Junmin Liu

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations (PDEs), yet their training is often plagued by gradient pathologies, spectral bias, and slow convergence on PDEs with strong nonlinearity, sharp gradients, or multiscale features. To address these issues, we propose the curriculum-guided Gaussian mixture PINN (CGMPINN), which couples a Gaussian mixture model (GMM) with dynamic curriculum learning. A GMM is periodically fitted to the PDE residuals to quantify spatiallyvarying learning difficulty; a smooth curriculum then progressively shifts training focus from easy to hard regions, while a precision-based variance modulation suppresses unreliable clusters during early optimization. The dual curriculum is governed by a single shared parameter and can be combined with self-adaptive loss balancing. We further establish three theoretical guarantees for the framework: uniform equivalence between the curriculum-weighted and standard PDE losses, sublinear convergence of the gradient norm undersummable objective drift, and a Rademacher-complexity generalization bound with an explicit weighting-induced bias. Numerical experiments on six benchmark PDEs spanning elliptic, parabolic, hyperbolic, advection-dominated, and nonlinear reaction-diffusion regimes show that CGMPINN consistently attains the lowest relative L2 and maximum absolute errors among all compared methods, reducing the relative L2 error by up to 97.8% over the standard PINN at comparable computational cost.

Object detection in aerial imagery faces significant challenges caused by extreme scale variation, dense object layouts, and the prevalence of tiny instances. Standard Intersection over Union (IoU) and its variants are sensitive to small localization errors: a minor coordinate deviation may cause a large IoU penalty for tiny objects, and non-overlapping boxes yield no gradients, which limits localization accuracy. To address these issues, we propose ThermalIoU, a heat-diffusion-inspired bounding-box regression loss that represents rigid boxes as continuous diffusive fields. A box is treated as a flat-top initial temperature distribution and diffused by the Gaussian heat kernel, preserving its rectangular geometry while providing smooth boundary support. We further introduce a scale-decoupled and epoch-annealed diffusion parameter, so that small objects obtain broader early-stage gradients whereas larger objects retain sharper localization fields. Experiments on AI-TOD and VisDrone, together with ablations, efficiency measurements, and qualitative visualizations, show that ThermalIoU is a practical training loss with overall gains over CIoU and competitive performance against Inner-IoU and MPDIoU.

Pansharpening is a fundamental task in remote sensing that aims to fuse high-spatial-resolution panchromatic images with low-spatial-resolution multispectral images. Inspired by the remarkable success of diffusion models in generative tasks, recent studies have introduced them to this field, yielding promising results. However, existing diffusion-based methods remain constrained by computationally expensive multi-step sampling processes or a heavy reliance on complex prior knowledge. To overcome these limitations, we propose InstaFlow-Pan, a novel flow-matching-based model capable of generating high-fidelity high-resolution multispectral images in a single inference step. Specifically, we employ a residual learning strategy and predict clean residuals instead of complex velocity fields directly. This reduces the information load, enabling the model to bypass iterative integration and achieve high-fidelity one-step synthesis. To support this paradigm, we design a conditional feature encoder based on the pyramid vision Transformer to extract robust conditional feature representations. We then build a generative network architecture leveraging multi-scale and attention mechanisms, which simultaneously preserves local details and global semantic information while enabling flexible guidance from conditional features. Furthermore, we introduce a novel progressive frequency-aware training strategy, which dynamically modulates the supervision focus along the flow trajectory, prioritizing global structure recovery in near-noise regions while progressively reinforcing high-frequency detail constraints as the generative process advances. Extensive experiments on multiple benchmark datasets demonstrate that InstaFlow-Pan outperforms state-of-the-art diffusion-based and regression-based methods, achieving superior spectral fidelity and spatial detail preservation.

