HarmoCore：用于振荡波场稀疏重建的函数潜在扩散
HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields
浏览论文内容
中文总结 AI 辅助
针对振荡波场稀疏重建的欠定逆问题，提出HarmoCore模型，通过函数潜在扩散在核心空间采样，在1%--2%传感下的多类实验中取得显著性能提升。
中文摘要 AI 辅助
从稀疏传感器重建振荡波场是一个严重欠定的逆问题。除了一般物理场重建的挑战外，波响应为复值、频率敏感且高度振荡，而昂贵的模拟和传感往往仅留下极稀疏的观测结果。现有的低秩、算子和扩散方法大多为实值、更平滑的场设计；密集像素空间扩散对于振荡复场效率极低，且难以扩展到三维。我们提出HarmoCore，其在紧凑、连续且结构化的波场潜在空间中放置生成先验。HarmoCore通过共享连续空间基上的函数Tucker核心表示联合实部-虚部通道，学习频率条件核心扩散先验，并直接在核心空间执行扩散后验采样。在固定传感器坐标下，多线性解码器诱导显式似然引导算子，避免密集像素空间校正；可选的目标方程残差引导进一步提升物理一致性。在2D亥姆霍兹、2D合成波场和3D亥姆霍兹上的实验表明，在1%--2%传感条件下取得了显著提升，同时在三维中仍具实用性。
英文摘要
Reconstructing oscillatory wave fields from scattered sensors is a severely underdetermined inverse problem. Beyond the challenges of general physical-field reconstruction, wave responses are complex-valued, frequency-sensitive, and highly oscillatory, while costly simulation and sensing often leave only extreme-sparse observations. Existing low-rank, operator, and diffusion approaches are largely designed for real-valued, smoother fields; dense pixel-space diffusion is particularly inefficient for oscillatory complex fields and difficult to scale to 3D. We propose HarmoCore, which places a generative prior in a compact, continuous, and structured wave-field latent. HarmoCore represents joint real--imaginary channels with Functional Tucker cores over shared continuous spatial bases, learns a frequency-conditioned core diffusion prior, and performs Diffusion Posterior Sampling directly in core space. At fixed sensor coordinates, the multilinear decoder induces an explicit likelihood guidance operator, avoiding dense pixel-space correction. Optional target-equation residual guidance further promotes physical consistency. Experiments on 2D Helmholtz, 2D synthetic wave fields, and 3D Helmholtz show substantial gains under 1%--2% sensing while remaining practical in three dimensions.
发表机构
- College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息科学与工程学院）
机构由 AI 辅助整理，请以论文原文为准。
