HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning

• URL: http://arxiv.org/abs/2602.22630v2
• Date: Sun, 01 Mar 2026 21:07:12 GMT
• Title: HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning
• Authors: Yahia Salaheldin Shaaban, Salem Lahlou, Abdelrahman Sayed Sayed,
• Abstract summary: HyperKKL is a novel learning approach for non-autonomous nonlinear systems.<n>Current learning-based approximations of the KKL observer are mostly designed for autonomous systems.<n>HyperKKL addresses this by employing a hypernetwork architecture that encodes the input signal to instantaneously generate the parameters of the KKL observer.
• Score: 3.340699005490366
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: This paper proposes HyperKKL, a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for non-autonomous nonlinear systems. While KKL observers offer a rigorous theoretical framework by immersing nonlinear dynamics into a stable linear latent space, its practical realization relies on solving Partial Differential Equations (PDE) that are analytically intractable. Current existing learning-based approximations of the KKL observer are mostly designed for autonomous systems, failing to generalize to driven dynamics without expensive retraining or online gradient updates. HyperKKL addresses this by employing a hypernetwork architecture that encodes the exogenous input signal to instantaneously generate the parameters of the KKL observer, effectively learning a family of immersion maps parameterized by the external drive. We rigorously evaluate this approach against a curriculum learning strategy that attempts to generalize from autonomous regimes via training heuristics alone. The novel approach is illustrated on four numerical simulations in benchmark examples including the Duffing, Van der Pol, Lorenz, and Rössler systems.

Related papers

• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• On-line learning of dynamic systems: sparse regression meets Kalman filtering [41.99844472131922]
  We extend sparsity-driven approaches to real-time learning by integrating a cornerstone algorithm from control theory -- the Kalman filter (KF)<n>The resulting Sindy Kalman Filter (KF) unifies both frameworks by treating unknown system parameters as state variables.<n>We demonstrate KF's effectiveness in the real-time identification of a sparse nonlinear aircraft model built from real flight data.
  arXiv  Detail & Related papers  (2025-11-14T11:24:05Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning [5.888531936968298]
  We propose a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems.<n>The design of a KKL observer involves finding an injective map that transforms the system state into a higher-dimensional observer state.<n>We generate synthetic data for training by numerically solving the system and observer dynamics.
  arXiv  Detail & Related papers  (2025-01-20T18:38:51Z)
• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Adaptive Meta-Learning-Based KKL Observer Design for Nonlinear Dynamical Systems [0.0]
  This paper presents a novel approach to observer design for nonlinear dynamical systems through meta-learning. We introduce a framework that leverages information from measurements of the system output to design a learning-based KKL observer capable of online adaptation to a variety of system conditions and attributes.
  arXiv  Detail & Related papers  (2023-10-30T12:25:14Z)
• Kalman Filter for Online Classification of Non-Stationary Data [101.26838049872651]
  In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. We introduce a probabilistic Bayesian online learning model by using a neural representation and a state space model over the linear predictor weights. In experiments in multi-class classification we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.
  arXiv  Detail & Related papers  (2023-06-14T11:41:42Z)
• Learning Robust State Observers using Neural ODEs (longer version) [1.0094821910320064]
  We present a methodology for the design of state observers for nonlinear systems based on Neural ODEs, learning Luenberger-like observers and their nonlinear extension. For tuneable KKL observers, the relationship between the design of the observer and its trade-off between convergence speed and robustness is analysed and used as a basis for improving the robustness of the learning-based observer in training.
  arXiv  Detail & Related papers  (2022-12-01T20:58:39Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• Model-Based Reinforcement Learning via Stochastic Hybrid Models [39.83837705993256]
  This paper adopts a hybrid-system view of nonlinear modeling and control. We consider a sequence modeling paradigm that captures the temporal structure of the data. We show that these time-series models naturally admit a closed-loop extension that we use to extract local feedback controllers.
  arXiv  Detail & Related papers  (2021-11-11T14:05:46Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.