While deep learning methods have demonstrated significant success in pan-sharpening, most existing approaches suffer from insufficient high-frequency guidance from panchromatic (PAN) images during the upsampling of low-resolution multi-spectral (LRMS) images, often failing to reconstruct fine-grained local details and maintain global contextual consistency. To alleviate these limitations, we propose a novel Detail-aware local and Context-aware global Dual-branch Upsampling (DCDU) method for pan-sharpening. The core of DCDU is a dual-branch architecture specifically designed to decouple and leverage both local structural details and global semantic information from both modalities: the detail-aware local branch calculates feature-space correlations between LRMS images and PAN images to derive adaptive kernels, guiding the reconstruction of local neighborhoods and facilitating high-fidelity injection of fine-grained spatial structures; the context-aware global branch mainly employs a cross-modality channel-specific spatial attention mechanism to holistically model long-range dependencies, dynamically re-calibrating spectral-spatial representations based on cross-modal context and capturing macro-level semantic coherence across the entire scene. The distinct information streams from the two branches are then integrated via an adaptive and learnable mapping function. We also provide a theoretical analysis under the minimum mean square error criterion to motivate our dual-stream strategy, the efficacy of which is robustly validated by our experimental results. As a generic and lightweight upsampling module, the collaborative design can be seamlessly integrated into various backbone networks, enabling superior performance across multiple datasets.

Gradient-based hyperparameter optimization (HPO) have emerged recently, leveraging bilevel programming techniques to optimize hyperparameter by estimating hypergradient w.r.t. validation loss. Nevertheless, previous theoretical works mainly focus on reducing the gap between the estimation and ground-truth (i.e., the bias), while ignoring the error due to data distribution (i.e., the variance), which degrades performance. To address this issue, we conduct a bias-variance decomposition for hypergradient estimation error and provide a supplemental detailed analysis of the variance term ignored by previous works. We also present a comprehensive analysis of the error bounds for hypergradient estimation. This facilitates an easy explanation of some phenomena commonly observed in practice, like overfitting to the validation set. Inspired by the derived theories, we propose an ensemble hypergradient strategy to reduce the variance in HPO algorithms effectively. Experimental results on tasks including regularization hyperparameter learning, data hyper-cleaning, and few-shot learning demonstrate that our variance reduction strategy improves hypergradient estimation. To explain the improved performance, we establish a connection between excess error and hypergradient estimation, offering some understanding of empirical observations.

All-in-one image restoration has emerged as a pivotal paradigm in low-level vision. Unlike conventional single-task approaches, this paradigm aims to learn a unified model capable of handling multiple degradation types within a single framework. However, most existing methods predominantly suffer from two critical limitations: i) cross-degradation knowledge contamination during joint optimization, and ii) catastrophic forgetting in sequential learning scenarios. To address these limitations, we introduce a Degradation-Guided Prompt Learning Network (DPLNet), a unified architecture that employs a plug-and-play prompt block to explicitly mine degradation-specific priors from the input, thereby injecting task-adaptive guidance into the restoration process. Complementing the architecture, we introduce the Dynamic Task Curriculum (DTC), a principled learning strategy that sequentially schedules multiple tasks within each training epoch. DTC quantifies per-instance hardness through an online uncertainty criterion and progressively enriches each task optimization by retaining the hard examples from previous tasks, yielding continual robustness gains. Extensive experiments demonstrate that DPLNet achieves state-of-the-art performance in both single-task and multi-task settings. And our proposed training strategy yields consistent improvements across existing architectures.

Pansharpening, a critical task in remote sensing, aims to fuse panchromatic (PAN) images with low-resolution multispectral (LRMS) images to generate high-resolution multispectral (HRMS) outputs. Existing deep learning methods primarily focus on pixel-level spatial and spectral features, often overlooking the deeper, text-level semantic information that can enhance fusion. To address this limitation, we introduce a novel Text-modulated Multiscale Guidance Transformer (TMGformer). Specifically, we first establish a self-contained workflow to generate text features, eliminating reliance on external Application Programming Interfaces (APIs). Subsequently, we develop a Text-modulated Visual Feature Refinement (TVFR) module that transforms these text features into spectrally compatible and semantically consistent guidance. This guidance is then injected into our Asymmetric Multiscale Fusion (AMF) module to guide the fusion process at multiple scales, effectively addressing the vast variance in the scale of terrestrial objects described in their corresponding texts. Furthermore, we introduce a hybrid text-visual loss function to provide comprehensive supervision. Extensive experiments demonstrate that TMGformer achieves state-of-the-art performance. Notably, on the GaoFen-2 dataset, our method reduces the ERGAS by 5.11% and the D_s by 16.44% compared to the second-best competitor. To facilitate future research, we release a new vision-language dataset containing textual descriptions and corresponding text features. The code and dataset are available at: https://github.com/PeterZhaoXJTU/TMGformer.