arXiv:2512.03476v1 Announce Type: new 
Abstract: Bridging the gap between theoretical conceptualization and computational implementation is a major bottleneck in Scientific Computing (SciC) and Scientific Machine Learning (SciML). We introduce ATHENA (Agentic Team for Hierarchical Evolutionary Numerical Algorithms), an agentic framework designed as an Autonomous Lab to manage the end-to-end computational research lifecycle. Its core is the HENA loop, a knowledge-driven diagnostic process framed as a Contextual Bandit problem. Acting as an online learner, the system analyzes prior trials to select structural `actions' ($A_n$) from combinatorial spaces guided by expert blueprints (e.g., Universal Approximation, Physics-Informed constraints). These actions are translated into executable code ($S_n$) to generate scientific rewards ($R_n$). ATHENA transcends standard automation: in SciC, it autonomously identifies mathematical symmetries for exact analytical solutions or derives stable numerical solvers where foundation models fail. In SciML, it performs deep diagnosis to tackle ill-posed formulations and combines hybrid symbolic-numeric workflows (e.g., coupling PINNs with FEM) to resolve multiphysics problems. The framework achieves super-human performance, reaching validation errors of $10^{-14}$. Furthermore, collaborative ``human-in-the-loop" intervention allows the system to bridge stability gaps, improving results by an order of magnitude. This paradigm shift focuses from implementation mechanics to methodological innovation, accelerating scientific discovery.

تم تقديم ATHENA، وهو إطار مبتكر لإدارة دورة حياة البحث الحسابي في الحوسبة العلمية وتعلم الآلة العلمية. يستخدم حلقة HENA، وهي عملية مدفوعة بالمعرفة تعمل كمشكلة لصوص سياقية، مما يسمح للنظام باختيار الإجراءات بشكل مستقل بناءً على التجارب السابقة والمخططات الخبراء.

ATHENA, un marco innovador para gestionar el ciclo de vida de la investigación computacional en Computación Científica y Aprendizaje Automático Científico, ha sido presentado. Utiliza el bucle HENA, un proceso impulsado por el conocimiento que opera como un problema de Bandido Contextual, permitiendo al sistema seleccionar de manera autónoma acciones basadas en ensayos previos y planos de expertos.

ATHENA, un cadre innovant pour gérer le cycle de vie de la recherche computationnelle en calcul scientifique et en apprentissage automatique scientifique, a été introduit. Il utilise la boucle HENA, un processus guidé par les connaissances qui fonctionne comme un problème de bandit contextuel, permettant au système de sélectionner de manière autonome des actions basées sur des essais antérieurs et des plans d'experts.

ATHENA, an innovative framework for managing the computational research lifecycle in Scientific Computing and Scientific Machine Learning, has been introduced. It utilizes the HENA loop, a knowledge-driven process that operates as a Contextual Bandit problem, enabling the system to autonomously select actions based on prior trials and expert blueprints.

ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

arXiv:2408.02697v4 Announce Type: replace 
Abstract: The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often suffer from critical issues such as vanishing or exploding values during training, rendering them unstable regardless of hyperparameter initialization. Leveraging the perspective of effective field theory, we identify the root causes of these failures and propose the Modified Rectified Power Unit (MRePU) activation function. MRePU addresses RePU's limitations while preserving its advantages, such as differentiability and universal approximation properties. Theoretical analysis demonstrates that MRePU satisfies criticality conditions necessary for stable training, placing it in a distinct universality class. Extensive experiments validate the effectiveness of MRePU, showing significant improvements in training stability and performance across various tasks, including polynomial regression, physics-informed neural networks (PINNs) and real-world vision tasks. Our findings highlight the potential of MRePU as a robust alternative for building deep neural networks.

تقدم وظيفة تنشيط Modified Rectified Power Unit (MRePU) حلاً للمشكلات الحرجة التي تواجه شبكات Rectified Power Unit (RePU) العميقة، مثل عدم الاستقرار أثناء التدريب بسبب القيم المتلاشية أو المتفجرة. تحتفظ هذه الوظيفة الجديدة بمزايا القابلية للاشتقاق والتقريب الشامل، مع ضمان ظروف تدريب مستقرة، كما يتضح من خلال التحليل النظري والتجارب الشاملة.

