arXiv:2510.24026v1 Announce Type: new 
Abstract: The accuracy of Physics-Informed Neural Networks (PINNs) critically depends on the placement of collocation points, as the PDE loss is approximated through sampling over the solution domain. Global sampling ensures stability by covering the entire domain but requires many samples and is computationally expensive, whereas local sampling improves efficiency by focusing on high-residual regions but may neglect well-learned areas, reducing robustness. We propose a Global-Local Fusion (GLF) Sampling Strategy that combines the strengths of both approaches. Specifically, new collocation points are generated by perturbing training points with Gaussian noise scaled inversely to the residual, thereby concentrating samples in difficult regions while preserving exploration. To further reduce computational overhead, a lightweight linear surrogate is introduced to approximate the global residual-based distribution, achieving similar effectiveness at a fraction of the cost. Together, these components, residual-adaptive sampling and residual-based approximation, preserve the stability of global methods while retaining the efficiency of local refinement. Extensive experiments on benchmark PDEs demonstrate that GLF consistently improves both accuracy and efficiency compared with global and local sampling strategies. This study provides a practical and scalable framework for enhancing the reliability and efficiency of PINNs in solving complex and high-dimensional PDEs.

تقدم دراسة حديثة نهجًا مبتكرًا لتحسين كفاءة الشبكات العصبية المستندة إلى الفيزياء (PINNs) من خلال تحسين أخذ عينات نقاط التلاقي. يوازن هذا الأسلوب بين تقنيات أخذ العينات العالمية والمحلية، مما يضمن الاستقرار مع تقليل التكاليف الحاسوبية. هذه الخطوة مهمة لأنها تعزز دقة PINNs، التي تعتبر حاسمة لحل المعادلات التفاضلية الجزئية المعقدة في مجالات علمية متنوعة.

Un estudio reciente presenta un enfoque innovador para mejorar la eficiencia de las Redes Neuronales Informadas por la Física (PINNs) al optimizar el muestreo de puntos de colocalización. Este método equilibra las técnicas de muestreo global y local, asegurando estabilidad mientras reduce los costos computacionales. Este avance es significativo ya que mejora la precisión de las PINNs, que son cruciales para resolver ecuaciones diferenciales parciales complejas en diversos campos científicos.

Une étude récente présente une approche innovante pour améliorer l'efficacité des réseaux de neurones informés par la physique (PINNs) en optimisant l'échantillonnage des points de collocation. Cette méthode équilibre les techniques d'échantillonnage global et local, garantissant la stabilité tout en réduisant les coûts computationnels. Cette avancée est significative car elle améliore la précision des PINNs, qui sont essentiels pour résoudre des équations différentielles partielles complexes dans divers domaines scientifiques.

A recent study introduces an innovative approach to improve the efficiency of Physics-Informed Neural Networks (PINNs) by optimizing the sampling of collocation points. This method balances global and local sampling techniques, ensuring stability while reducing computational costs. This advancement is significant as it enhances the accuracy of PINNs, which are crucial for solving complex partial differential equations in various scientific fields.

Efficient Global-Local Fusion Sampling for Physics-Informed Neural Networks

arXiv:2511.11048v2 Announce Type: replace-cross 
Abstract: 4D flow magnetic resonance imaging (MRI) is a reliable, non-invasive approach for estimating blood flow velocities, vital for cardiovascular diagnostics. Unlike conventional MRI focused on anatomical structures, 4D flow MRI requires high spatiotemporal resolution for early detection of critical conditions such as stenosis or aneurysms. However, achieving such resolution typically results in prolonged scan times, creating a trade-off between acquisition speed and prediction accuracy. Recent studies have leveraged physics-informed neural networks (PINNs) for super-resolution of MRI data, but their practical applicability is limited as the prohibitively slow training process must be performed for each patient. To overcome this limitation, we propose PINGS-X, a novel framework modeling high-resolution flow velocities using axes-aligned spatiotemporal Gaussian representations. Inspired by the effectiveness of 3D Gaussian splatting (3DGS) in novel view synthesis, PINGS-X extends this concept through several non-trivial novel innovations: (i) normalized Gaussian splatting with a formal convergence guarantee, (ii) axes-aligned Gaussians that simplify training for high-dimensional data while preserving accuracy and the convergence guarantee, and (iii) a Gaussian merging procedure to prevent degenerate solutions and boost computational efficiency. Experimental results on computational fluid dynamics (CFD) and real 4D flow MRI datasets demonstrate that PINGS-X substantially reduces training time while achieving superior super-resolution accuracy. Our code and datasets are available at https://github.com/SpatialAILab/PINGS-X.

تم تقديم إطار عمل جديد يسمى PINGS-X لتحسين كفاءة الدقة الفائقة في التصوير بالرنين المغناطيسي بتدفق 4D، وهو أمر حاسم لتقدير سرعات تدفق الدم بدقة في تشخيص القلب والأوعية الدموية. تستخدم هذه الطريقة تمثيلات غاوسية موحدة مستندة إلى الفيزياء مع محاذاة المحاور لمعالجة التحديات المتعلقة بأوقات المسح المطولة والتوازن بين سرعة الاكتساب ودقة التنبؤ.

Se ha introducido un nuevo marco llamado PINGS-X para mejorar la eficiencia de la super-resolución en la IRM 4D, que es crucial para la estimación precisa de las velocidades del flujo sanguíneo en el diagnóstico cardiovascular. Este enfoque utiliza un splatting gaussiano normalizado informado por la física con alineación de ejes para abordar los desafíos de los tiempos de escaneo prolongados y el compromiso entre la velocidad de adquisición y la precisión de las predicciones.

Un nouveau cadre nommé PINGS-X a été introduit pour améliorer l'efficacité de la super-résolution en IRM 4D, qui est cruciale pour une estimation précise des vitesses de flux sanguin dans le diagnostic cardiovasculaire. Cette approche utilise un splatting gaussien normalisé informé par la physique avec alignement des axes pour relever les défis des temps de scan prolongés et du compromis entre la vitesse d'acquisition et la précision des prédictions.

A novel framework named PINGS-X has been introduced to enhance the efficiency of super-resolution in 4D flow MRI, which is crucial for accurate blood flow velocity estimation in cardiovascular diagnostics. This approach utilizes physics-informed normalized Gaussian splatting with axes alignment to address the challenges of prolonged scan times and the trade-off between acquisition speed and prediction accuracy.

Efficient Global-Local Fusion Sampling for Physics-Informed Neural Networks

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