Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often computationally expensive. Recently, data-driven methods have emerged as alternatives, but they frequently suffer from error accumulation and limited physical consistency, especially in multiphysics and complex geometries. To address these challenges, we propose PEGNet, a Physics-Embedded Graph Network that incorporates PDE-guided message passing to redesign the graph neural network architecture. By embedding key PDE dynamics like convection, viscosity, and diffusion into distinct message functions, the model naturally integrates physical constraints into its forward propagation, producing more stable and physically consistent solutions. Additionally, a hierarchical architecture is employed to capture multi-scale features, and physical regularization is integrated into the loss function to further enforce adherence to governing physics. We evaluated PEGNet on benchmarks, including custom datasets for respiratory airflow and drug delivery, showing significant improvements in long-term prediction accuracy and physical consistency over existing methods.

Abstract While semi‐analytical boundary handling techniques have proven effective for modeling particle‐based fluid‐solid interactions, they can become unstable when applied to mesh boundaries undergoing dynamic motion or featuring complex, sharp geometries. We propose a novel semi‐analytical energy model for boundary handling that unifies fluid simulation and boundary interactions within a variational framework. The model comprises two key components: a semi‐analytical bulk energy formulation that mitigates particle deficiency issues in the evaluation of bulk energy, and a nonlocal contact potential that effectively prevents particle penetration into boundaries. Both energy terms are naturally compatible with the Semi‐Implicit SPH (SISPH), and a unified Hessian‐free solver combined with reduced‐order collision detection enables an efficient and stable GPU‐based implementation for both fluid dynamics and nonlinear fluid‐solid interactions. Furthermore, the unified treatment of fluid bulk energy and boundary energy via the semi‐analytical formulation robustly corrects penetrations in practice, even under severe compression scenarios involving complex moving boundaries. Compared with existing semi‐analytical boundary treatments, our method is more robust under fast boundary motion and strong compression. Across challenging benchmarks with sharp features, narrow gaps, and moving meshes, it remains stable and penetration‐free where prior methods often fail.

Predicting individuals' next locations is a core task in human mobility modelling, with wide-ranging implications for urban planning, transportation, public policy and personalised mobility services. Traditional approaches largely depend on location embeddings learned from historical mobility patterns, limiting their ability to encode explicit spatial information, integrate rich urban semantic context, and accommodate previously unseen locations. To address these challenges, we explore the application of CaLLiPer—a multi-modal representation learning framework that fuses spatial coordinates and semantic features of points of interest through contrastive learning—for location embedding in individual mobility prediction. CaLLiPer's embeddings are spatially explicit, semantically enriched, and inductive by design, enabling robust prediction performance even in scenarios involving emerging locations. Through extensive experiments on four public mobility datasets under both conventional and inductive settings, we demonstrate that CaLLiPer consistently outperforms strong baselines, particularly excelling in inductive scenarios. Our findings highlight the potential of multi-modal, inductive location embeddings to advance the capabilities of human mobility prediction systems. We also release the code and data (https://github.com/xlwang233/Into-the-Unknown) to foster reproducibility and future research.

Despite recent advancements in semantic representation driven by pre-trained and large-scale language models, addressing long tail challenges in multi-label text classification remains a significant issue. Long tail challenges have persistently posed difficulties in accurately classifying less frequent labels. Current approaches often focus on improving text semantics while neglecting the crucial role of label relationships. This paper introduces LabelCoRank, a novel approach inspired by ranking principles. LabelCoRank leverages label co-occurrence relationships to refine initial label classifications through a dual-stage reranking process. The first stage uses initial classification results to form a preliminary ranking. In the second stage, a label co-occurrence matrix is utilized to rerank the preliminary results, enhancing the accuracy and relevance of the final classifications. By integrating the reranked label representations as additional text features, LabelCoRank effectively mitigates long tail issues in multi-label text classification. Experimental evaluations on popular datasets including MAG-CS, PubMed, and AAPD demonstrate the effectiveness and robustness of LabelCoRank. The implementation code is publicly available on https://github.com/821code/LabelCoRank.