Predicting the evolution of physical systems governed by PDEs from sparse, irregular observations remains a major challenge. While most data-driven methods focus on dense, grid-structured data, real-world applications often involve limited, noisy measurements. We extend the DynaBench benchmark to evaluate fourteen modern models—including neural operators and graph-based methods—across multiple PDEs, spatial resolutions, and observation patterns. Our study reveals how sparsity and spatial structure affect model performance in low-data regimes. All code and resources are publicly released to support reproducibility and future work.

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Evaluating Spatiotemporal Prediction Models in a Low-Data Regime

  • Andrzej Dulny,
  • Paul Heinisch,
  • Andreas Hotho,
  • Anna Krause

摘要

Predicting the evolution of physical systems governed by PDEs from sparse, irregular observations remains a major challenge. While most data-driven methods focus on dense, grid-structured data, real-world applications often involve limited, noisy measurements. We extend the DynaBench benchmark to evaluate fourteen modern models—including neural operators and graph-based methods—across multiple PDEs, spatial resolutions, and observation patterns. Our study reveals how sparsity and spatial structure affect model performance in low-data regimes. All code and resources are publicly released to support reproducibility and future work.