Transferable reduced order modeling of physical systems via a dilated vector quantized variational autoencoder

Reduced-order models (ROMs) are critically important for the efficient simulation of complex physical systems. However, ROM performance often degrades under out-of-training operating conditions. To overcome this challenge, we propose a transferable reduced-order modeling framework called the dilated vector-quantized variational autoencoder (DVQVAE), which is developed for compact field representation, structural analysis, and adaptation across operating conditions. By integrating multiscale convolutions with vector quantization, the DVQVAE compresses high-dimensional physical field data while retaining important spatial structures. The resulting discrete latent variables can be examined through code maps and masking tests, which provide structural information about the learned representation without assuming that each code corresponds to a unique physical mode. Furthermore, a KAN-transformer is introduced to model the nonlinear evolution of the latent variables. Validated across a series of benchmark cases in fluid dynamics and electromagnetics, our framework consistently outperforms conventional ROMs in terms of reconstruction accuracy, structural interpretability, and transfer efficiency—offering a new paradigm for efficient, structurally interpretable, and transferable ROMs. These capabilities demonstrate the potential of our method as a practical surrogate model for accelerating simulation-driven engineering tasks across diverse physical systems.