Title: Kolmogorov-Arnold Hierarchical Implicit Neural Representation Model for Physical Field Reconstruction
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Physical Field Reconstruction, Implicit Neural Representation, Kolmogorov-Arnold Network

Abstract: Reconstructing continuous fields from sparse observations poses one of the most persistent challenges in scientific machine learning, with critical implications for understanding geophysical phenomena from limited sensor networks. Although implicit neural representations (INRs) have recently emerged as promising solutions, capturing fine-scale structures in complex domains such as atmospheric and oceanic systems remains elusive. We introduce KHINR (Kolmogorov-Arnold Hierarchical Implicit Neural Representation) that achieves state-of-the-art spatial field reconstruction through a fusion of learnable Gabor filters and Kolmogorov-Arnold Network (KAN) blocks in a hierarchical structure. The sparse spatial data points are first encoded using learnable Gabor filters to extract localized, frequency-aware spatial features that are further processed in the latent space via a hierarchical structure with KAN blocks. For reconstruction, the Gabor-encoded unknown spatial points are passed through a gating mechanism on the latent representation learned by the hierarchical KAN blocks. Rigorous evaluation across four distinct physical fields from meteorological and ocean datasets reveals KHINR's superior performance compared to other leading models on multiple reconstruction tasks under varying sparsity conditions. Comprehensive ablation studies validate the critical contribution of each architectural component, establishing KHINR as a new standard for sparse-to-continuous field reconstruction in scientific applications.