Multiscale super-resolution reconstruction of fluid flows with deep neural networks
We present a novel multiscale super-resolution framework (SRLBM) that applies deep learning directly to the mesoscopic density distribution functions of the lattice Boltzmann method for high-fidelity flow reconstruction. Two neural network architectures, a standard convolutional neural network (CNN) and a deeper residual dense network (RDN), are trained to upscale distribution functions from coarse grids by factors of 2, 4 and 8, and then recover velocity, pressure, and vorticity from a single model. For flow past a single cylinder at $\mathrm{Re}=100$, RDN reduces the mean relative error in distribution functions by an order of magnitude compared to CNN and avoids spurious pressure oscillations and vorticity smoothing that affect interpolation and simpler networks. To examine the generalization ability, both models are trained using data from the flow past two cylinders of diameter $d$ at a spanwise distance between the centers of $1.5d$ and a Reynolds number of 200. They are then applied without retraining to wake configurations with distances ranging from $2.0d$ to $3.0d$. In these tests, the mean errors remain essentially unchanged across all distances. However, RDN consistently produces sharper shear-layer roll-ups and secondary eddies. These results demonstrate that super-resolving mesoscopic distribution functions yields richer and more transferable features than operating on macroscopic fields alone. By integrating kinetic theory with deep learning, SRLBM offers a compelling alternative for fluid flow reconstruction, enabling a single model to simultaneously recover multiple high-fidelity flow fields while substantially reducing computational cost.