arXiv:2511.18515v1 Announce Type: new 
Abstract: Physics-informed neural networks (PINNs) typically minimize average residuals, which can conceal large, localized errors. We propose Residual Risk-Aware Physics-Informed Neural Networks PINNs (RRaPINNs), a single-network framework that optimizes tail-focused objectives using Conditional Value-at-Risk (CVaR), we also introduced a Mean-Excess (ME) surrogate penalty to directly control worst-case PDE residuals. This casts PINN training as risk-sensitive optimization and links it to chance-constrained formulations. The method is effective and simple to implement. Across several partial differential equations (PDEs) such as Burgers, Heat, Korteweg-de-Vries, and Poisson (including a Poisson interface problem with a source jump at x=0.5) equations, RRaPINNs reduce tail residuals while maintaining or improving mean errors compared to vanilla PINNs, Residual-Based Attention and its variant using convolution weighting; the ME surrogate yields smoother optimization than a direct CVaR hinge. The chance constraint reliability level $\alpha$ acts as a transparent knob trading bulk accuracy (lower $\alpha$ ) for stricter tail control (higher $\alpha$ ). We discuss the framework limitations, including memoryless sampling, global-only tail budgeting, and residual-centric risk, and outline remedies via persistent hard-point replay, local risk budgets, and multi-objective risk over BC/IC terms. RRaPINNs offer a practical path to reliability-aware scientific ML for both smooth and discontinuous PDEs.

قدم الباحثون الشبكات العصبية المستندة إلى الفيزياء الحساسة للمخاطر المتبقية (RRaPINNs)، وهو إطار جديد يقوم بتحسين الأهداف المركزة على الذيل باستخدام قيمة المخاطر الشرطية (CVaR) وعقوبة الفائض المتوسط (ME). تهدف هذه الطريقة إلى تحسين تدريب الشبكات العصبية المستندة إلى الفيزياء (PINNs) من خلال تقليل الأخطاء المحلية في سياق مجموعة متنوعة من المعادلات التفاضلية الجزئية (PDEs) بما في ذلك معادلات بورجرز وبواسون.

Investigadores han presentado las Redes Neuronales Informadas por la Física Sensibles al Riesgo Residual (RRaPINNs), un nuevo marco que optimiza objetivos enfocados en las colas utilizando el Valor en Riesgo Condicional (CVaR) y una penalización de Exceso Medio (ME). Este enfoque busca mejorar el entrenamiento de las redes neuronales informadas por la física (PINNs) al reducir errores localizados en el contexto de diversas ecuaciones en derivadas parciales (EDP), incluidas las ecuaciones de Burgers y Poisson.

Des chercheurs ont introduit les Réseaux de Neurones Informés par la Physique Sensibles au Risque Résiduel (RRaPINNs), un cadre novateur qui optimise les objectifs axés sur les queues en utilisant la Valeur à Risque Conditionnelle (CVaR) et une pénalité de Surplus Moyen (ME). Cette approche vise à améliorer l'entraînement des réseaux de neurones informés par la physique (PINNs) en réduisant les erreurs localisées dans le contexte de diverses équations aux dérivées partielles (EDP) telles que les équations de Burgers et de Poisson.

Researchers have introduced Residual Risk-Aware Physics-Informed Neural Networks (RRaPINNs), a novel framework that optimizes tail-focused objectives using Conditional Value-at-Risk (CVaR) and a Mean-Excess (ME) surrogate penalty. This approach aims to enhance the training of physics-informed neural networks (PINNs) by reducing localized errors in the context of various partial differential equations (PDEs) including Burgers and Poisson equations.

RRaPINNs: Residual Risk-Aware Physics Informed Neural Networks

arXiv:2310.11789v2 Announce Type: replace 
Abstract: Physics-informed neural networks (PINNs) have shown great promise in solving partial differential equations (PDEs). However, vanilla PINNs often face challenges when solving complex PDEs, especially those involving multi-scale behaviors or solutions with sharp or oscillatory characteristics. To precisely and adaptively locate the critical regions that fail in the solving process we propose a sampling strategy grounded in white-box adversarial attacks, referred to as WbAR. WbAR search for failure regions in the direction of the loss gradient, thus directly locating the most critical positions. WbAR generates adversarial samples in a random walk manner and iteratively refines PINNs to guide the model's focus towards dynamically updated critical regions during training. We implement WbAR to the elliptic equation with multi-scale coefficients, Poisson equation with multi-peak solutions, high-dimensional Poisson equations, and Burgers equation with sharp solutions. The results demonstrate that WbAR can effectively locate and reduce failure regions. Moreover, WbAR is suitable for solving complex PDEs, since locating failure regions through adversarial attacks is independent of the size of failure regions or the complexity of the distribution.

قدم الباحثون استراتيجية جديدة للت sampling تُعرف باسم WbAR، والتي تستخدم الهجمات العدائية من نوع الصندوق الأبيض لتحسين تحديد وتحسين مناطق الفشل في الشبكات العصبية المستندة إلى الفيزياء (PINNs). تهدف هذه الطريقة إلى معالجة التحديات التي تواجهها PINNs التقليدية عند حل المعادلات التفاضلية الجزئية المعقدة ذات السلوكيات متعددة المقاييس والخصائص الحادة.

Investigadores han introducido una nueva estrategia de muestreo llamada WbAR, que utiliza ataques adversariales de caja blanca para mejorar la localización y el refinamiento de las regiones de fallo en las redes neuronales informadas por la física (PINNs). Este enfoque busca abordar los desafíos que enfrentan las PINNs convencionales al resolver ecuaciones diferenciales parciales (EDP) complejas con comportamientos multiescala y características agudas.

Des chercheurs ont introduit une nouvelle stratégie d'échantillonnage appelée WbAR, qui utilise des attaques adversariales en boîte blanche pour améliorer la localisation et le raffinement des régions d'échec dans les réseaux de neurones informés par la physique (PINNs). Cette approche vise à résoudre les défis rencontrés par les PINNs classiques lors de la résolution d'équations aux dérivées partielles (EDP) complexes avec des comportements multi-échelles et des caractéristiques nettes.

Researchers have introduced a novel sampling strategy called WbAR, which utilizes white-box adversarial attacks to enhance the localization and refinement of failure regions in physics-informed neural networks (PINNs). This approach aims to address the challenges faced by vanilla PINNs when solving complex partial differential equations (PDEs) with multi-scale behaviors and sharp characteristics.

RRaPINNs: Residual Risk-Aware Physics Informed Neural Networks

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