  Data-driven deep learning has emerged as the new paradigm to model complex
physical space-time systems. These data-driven methods learn patterns by
optimizing statistical metrics and tend to overlook the adherence to physical
laws, unlike traditional model-driven numerical methods. Thus, they often
generate predictions that are not physically realistic. On the other hand, by
sampling a large amount of high quality predictions from a data-driven model,
some predictions will be more physically plausible than the others and closer
to what will happen in the future. Based on this observation, we propose
\emph{Beam search by Vector Quantization} (BeamVQ) to enhance the physical
alignment of data-driven space-time forecasting models. The key of BeamVQ is to
train model on self-generated samples filtered with physics-aware metrics. To
be flexibly support different backbone architectures, BeamVQ leverages a code
bank to transform any encoder-decoder model to the continuous state space into
discrete codes. Afterwards, it iteratively employs beam search to sample
high-quality sequences, retains those with the highest physics-aware scores,
and trains model on the new dataset. Comprehensive experiments show that BeamVQ
not only gave an average statistical skill score boost for more than 32% for
ten backbones on five datasets, but also significantly enhances physics-aware
metrics.
