From Sparse Sensors to Continuous Fields: STRIDE for Spatiotemporal Reconstruction

TL;DR

STRIDE is a novel two-stage neural framework that accurately reconstructs complex spatiotemporal fields from sparse sensors, generalizing across resolutions and noise levels, with theoretical support for its stability and effectiveness.

Contribution

The paper introduces STRIDE, a new spatiotemporal reconstruction method combining a temporal encoder and an INR decoder, with theoretical analysis and superior empirical performance.

Findings

Outperforms baselines on chaotic and wave benchmarks

Supports super-resolution and noise robustness

Provides theoretical justification for stable reconstruction

Abstract

Reconstructing high-dimensional spatiotemporal fields from sparse point-sensor measurements is a central challenge in learning parametric PDE dynamics. Existing approaches often struggle to generalize across trajectories and parameter settings, or rely on discretization-tied decoders that do not naturally transfer across meshes and resolutions. We propose STRIDE (Spatio-Temporal Recurrent Implicit DEcoder), a two-stage framework that maps a short window of sensor measurements to a latent state with a temporal encoder and reconstructs the field at arbitrary query locations with a modulated implicit neural representation (INR) decoder. Using the Fourier Multi-Component and Multi-Layer Neural Network (FMMNN) as the INR backbone improves representation of complex spatial fields and yields more stable optimization than sine-based INRs. We provide a conditional theoretical justification: under stable delay observability of point measurements on a low-dimensional parametric invariant set, the reconstruction operator factors through a finite-dimensional embedding, making STRIDE-type architectures natural approximators. Experiments on four challenging benchmarks spanning chaotic dynamics and wave propagation show that STRIDE outperforms strong baselines under extremely sparse sensing, supports super-resolution, and remains robust to noise.