predict spatial heatmaps

To address the low reliability of conventional spatial interpolation and insufficient visualization credibility caused by sparse and irregularly distributed sensor networks, this paper proposes an end-to-end graph neural network (GNN)-based interpolation framework. The method integrates Principal Neighborhood Aggregation (PNA) with Geographic Position Encoding (GPE) to enhance interpolation accuracy via GNN-driven reference data completion. Additionally, it introduces an explicit uncertainty visualization technique based on static heatmaps, encoding model prediction uncertainty into perceptible visual channels. Experiments on real-world environmental and meteorological datasets demonstrate that the proposed approach significantly outperforms baseline methods in both interpolation accuracy and data imputation performance. A user study further confirms its effectiveness in communicating uncertainty and improving decision-making trustworthiness.

Maximum likelihood estimation (MLE) for nonstationary spatial fields—such as climate sensitivity fields—in few-shot settings suffers from prohibitive computational cost and poor scalability. Method: We propose an end-to-end deep regression framework for parameter estimation, treating the gridded parameters of a nonstationary spatial autoregressive (SAR) model as 2D images and directly regressing them from input field images using image-to-image (I2I) architectures (e.g., U-Net). Contribution/Results: Our approach entirely bypasses iterative MLE optimization, achieving over 100× speedup on synthetic climate field modeling while preserving physical consistency and statistical fidelity. It delivers high accuracy without sacrificing interpretability or domain alignment. This work establishes a scalable, high-fidelity paradigm for complex nonstationary spatial modeling, enabling efficient few-shot inference in geoscientific and environmental applications.

Heatmap-based facial landmark detection suffers from slow convergence and approximation errors due to overreliance on the non-differentiable Soft-argmax operator for coordinate decoding. Method: This paper proposes a novel end-to-end training paradigm that eliminates Soft-argmax entirely. It introduces a differentiable, structured-prediction-inspired loss function that directly optimizes global consistency between heatmaps and ground-truth landmark coordinates, bypassing the non-differentiable decoding bottleneck. Contribution/Results: The method achieves state-of-the-art performance on WFLW, COFW, and 300W benchmarks, with mean normalized error (NME) matching or surpassing leading approaches. Training convergence accelerates by 2.2×, significantly reducing computational overhead. Crucially, this work provides the first theoretical and empirical validation that Soft-argmax is not essential for heatmap regression—establishing a simpler, more efficient, and robust training framework for facial landmark detection.

In spatial prediction tasks—such as weather forecasting and pollution modeling—the validation and prediction locations are fixed and non-overlapping, violating the i.i.d. assumption underlying conventional validation methods (including those correcting for covariate shift), which presume stochastic sampling rather than deterministic spatial sampling. This work formally introduces the notion of *validation consistency*: as the density of validation locations tends to infinity, the validation error must converge arbitrarily closely to the true prediction error. Building upon this principle, we propose the first theoretically guaranteed consistent spatial validation framework, integrating spatial sampling theory with weighted density estimation to accommodate both gridded and irregularly spaced observational structures. We prove its consistency under mild regularity conditions. Empirical evaluation on meteorological and air pollution datasets demonstrates that our method significantly outperforms standard cross-validation and importance-weighting baselines, achieving an average 37% reduction in estimation error.

This study addresses the limitations of traditional Kriging in non-stationary environments, where performance is hindered by its reliance on covariance modeling. To overcome this, the authors propose an end-to-end spatial interpolation method based on convolutional neural networks (CNNs). Requiring only a single partially observed field, the approach is trained under sparse supervision on user-defined grids without external data, prior assumptions, or explicit variogram estimation. As the first work to apply CNNs to single-instance, sparsely supervised spatial interpolation, it effectively captures local spatial patterns and demonstrates significantly superior performance over conventional Kriging in non-stationary settings, thereby highlighting the potential of deep learning to establish a new paradigm in spatial statistics.

This study addresses the lack of systematic best practices in large-scale Earth observation (EO) mapping, which often introduces errors during data preprocessing, model training, inference deployment, and validation, thereby compromising the reliability and scientific credibility of map products. To remedy this, we propose the first end-to-end best practice framework for EO mapping, encompassing the entire workflow from satellite data acquisition to operational map delivery. The framework integrates six core components: EO data infrastructure, preprocessing, machine learning dataset construction, uncertainty quantification, map production and dissemination, and independent validation. Emphasizing the interdependence of these stages, it embeds uncertainty quantification and independent validation as integral elements. By synergizing machine learning, distributed computing, and geospatial validation techniques, the framework establishes a reproducible and scalable mapping pipeline that substantially enhances the quality, consistency, and scientific rigor of EO-derived maps, supported by open-source resources to foster community adoption.

This study addresses the challenge of modeling spatiotemporal observational data with missing values in river network systems by proposing a novel Bayesian Gaussian process latent variable model tailored for upstream-to-downstream flow processes. The method constructs a separable spatiotemporal covariance function based on flow distance, integrating both autocorrelation and cross-correlation structures, and employs process convolution to capture complex dependencies inherent in stream networks. To enhance computational efficiency, the framework incorporates sparse inducing variables and local variational inference, enabling scalable training via gradient-based optimization. This work represents the first integration of Gaussian process latent variable models with river network topology, demonstrating superior modeling accuracy and predictive performance over existing benchmark methods in simulation experiments.