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

arXiv: https://arxiv.org/abs/2602.22630 · HTML: https://mlsanity.com/paper/2602.22630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [A Brief Review of Hypernetworks in Deep Learning](https://mlsanity.com/paper/2306.06955/) (2023)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks](https://mlsanity.com/paper/2111.01008/) (2021)
- [Towards gain tuning for numerical KKL observers](https://mlsanity.com/paper/2204.00318/) (2022)
- [Neural Pharmacodynamic State Space Modeling](https://mlsanity.com/paper/2102.11218/) (2021)
- [Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems](https://mlsanity.com/paper/2210.01476/) (2022)
- [Deep KKL: Data-driven Output Prediction for Non-Linear Systems](https://mlsanity.com/paper/2103.12443/) (2021)
- [HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions](https://mlsanity.com/paper/2509.05117/) (2025)
- [Learning Robust State Observers using Neural ODEs (longer version)](https://mlsanity.com/paper/2212.00866/) (2022)
- [Unsupervised Physics-Informed Neural Network-based Nonlinear Observer design for autonomous systems using contraction analysis](https://mlsanity.com/paper/2411.09237/) (2024)
- [KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning](https://mlsanity.com/paper/2501.11655/) (2025)
- [Reconstructing Indistinguishable Solutions Via Set-Valued KKL Observer](https://mlsanity.com/paper/2301.09690/) (2023)
- [Adaptive Meta-Learning-Based KKL Observer Design for Nonlinear Dynamical Systems](https://mlsanity.com/paper/2310.19489/) (2023)
- [Simultaneous Ground Reaction Force and State Estimation via Constrained Moving Horizon Estimation](https://mlsanity.com/paper/2411.12047/) (2024)

## Abstract (arXiv)

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 R"ossler systems.