arXiv:2602.04201cs.LGmath.DS2026-02被引 2

用稀疏传感器数据重建连续时空场,支持超分辨率与噪声鲁棒性。

From Sparse Sensors to Continuous Fields: STRIDE for Spatiotemporal Reconstruction

论文配图:From Sparse Sensors to Continuous Fields: STRIDE for Spatiotemporal Reconstruction
图 1 · 摘自论文原文
  • 两阶段框架:先编码时序传感器数据,再用调制隐式神经网络解码
  • 在极稀疏传感下优于强基线,支持任意位置查询与超分辨率重建
  • 理论支撑重构算子可分解为有限维嵌入,适合参数化动力系统

从稀疏点传感器测量中重建高维时空场是学习参数化偏微分方程动力学的核心挑战。现有方法常难以跨轨迹和参数设置泛化,或依赖网格绑定的解码器,无法自然迁移至不同网格与分辨率。我们提出STRIDE(时空循环隐式解码器),一个两阶段框架:首先通过时序编码器将短窗口传感器数据映射为潜在状态,再利用调制隐式神经网络(INR)解码器在任意查询位置重建场。采用傅里叶多组件多层神经网络(FMMNN)作为INR主干,提升复杂空间场表示能力,并实现比基于正弦的INR更稳定的优化。我们提供条件性理论证明:在低维参数不变集上的点测量具有稳定延迟可观测性时,重构算子可分解为有限维嵌入,使STRIDE类架构成为自然逼近器。在四个涵盖混沌动力学与波传播的挑战性基准上,实验表明STRIDE在极端稀疏传感下优于强基线,支持超分辨率,并对噪声保持鲁棒。

原文摘要 · Abstract (English)

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.

时空重建隐式神经网络稀疏传感参数化PDE

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