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.

翻译：数据驱动的深度学习已成为建模复杂物理时空系统的新范式。与传统的模型驱动数值方法不同，这些数据驱动方法通过优化统计度量来学习模式，往往忽略了其对物理定律的遵循。因此，它们生成的预测通常在物理上不真实。另一方面，通过从数据驱动模型中采样大量高质量预测，其中一些预测会比另一些在物理上更合理，也更接近未来实际发生的情况。基于这一观察，我们提出**基于矢量量化的波束搜索**（BeamVQ），以增强数据驱动时空预测模型的物理对齐性。BeamVQ的关键在于使用基于物理感知度量筛选的自生成样本来训练模型。为了灵活支持不同的骨干架构，BeamVQ利用一个码本，将任何编码器-解码器模型从连续状态空间转换到离散码空间。随后，它迭代地采用波束搜索来采样高质量序列，保留那些具有最高物理感知得分的序列，并在新数据集上训练模型。综合实验表明，BeamVQ不仅在五个数据集上为十种骨干模型平均提升了超过32%的统计技能得分，而且显著增强了物理感知度量。