La introducción de la función de activación Modified Rectified Power Unit (MRePU) aborda problemas críticos que enfrentan las redes de Rectified Power Unit (RePU) profundas, como la inestabilidad durante el entrenamiento debido a valores que se desvanecen o explotan. Esta nueva función conserva las ventajas de la diferenciabilidad y la aproximación universal, al tiempo que garantiza condiciones de entrenamiento estables, como se demuestra a través de un análisis teórico y experimentos extensos.

L'introduction de la fonction d'activation Modified Rectified Power Unit (MRePU) répond aux problèmes critiques rencontrés par les réseaux de Rectified Power Unit (RePU) profonds, tels que l'instabilité pendant l'entraînement due à des valeurs qui s'annulent ou explosent. Cette nouvelle fonction conserve les avantages de la différentiabilité et de l'approximation universelle tout en garantissant des conditions d'entraînement stables, comme le démontre une analyse théorique et des expériences approfondies.

The introduction of the Modified Rectified Power Unit (MRePU) activation function addresses critical issues faced by deep Rectified Power Unit (RePU) networks, such as instability during training due to vanishing or exploding values. This new function retains the advantages of differentiability and universal approximation while ensuring stable training conditions, as demonstrated through extensive theoretical analysis and experiments.

Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Field Theory Perspective

arXiv:2512.02618v1 Announce Type: new 
Abstract: Heat transfer in semiconductor devices is dominated by chip and substrate assemblies, where heat generated within a finite chip layer dissipates into a semi-infinite substrate with much higher thermophysical properties. This mismatch produces steep interfacial temperature gradients, making the transient thermal response highly sensitive to the interface. Conventional numerical solvers require excessive discretization to resolve these dynamics, while physics-informed neural networks (PINNs) often exhibit unstable convergence and loss of physical consistency near the material interface. To address these challenges, we introduce HeatTransFormer, a physics-guided Transformer architecture for interface-dominated diffusion problems. The framework integrates physically informed spatiotemporal sampling, a Laplace-based activation emulating analytical diffusion solutions, and a mask-free attention mechanism supporting bidirectional spatiotemporal coupling. These components enable the model to resolve steep gradients, maintain physical consistency, and remain stable where PINNs typically fail. HeatTransFormer produces coherent temperature fields across the interface when applied to a finite layer and semi-infinite substrate configuration. Coupled with a physics-constrained inverse strategy, it further enables reliable identification of three unknown thermal properties simultaneously using only external measurements. Overall, this work demonstrates that physics-guided Transformer architectures provide a unified framework for forward and inverse modeling in interface-dominated thermal systems.

تم تقديم إطار عمل جديد يسمى HeatTransFormer لنمذجة توصيل الحرارة بين الواجهات في أجهزة أشباه الموصلات، حيث يتناول التحديات التي تطرحها التدرجات الحادة في درجات الحرارة عند الواجهة بين طبقة رقاقة محدودة وركيزة شبه لانهائية. تهدف هذه البنية المعمارية المستندة إلى الفيزياء إلى تحسين الاستجابة الحرارية العابرة دون الحاجة إلى تقسيم مفرط يتطلبه الحلول العددية التقليدية.

Se ha introducido un nuevo marco llamado HeatTransFormer para modelar la conducción de calor interfacial en dispositivos semiconductores, abordando los desafíos que presentan los pronunciados gradientes de temperatura en la interfaz entre una capa de chip finita y un sustrato semi-infinito. Esta arquitectura de transformador guiada por la física busca mejorar la respuesta térmica transitoria sin la excesiva discretización requerida por los solucionadores numéricos convencionales.

Un nouveau cadre nommé HeatTransFormer a été introduit pour modéliser la conduction de chaleur interfaciale dans les dispositifs semi-conducteurs, abordant les défis posés par les fortes gradients de température à l'interface entre une couche de puce finie et un substrat semi-infini. Cette architecture de transformateur guidée par la physique vise à améliorer la réponse thermique transitoire sans la discrétisation excessive requise par les solveurs numériques conventionnels.

A new framework named HeatTransFormer has been introduced to model interfacial heat conduction in semiconductor devices, addressing the challenges posed by steep temperature gradients at the interface between a finite chip layer and a semi-infinite substrate. This physics-guided Transformer architecture aims to enhance the transient thermal response without the excessive discretization required by conventional numerical solvers.

Modeling and Inverse Identification of Interfacial Heat Conduction in Finite Layer and Semi-Infinite Substrate Systems via a Physics-Guided Neural Framework

ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

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