Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end, neural ODEs regularized with neural Lyapunov functions are a promising approach when states are fully observed. For practical applications however, partial observations are the norm. As we will demonstrate, initialization of unobserved augmented states can become a key problem for neural ODEs. To alleviate this issue, we propose to augment the system's state with its history. Inspired by state augmentation in discrete-time systems, we thus obtain neural delay differential equations. Based on classical time delay stability analysis, we then show how to ensure stability of the learned models, and theoretically analyze our approach. Our experiments demonstrate its applicability to stable system identification of partially observed systems and learning a stabilizing feedback policy in delayed feedback control.
Code (1)
Similar Papers 제목 키워드 기반
Learning partially observed systems with neural Hamiltonian ordinary differential equations
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits th…
Flow Equivariant World Models: Memory for Partially Observed Dynamic Environments
Embodied systems experience the world as 'a symphony of flows': a combination of many continuous streams of sensory input coupled to self-motion, interwoven with the dynamics of external objects. These sensory streams an…
EyeWorld: A Generative World Model of Ocular State and Dynamics
Ophthalmic decision-making depends on subtle lesion-scale cues interpreted across multimodal imaging and over time, yet most medical foundation models remain static and degrade under modality and acquisition shifts. Here…
Representation LearningGeometric Dictionary Learning of Dynamical Systems with Optimal Transport
Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristi…
Representation LearningBounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving p…