1d-cnn channel reconstruction

This work addresses the "black-box" nature of convolutional neural networks (CNNs) in solving image inverse problems by proposing LE-MMSE, the first analytically tractable theoretical framework that explicitly incorporates CNN inductive biases. Built upon minimum mean square error (MMSE) estimation, LE-MMSE formally integrates translation equivariance and local receptive field constraints to yield an interpretable and solvable inverse problem model. Theoretical analysis elucidates the fundamental distinction between physics-aware and physics-agnostic estimators and clarifies the role of high-density regions in the training distribution. Extensive experiments across diverse inverse problems, datasets, and mainstream architectures—including U-Net, ResNet, and PatchMLP—demonstrate remarkable alignment between theoretical predictions and actual CNN outputs, achieving PSNR values consistently above 25 dB, thereby validating the effectiveness and broad applicability of the LE-MMSE framework.

Channel estimation in OFDM systems via sparse time–frequency pilot sampling is severely ill-posed due to pilot sparsity and rapid channel time-variations; existing deep learning approaches rely heavily on large-scale labeled datasets, accurate channel priors, and high computational resources. Method: We propose a novel kernel-based method that requires neither labeled data nor channel prior knowledge. Specifically, we introduce the Convolutional Neural Tangent Kernel (CNTK) for channel matrix interpolation, leveraging infinite-width CNN theory to reformulate training dynamics as a closed-form kernel ridge regression solution. Contribution/Results: Evaluated on real-world channel datasets, our method achieves high-accuracy channel estimation while accelerating inference by over 10× and reducing GPU memory consumption by 90%, significantly outperforming state-of-the-art deep learning baselines.

This study addresses the limited capability of convolutional neural networks (CNNs) in modeling scalar features—such as frequency and distance—in path loss prediction. To overcome this, we propose encoding scalar features as dedicated input channels, jointly fed with multi-scale geographic raster maps into a CNN. Unlike conventional late-fusion paradigms, our approach systematically validates, for the first time, the effectiveness of “feature channelization”—i.e., explicit embedding of scalars as spatially aligned channels. In three comparative experiments, the channelized architecture significantly improves cross-scenario generalization: mean prediction error decreases by 12.7%, and model robustness is enhanced. Results demonstrate that spatially aligned scalar representations better synergize with geographic context, enabling more accurate and transferable propagation modeling. This work establishes a novel paradigm for spectrum-aware intelligent sensing, bridging scalar radio parameters and spatially structured environmental data within a unified deep learning framework.

Convolutional neural networks (CNNs) for surrogate modeling of high-dimensional partial differential equations (PDEs) suffer from prohibitive computational costs due to reliance on large-scale, high-fidelity numerical simulations. Method: We propose a cross-dimensional transfer learning framework featuring a novel hybrid-dimensional (d- and (d−1)-dimensional) joint training paradigm. It leverages approximate solutions of lower-dimensional PDEs to guide training of high-dimensional CNN surrogates, enabling knowledge transfer and error compensation. The architecture employs a fully convolutional encoder–decoder, multi-scale transfer mechanisms, and PDE-informed dimensionality-reduced data generation, augmented with uncertainty quantification. Contribution/Results: On multiphase flow benchmark problems, our method achieves higher accuracy than Monte Carlo methods using only a few times fewer simulation budgets. Forward inference is negligible in cost, dramatically improving the cost-effectiveness and practicality of PDE surrogates.

This paper addresses sparse signal reconstruction in one-bit compressive sensing by proposing the first reconstruction framework leveraging pre-trained generative models. Methodologically, it models the target signal as a low-dimensional latent variable on a learned generative manifold and directly optimizes this latent variable under one-bit measurement constraints, integrating gradient-based search with theoretically grounded regularization. Its key contribution lies in moving beyond conventional ℓ₁ sparsity priors: it exploits expressive generative priors to capture broader classes of structured signals and establishes, for the first time, a theoretical reconstruction error bound under a RIP-like condition on the measurement operator. Experiments on standard benchmarks demonstrate substantial improvements—3–8 dB higher PSNR—over state-of-the-art methods including ℓ₁ minimization and AQI, confirming the superior representational power and robustness of generative priors in one-bit reconstruction.

This study addresses the challenge of channel embedding for multivariate time series inputs in Transformer-based models by systematically evaluating eight input encoding strategies on both synthetic and real-world data (ETTh1), using negative log-likelihood as the primary metric. The findings reveal that the standard per-channel linear projection (nn.Linear(C, d_model)) consistently achieves superior and robust performance across most scenarios. While positional encoding with projection shows marginal gains for small channel counts and nonlinear MLP backbones offer slight improvements for large channel counts, these advantages diminish as data volume increases. Through geometric probing and paired significance tests, the work uncovers fundamental limitations in both shared-scalar and channel-independent architectures, demonstrating that mainstream encoders exhibit remarkably similar empirical performance, thereby offering practical guidance for multivariate time series modeling.

This study addresses the inadequacy of conventional field reconstruction errors in predicting the impact of lossy compression on downstream operator accuracy in PDE operator learning. We present the first formal proof demonstrating the failure of reconstruction metrics, and propose a forward-propagation probing technique based on pretrained surrogate models. By quantifying perturbation attenuation and leveraging the inherent smoothness properties of PDEs, this method captures differential error amplification to assess true compression costs. Extensive multi-architecture experiments, grounded in rate-distortion theory and the PDEBench benchmark, reveal that transmission factors vary by two orders of magnitude across different PDE families, with ranking inversions occurring in 36 out of 104 cases. These findings validate the consistency and effectiveness of the proposed probing approach across diverse datasets and architectures.

This work addresses the limitation of conventional optimizers, which employ fixed update structures and struggle to adapt to the dynamic shifts in gradient behavior—ranging from stable to noisy or inconsistent—during training. To overcome this, the authors propose PILOT, an online adaptive optimizer that, for the first time, leverages gradient direction consistency as a policy signal to dynamically modulate the combination of momentum, normalization, and sign-based updates in real time. Relying solely on first-order gradient information, PILOT maintains algorithmic simplicity while achieving substantial performance gains. Empirical results demonstrate that PILOT attains state-of-the-art accuracy of 95.71% on FashionMNIST with a CNN and 93.42% on CIFAR-10 with ResNet-18, outperforming existing optimizers.

Reconstructing flow fields from sparse measurements remains a fundamental challenge in fluid dynamics. This work proposes the first application of language model architectures to this task, formulating it as a sequence-to-sequence learning problem. By leveraging a mesh-free representation and a query-based mechanism, the method effectively captures spatial correlations and long-range dependencies inherent in fluid systems. Evaluated across four benchmark datasets—two-dimensional von Kármán vortex streets, daily U.S. temperature maps, three-dimensional blood flow, and turbulent jets—the approach achieves high-fidelity reconstructions even under extreme sparsity, with observation rates below 10%. The results demonstrate both computational efficiency and superior accuracy, significantly advancing the integration of scientific foundation models into flow field reconstruction.

为解决压缩感知中测量数据有限及现有方法优化状态利用不足的问题，提出了一种基于二阶优化的Newton深度展开网络(NDU-Net)，通过引入Newton更新模块和多尺度先验模块提升重建性能。