<p>For partial differential equations (PDE), neural operators can learn the mapping of input and output functions in infinite dimensional Spaces by introducing kernel functions into linear transformations. latent Spectral Model (LSM) is an advanced neural operator, that does not solve PDE directly in coordinate space, but first simplifies complex high-dimensional data into a compact Latent space through hierarchical projection networks, then approximates the solution mapping through neural spectral blocks. However, LSM does not deeply extract the Latent features of PDE, nor does it fuse the different coordinate space features of PDE. To extract more effective features of PDE to improve the solution accuracy further, we propose MU-LSM: Latent spectral model based on multi-scale fusion and UNet. Unlike LSM, MU-LSM introduces UNet and multi-scale fusion in PDE solution procedure. First, when PDE is converted from coordinate space to latent space, MU-LSM extracts the smooth global features and sharp local features of PDE by UNet. Then, MU-LSM concatenates the latent features extracted by UNet with latent tokens. Finally, after the processing of all neural spectrum blocks, MU-LSM fuses the new coordinate space features and the original coordinate space features by jumping connections. The experimental results show that on three solid PDE and four fluid PDE, compared with 15 advanced PDE solvers such as DeepONet, FNO, and LSM, MU-LSM has the highest overall accuracy, with an average accuracy improvement of 7.7%.</p>