发表机构
Heidelberg University; Interdisciplinary Centre for Scientific Computing (IWR); Department of Mathematics and Computer Science（海德堡大学; 跨学科科学计算中心（IWR）; 数学与计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维神经动力学重建难题，提出PCA-DMD框架，在多数据集及不同规模样本实验中，其重建性能、泛化能力及可扩展性均优于现有方法，可实现准确的神经信号重建。
AI 中文摘要
长时程神经记录的准确重建颇具挑战，因为局部场电位（LFPs）具有高分辨率、多通道、瞬态且被试间存在差异的特点。本文提出PCA-DMD，这是一种可扩展的算子理论框架，将LFP记录分割为重叠窗口，投影到紧凑的PCA空间，在潜在空间学习线性Koopman演化，并通过逆投影和重叠相加聚合重建连续信号。在200000样本的海马记录上，PCA-DMD优于Classical DMD、SpDMD、MrDMD和HODMD，实现KLD=0.0761、HD=0.0847；在300000样本的全对被试间零样本泛化中，相关系数为0.9504-0.9800，HD=0.0010-0.0072，KLD=0.0005-0.0022，无需目标被试微调。样本外时间预测在未见过的区间和多个通道的时间保留LFP片段上表现出紧密的单步一致性。对400000至900000样本的可扩展性分析显示，零样本重建稳定，平均相关系数保持在0.965-0.968左右，计算成本可预测增长。对独立93通道Allen Neuropixels记录的外部验证显示，逐通道平均和中位数相关系数分别为0.7427和0.7990。Koopman谱与模式分析揭示，主导特征值集中在单位圆附近。因此，PCA-DMD为高维神经动力学重建提供了可解释、可泛化且计算可扩展的框架。
英文摘要
Accurate reconstruction of long-duration neural recordings is challenging because local field potentials (LFPs) are high-resolution, multichannel, transient, and variable across subjects. We present PCA-DMD, a scalable operator-theoretic framework that segments LFP recordings into overlapping windows, projects them into a compact PCA space, learns linear Koopman evolution in the latent space, and reconstructs continuous signals through inverse projection and overlap-add aggregation. On 200,000-sample hippocampal recordings, PCA-DMD outperformed Classical DMD, SpDMD, MrDMD, and HODMD, achieving KLD=0.0761 and HD=0.0847. In all-pair cross-subject zero-shot generalization at 300,000 samples, correlations were 0.9504-0.9800, with HD=0.0010-0.0072 and KLD=0.0005-0.0022, without target-subject fine-tuning. The prediction showed close one-step agreement on temporally held-out LFP segments across the unseen interval and multiple channels. Scalability analysis from 400,000 to 900,000 samples showed stable zero-shot reconstruction, with mean correlation remaining about 0.965-0.968 while computational cost increased predictably. External validation on an independent 93-channel Allen Neuropixels recording yielded mean and median channel-wise correlations of 0.7427 and 0.7990, respectively. Koopman spectral and mode analyses revealed dominant eigenvalues concentrated near the unit circle. PCA-DMD therefore provides an interpretable, generalizable, and computationally scalable framework for reconstructing high-dimensional neural dynamics.
