Fine-grained wildfire spread prediction is crucial for enhancing emergency response efficacy and decision-making precision. However, existing research predominantly focuses on coarse spatiotemporal scales and relies on low-resolution satellite data, capturing only macroscopic fire states while fundamentally constraining high-precision localized fire dynamics modeling capabilities. To bridge this gap, we present FireSentry, a provincial-scale multi-modal wildfire dataset characterized by sub-meter spatial and sub-second temporal resolution. Collected using synchronized UAV platforms, FireSentry provides visible and infrared video streams, in-situ environmental measurements, and manually validated fire masks. Building on FireSentry, we establish a comprehensive benchmark encompassing physics-based, data-driven, and generative models, revealing the limitations of existing mask-only approaches. Our analysis proposes FiReDiff, a novel dual-modality paradigm that first predicts future video sequences in the infrared modality, and then precisely segments fire masks in the mask modality based on the generated dynamics. FiReDiff achieves state-of-the-art performance, with video quality gains of 39.2% in PSNR, 36.1% in SSIM, 50.0% in LPIPS, 29.4% in FVD, and mask accuracy gains of 3.3% in AUPRC, 59.1% in F1 score, 42.9% in IoU, and 62.5% in MSE when applied to generative models. The FireSentry benchmark dataset and FiReDiff paradigm collectively advance fine-grained wildfire forecasting and dynamic disaster simulation. The processed benchmark dataset is publicly available at: this https URL.

Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage data collection solution. However, due to the random and uncontrollable movement patterns of these non-dedicated mobile platforms, the resulting sensor data are often incomplete and temporally inconsistent. By exploring potential training patterns in the reverse process of diffusion models, we propose Spatio-Temporal Physics-Informed Diffusion Models (STeP-Diff). STeP-Diff leverages DeepONet to model the spatial sequence of measurements along with a PDE-informed diffusion model to forecast the spatio-temporal field from incomplete and time-varying data. Through a PDE-constrained regularization framework, the denoising process asymptotically converges to the convection-diffusion dynamics, ensuring that predictions are both grounded in real-world measurements and aligned with the fundamental physics governing pollution dispersion. To assess the performance of the system, we deployed 59 self-designed portable sensing devices in two cities, operating for 14 days to collect air pollution data. Compared to the second-best performing algorithm, our model achieved improvements of up to 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE, with extensive evaluations demonstrating that STeP-Diff effectively captures the spatio-temporal dependencies in air pollution fields.

The $\text{Cu}_7\text{P}\text{S}_6$ compound has garnered significant attention due to its potential in thermoelectric applications. In this study, we introduce a neuroevolution potential (NEP), trained on a dataset generated from ab initio molecular dynamics (AIMD) simulations, using the moment tensor potential (MTP) as a reference. The low root mean square errors (RMSEs) for total energy and atomic forces demonstrate the high accuracy and transferability of both the MTP and NEP. We further calculate the phonon density of states (DOS) and radial distribution function (RDF) using both machine learning potentials, comparing the results to density functional theory (DFT) calculations. While the MTP potential offers slightly higher accuracy, the NEP achieves a remarkable 41-fold increase in computational speed. These findings provide detailed microscopic insights into the dynamics and rapid Cu-ion diffusion, paving the way for future studies on Cu-based solid electrolytes and their applications in energy devices.

Sparse optimization has seen its advances in recent decades. For scenarios where the true sparsity is unknown, regularization turns out to be a promising solution. Two popular non-convex regularizations are the so-called $L_0$ norm and $L_q$ norm with $q\in(0,1)$, giving rise to extensive research on their induced optimization. However, the majority of these work centered around the main function that is twice continuously differentiable and the best convergence rate for an algorithm solving the optimization with $q\in(0,1)$ is superlinear. This paper explores the $L_q$ norm regularized optimization in a unified way for any $q\in[0,1)$, where the main function has a semismooth gradient. In particular, we establish the first-order and the second-order optimality conditions under mild assumptions and then integrate the proximal operator and semismooth Newton method to develop a proximal semismooth Newton pursuit algorithm. Under the second sufficient condition, the whole sequence generated by the algorithm converges to a unique local minimizer. Moreover, the convergence is superlinear and quadratic if the gradient of the main function is semismooth and strongly semismooth at the local minimizer, respectively. Hence, this paper accomplishes the quadratic rate for an algorithm designed to solve the $L_q$ norm regularization problem for any $q\in(0,1)$. Finally, some numerical experiments have showcased its nice performance when compared with several existing solvers.

To address the problem of the low accuracy of transverse velocity field measurements for small targets in high-resolution solar images, we proposed a novel velocity field measurement method for high-resolution solar images based on PWCNet. This method transforms the transverse velocity field measurements into an optical flow field prediction problem. We evaluated the performance of the proposed method using the Ha and TiO datasets obtained from New Vacuum Solar Telescope (NVST) observations. The experimental results show that our method effectively predicts the optical flow of small targets in images compared with several typical machine- and deep-learning methods. On the Ha dataset, the proposed method improves the image structure similarity from 0.9182 to 0.9587 and reduces the mean of residuals from 24.9931 to 15.2818; on the TiO dataset, the proposed method improves the image structure similarity from 0.9289 to 0.9628 and reduces the mean of residuals from 25.9908 to 17.0194. The optical flow predicted using the proposed method can provide accurate data for the atmospheric motion information of solar images. The code implementing the proposed method is available on this https URL

This paper builds rigorous analysis on the root-exponential convergence for the lightning schemes via rational functions in approximating corner singularity problems with uniform exponentially clustered poles proposed by Gopal and Trefethen. The start point is to set up the representations of $z^\alpha$ and $z^\alpha\log z$ in the slit disk and develop results akin to Paley-Wiener theorem, from which, together with the Poisson summation formula, the root-exponential convergence of the lightning plus polynomial scheme with an exact order for each clustered parameter is established in approximation of prototype functions $g(z)z^\alpha$ or $g(z)z^\alpha\log z$ on a sector-shaped domain, which includes $[0,1]$ as a special case. In addition, the fastest convergence rate is confirmed based upon the best choice of the clustered parameter. Furthermore, the optimal choice of the clustered parameter and the convergence rate for corner singularity problems in solving Laplace equations are attested based on Lehman and Wasow's study of corner singularities and along with the decomposition of Gopal and Trefethen. The thorough analysis provides a solid foundation for lightning schemes and rational approximation. Ample numerical evidences demonstrate the optimality and sharpness of the estimates.