arXiv:2501.11655v2 Announce Type: replace-cross 
Abstract: This paper proposes a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observer involves finding an injective map that transforms the system state into a higher-dimensional observer state, whose dynamics is linear and stable. The observer's state is then mapped back to the original system coordinates via the inverse map to obtain the state estimate. However, finding this transformation and its inverse is quite challenging. We propose learning the forward mapping using a physics-informed neural network, and then learning its inverse mapping with a conventional feedforward neural network. Theoretical guarantees for the robustness of state estimation against approximation error and system uncertainties are provided, including non-asymptotic learning guarantees that link approximation quality to finite sample sizes. The effectiveness of the proposed approach is demonstrated through numerical simulations on benchmark examples, showing superior generalization capability outside the training domain compared to state-of-the-art methods.

تم اقتراح نهج تعلم جديد لتصميم مراقبين Kazantzis-Kravaris/Luenberger (KKL) للأنظمة غير الخطية المستقلة، باستخدام الشبكات العصبية المستندة إلى الفيزياء لتعلم التحويل الأمامي والشبكات العصبية التقليدية لتعلم التحويل العكسي. يتناول هذا الأسلوب التحديات المتعلقة بتحويل حالات النظام إلى حالات مراقب ذات أبعاد أعلى والعكس بالعكس.

Se ha propuesto un nuevo enfoque de aprendizaje para diseñar observadores Kazantzis-Kravaris/Luenberger (KKL) para sistemas no lineales autónomos, utilizando redes neuronales informadas por la física para aprender el mapeo directo y redes neuronales feedforward convencionales para el mapeo inverso. Este método aborda los desafíos de transformar los estados del sistema en estados de observador de mayor dimensión y viceversa.

Une nouvelle approche d'apprentissage a été proposée pour concevoir des observateurs Kazantzis-Kravaris/Luenberger (KKL) pour des systèmes non linéaires autonomes, utilisant des réseaux de neurones informés par la physique pour apprendre la cartographie directe et des réseaux de neurones feedforward conventionnels pour la cartographie inverse. Cette méthode répond aux défis de la transformation des états du système en états d'observateur de dimension supérieure et vice versa.

A novel learning approach has been proposed for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems, utilizing physics-informed neural networks to learn the forward mapping and conventional feedforward neural networks for the inverse mapping. This method addresses the challenges in transforming system states into higher-dimensional observer states and back.

KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning

arXiv:2512.10287v1 Announce Type: new 
Abstract: Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes the use of a recent kernel-based neural surrogate, KHRONOS. In this work, we blend sparse high-fidelity (HF) data with low-fidelity (LF) information to predict aerodynamic fields under varying constraints in computational resources. Unlike traditional approaches, KHRONOS is built upon variational principles, interpolation theory, and tensor decomposition. These elements provide a mathematical basis for heavy pruning compared to dense neural networks. Using the AirfRANS dataset as a high-fidelity benchmark and NeuralFoil to generate low-fidelity counterparts, this work compares the performance of KHRONOS with three contemporary model architectures: a multilayer perceptron (MLP), a graph neural network (GNN), and a physics-informed neural network (PINN). We consider varying levels of high-fidelity data availability (0%, 10%, and 30%) and increasingly complex geometry parameterizations. These are used to predict the surface pressure coefficient distribution over the airfoil. Results indicate that, whilst all models eventually achieve comparable predictive accuracy, KHRONOS excels in resource-constrained conditions. In this domain, KHRONOS consistently requires orders of magnitude fewer trainable parameters and delivers much faster training and inference than contemporary dense neural networks at comparable accuracy. These findings highlight the potential of KHRONOS and similar architectures to balance accuracy and efficiency in multi-fidelity aerodynamic field prediction.

تقدم دراسة جديدة نموذج KHRONOS، وهو نموذج بديل عصبي يعتمد على النواة، مصمم للتنبؤ متعدد الدقة بكفاءة في المجالات الديناميكية الهوائية. يدمج هذا النموذج بيانات عالية الدقة متناثرة مع معلومات منخفضة الدقة، مستفيدًا من المبادئ التغايرية وتحليل التنسور لتحسين الكفاءة الحسابية مقارنة بالشبكات العصبية الكثيفة التقليدية.

Un nuevo estudio presenta KHRONOS, un modelo de sustitución neuronal basado en núcleos, diseñado para la predicción multi-fidelidad eficiente de campos aerodinámicos. Este modelo integra datos de alta fidelidad dispersos con información de baja fidelidad, aprovechando principios variacionales y descomposición tensorial para mejorar la eficiencia computacional en comparación con redes neuronales densas tradicionales.

Une nouvelle étude présente KHRONOS, un modèle de substitution neuronal basé sur des noyaux, conçu pour la prédiction multi-fidélité efficace des champs aérodynamiques. Ce modèle intègre des données haute-fidélité éparses avec des informations basse-fidélité, tirant parti des principes variationnels et de la décomposition tensorielle pour améliorer l'efficacité computationnelle par rapport aux réseaux neuronaux denses traditionnels.

A new study introduces KHRONOS, a kernel-based neural surrogate model designed for efficient multi-fidelity prediction of aerodynamic fields. This model integrates sparse high-fidelity data with low-fidelity information, leveraging variational principles and tensor decomposition to enhance computational efficiency compared to traditional dense neural networks.

KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning

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