In this study, we devise a framework for volumetrically reconstructing fluid from observable, measurable free surface motion. Our innovative method amalgamates the benefits of deep learning and conventional simulation to preserve the guiding motion and temporal coherence of the reproduced fluid. We infer surface velocities by encoding and decoding spatiotemporal features of surface sequences, and a 3D CNN is used to generate the volumetric velocity field, which is then combined with 3D labels of obstacles and boundaries. Concurrently, we employ a network to estimate the fluid's physical properties. To progressively evolve the flow field over time, we input the reconstructed velocity field and estimated parameters into the physical simulator as the initial state. Our approach yields promising results for both synthetic fluid generated by different fluid solvers and captured real fluid. The developed framework naturally lends itself to a variety of graphics applications, such as 1) effective reproductions of fluid behaviors visually congruent with the observed surface motion, and 2) physics-guided re-editing of fluid scenes. Extensive experiments affirm that our novel method surpasses state-of-the-art approaches for 3D fluid inverse modeling and animation in graphics.