PaxNet, we compare it with state-of-the-art baselines in two tasks. On small molecule dataset for predicting quantum chemical properties, PaxNet reduces the prediction error by 15% and uses 73% less memory than the best baseline. On macromolecule dataset for predicting protein-ligand binding affinities, PaxNet outperforms the best baseline while reducing the memory consumption by 33% and the inference time by 85%. Thus, PaxNet provides a universal, robust and accurate method for large-scale machine learning of molecules. Our code is available at https://github.com/zetayue/Physics-aware-Multiplex-GNN.