arXiv:2511.16815v1 Announce Type: new 
Abstract: We introduce the Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates (BITS for GAPS) framework to emulate latent components in hybrid physical systems. BITS for GAPS supports serial hybrid modeling, where known physics governs part of the system and residual dynamics are represented as a latent function inferred from data. A Gaussian process prior is placed over the latent function, with hierarchical priors on its hyperparameters to encode physically meaningful structure in the predictive posterior.
  To guide data acquisition, we derive entropy-based acquisition functions that quantify expected information gain from candidate input locations, identifying samples most informative for training the surrogate. Specifically, we obtain a closed-form expression for the differential entropy of the predictive posterior and establish a tractable lower bound for efficient evaluation. These derivations approximate the predictive posterior as a finite, uniformly weighted mixture of Gaussian processes.
  We demonstrate the framework's utility by modeling activity coefficients in vapor-liquid equilibrium systems, embedding the surrogate into extended Raoult's law for distillation design. Numerical results show that entropy-guided sampling improves sample efficiency by targeting regions of high uncertainty and potential information gain. This accelerates surrogate convergence, enhances predictive accuracy in non-ideal regimes, and preserves physical consistency. Overall, BITS for GAPS provides an efficient, interpretable, and uncertainty-aware framework for hybrid modeling of complex physical systems.

تم تقديم إطار BITS for GAPS لتعزيز محاكاة المكونات الكامنة في الأنظمة الفيزيائية الهجينة من خلال أخذ عينات نظرية المعلومات البايزية. تستخدم هذه الطريقة نماذج عملية غاوسية مع أولويات هرمية على المعلمات الفائقة، مما يسهل اكتساب البيانات من خلال تحديد العينات الأكثر إفادة للتدريب.

Se ha introducido el marco BITS for GAPS para mejorar la emulación de componentes latentes en sistemas físicos híbridos mediante el muestreo teórico de la información bayesiana. Este método emplea surrogados de procesos gaussianos con priors jerárquicos sobre los hiperparámetros, facilitando la adquisición de datos al identificar las muestras más informativas para el entrenamiento.

Le cadre BITS for GAPS a été introduit pour améliorer l'émulation des composants latents dans les systèmes physiques hybrides grâce à l'échantillonnage théorique de l'information bayésienne. Cette méthode utilise des surrogates de processus gaussiens avec des prioris hiérarchiques sur les hyperparamètres, facilitant l'acquisition de données en identifiant les échantillons les plus informatifs pour l'entraînement.

The BITS for GAPS framework has been introduced to enhance the emulation of latent components in hybrid physical systems through Bayesian Information-Theoretic Sampling. This method employs Gaussian process surrogates with hierarchical priors on hyperparameters, facilitating effective data acquisition by identifying the most informative samples for training.

BITS for GAPS: Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates

arXiv:2512.08879v1 Announce Type: new 
Abstract: Real-world datasets often exhibit temporal dynamics characterized by evolving data distributions. Disregarding this phenomenon, commonly referred to as concept drift, can significantly diminish a model's predictive accuracy. Furthermore, the presence of hyperparameters in online models exacerbates this issue. These parameters are typically fixed and cannot be dynamically adjusted by the user in response to the evolving data distribution. Gaussian Process (GP) models offer powerful non-parametric regression capabilities with uncertainty quantification, making them ideal for modeling complex data relationships in an online setting. However, conventional online GP methods face several critical limitations, including a lack of drift-awareness, reliance on fixed hyperparameters, vulnerability to data snooping, absence of a principled decay mechanism, and memory inefficiencies. In response, we propose DAO-GP (Drift-Aware Online Gaussian Process), a novel, fully adaptive, hyperparameter-free, decayed, and sparse non-linear regression model. DAO-GP features a built-in drift detection and adaptation mechanism that dynamically adjusts model behavior based on the severity of drift. Extensive empirical evaluations confirm DAO-GP's robustness across stationary conditions, diverse drift types (abrupt, incremental, gradual), and varied data characteristics. Analyses demonstrate its dynamic adaptation, efficient in-memory and decay-based management, and evolving inducing points. Compared with state-of-the-art parametric and non-parametric models, DAO-GP consistently achieves superior or competitive performance, establishing it as a drift-resilient solution for online non-linear regression.

تم اقتراح طريقة جديدة تُدعى DAO-GP (عملية غاوسية على الإنترنت مع الوعي بالانحراف) لمعالجة التحديات التي تطرحها ظاهرة انحراف المفهوم في مجموعات البيانات الواقعية، والتي يمكن أن تؤثر بشكل كبير على دقة التنبؤ. تعزز هذه الطريقة المبتكرة نماذج عملية غاوسية من خلال السماح بإجراء تعديلات ديناميكية على المعلمات الفائقة استجابةً لتطور توزيعات البيانات، مما يحسن أداء النموذج في البيئات عبر الإنترنت.

Se ha propuesto un nuevo método llamado DAO-GP (Drift-Aware Online Gaussian Process) para abordar los desafíos que plantea la deriva de concepto en conjuntos de datos del mundo real, que pueden afectar significativamente la precisión predictiva. Este enfoque innovador mejora los modelos de Proceso Gaussiano al permitir ajustes dinámicos de los hiperparámetros en respuesta a la evolución de las distribuciones de datos, mejorando así el rendimiento del modelo en entornos en línea.

Une nouvelle méthode appelée DAO-GP (Drift-Aware Online Gaussian Process) a été proposée pour relever les défis posés par le concept de dérive dans les ensembles de données du monde réel, qui peuvent avoir un impact significatif sur la précision prédictive. Cette approche innovante améliore les modèles de processus gaussiens en permettant des ajustements dynamiques des hyperparamètres en réponse à l'évolution des distributions de données, améliorant ainsi les performances du modèle dans des contextes en ligne.

A new method called DAO-GP (Drift-Aware Online Gaussian Process) has been proposed to address the challenges posed by concept drift in real-world datasets, which can significantly impact predictive accuracy. This innovative approach enhances Gaussian Process models by allowing dynamic adjustments to hyperparameters in response to evolving data distributions, thereby improving model performance in online settings.

BITS for GAPS: Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates

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