nonlinear-dynamics

This paper introduces Sparse Koopman Autoencoders (SKAEs) to identify local dynamical regimes in multibasin nonlinear systems, demonstrating superior forecasting performance and interpretable latent supports.

This paper presents a Bayesian control framework that integrates spike-based dynamics with probabilistic inference for adaptive control in nonlinear dynamical systems, using a spiking neural network model demonstrated on a benchmark problem.

This paper proposes a provable two-stage pipeline that distills nonlinear dynamical systems into compact linear state-space models using convex optimization, with theoretical guarantees and experiments on LDS benchmarks and MuJoCo.

This paper introduces equivariant spectral submanifold (eSSM) reduction, an extension of SSM-based reduced-order modelling that incorporates symmetries to accelerate computations and improve robustness for nonlinear dynamical systems.

This paper introduces Unscented KalmanNet (UKN), a hybrid deep learning filter that augments the Unscented Kalman Filter with learned components to improve state estimation accuracy and covariance calibration under unknown noise statistics and model mismatch. Experiments show significant RMSE reductions over UKF and other KalmanNet variants.

MetaKoopman proposes a Bayesian meta-learning framework for modeling nonlinear dynamics using linear latent representations via Koopman operators, enabling closed-form updates and uncertainty quantification. It is validated on autonomous truck and trailer systems under adverse winter conditions, outperforming prior methods in prediction accuracy and robustness.

This is a popular science article of over 25,000 characters, starting from the origin of entropy, reviewing the development of dissipative system theory, and exploring a three-level analysis of whether AI belongs to dissipative systems (hardware level, training level, static model).

DeepMDMD combines deep learning with algebraic constraints to learn compact, dynamically coherent Koopman operator representations that enforce the product rule as an exact constraint. The method outperforms geometric approaches on high-dimensional chaotic and fluid dynamics problems, reducing spectral pollution and enabling stable long-term forecasting.

This paper extends Port-Hamiltonian Neural Networks (PHNNs) to partial differential equations (PDEs) for learning nonlinear string dynamics from data. The approach recovers both the Hamiltonian and dissipation, outperforming non-physics-informed baselines in accuracy and interpretability.