To repair noisy or partially missing fluid flow data and achieve
accurate fluid dynamics
analysis,
a physics-informed variational autoencoder model is proposed. First, the
variational autoencoder is employed to learn the latent representation of fluid
flow. Second, spatiotemporal coordinate information is combined with this
latent representation, and the partial derivatives of the decoded flow field information
with respect to the spatiotemporal coordinates are obtained by automatic
differentiation technology. Finally, physical prior information of fluid
dynamics is introduced to construct a physical constraint loss term. This
ensures that the generated data conforms to both the key features of the flow
and the underlying physical laws, thereby enhancing the physical consistency
and reconstruction accuracy while providing a certain level of
interpretability. Experimental results demonstrate that the proposed model
achieves higher accuracy than existing methods in dealing with flow field noise
and data missing issues. Its effectiveness is also proven in both two-dimensional
and three-dimensional complex vortex flow fields.