DEFT: Data-Efficient Frequency-domain Top-k Sampling via Inverse Discrete Fourier Transform for Spatiotemporal Dynamical Systems Modeling

Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions. We propose DEFT, a frequency-domain data sampling method that identifies the dominant Fourier modes of a physical system and systematically varies the corresponding amplitudes and phases to generate physically consistent training data via the inverse discrete Fourier transform. In addition, we derive a generalization bound of this method. We note that it also provides a theoretically principled criterion for selecting $K$. We evaluate the proposed method through three sets of experiments, each targeting a distinct aspect of its utility. First, we validate the framework on canonical PDEs solving demonstrating that it outperforms traditional methods when the system is dominated by a few prominent frequency components. Second, we employ DEFT as a data-value filter on the diffusion--sorption and Burgers equations of PDEBench, showing that it reduces data requirements by $40\%$ while sacrificing less than $2\%$ in predictive accuracy. Third, to evaluate DEFT for more challenging and practically relevant problems, we validate it in the battery degradation PDE system, achieving consistently high predictive ac