Learning Chaotic Dynamics
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Related Articles from SNS
Learning Chaotic Dynamics through Second-Order Geometric Supervision
arXiv:2606.01596v1 Announce Type: new Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector field, but neither constrains how the field bends away from its tangent plane. A model can thus match values and tangents at the supervised states yet...
The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling
arXiv:2605.31547v1 Announce Type: new Abstract: Dynamical systems reconstruction (DSR) aims to learn surrogate models that capture the dynamics underlying time-series data. Reliably deploying these surrogates requires uncertainty estimates consistent with the learned dynamics. We expose a dynamic-probabilistic consistency (DPC) gap: the pursuit of finite-horizon probabilistic objectives can degrade dynamics or decouple predictive uncertainty from the local tangent dynamics it ought to reflect.
Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting
arXiv:2605.15470v2 Announce Type: replace Abstract: Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass.
Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting
arXiv:2605.15470v2 Announce Type: replace-cross Abstract: Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass.
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem. In computation, however, everything depends on a hard finite-dimensional choice: the observables must be expressive, nearly invariant under the dynamics, and, ideally, compatible with composition. Deep Koopman methods learn flexible coordinates, whereas structure-preserving methods enforce operator identities on fixed dictionaries.
Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections
arXiv:2606.05618v1 Announce Type: cross Abstract: Extreme events -- such as earthquakes and coronal mass ejections -- are common in many chaotic dynamical systems, yet are difficult to characterize and predict due to the subtle instability mechanisms that drive them. In this work, we develop an interpretable technique that reveals the underlying mechanisms behind extreme events and uses them to build data-driven forecasts and intuitive event suppression controllers. In particular, we utilize...
Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error
arXiv:2605.31438v1 Announce Type: new Abstract: Time series forecasting often requires learning nonlinear and time-delayed dependencies. A paradigmatic class of forecasting models are nonlinear vector autoregressive processes (NVAR), also known as next-generation reservoir computers (NG-RCs). These models approximate the Koopman operator on the space spanned by their explicit feature library.
Koopman operator learning for predictive control via Khatri-Rao kernel regression
arXiv:2606.02938v1 Announce Type: cross Abstract: This paper develops a data-driven realization of the generalized Koopman operator (GeKo), in which states and inputs are lifted independently and the dynamics are expressed as a tensor bilinear system. The first contribution is a time-sequenced multi-step Khatri-Rao kernel regression formulation that exposes the operator to evolved snapshots along trajectories rather than only single one-step pairs, which reduces compounded prediction error....
Mean-Field Diffuser: Scaling Offline MARL to Thousands of Agents
arXiv:2605.30190v2 Announce Type: replace Abstract: Diffusion-based planning has achieved strong results in single-agent offline reinforcement learning, yet scaling to many-agent systems remains intractable due to the curse of dimensionality in the joint trajectory space. We introduce MF-Diffuser, a framework that lifts trajectory planning to the Wasserstein space of trajectory distributions, where the propagation of chaos ensures a small representative subset of agents captures the full...
ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics
Announce Type: new Abstract: Modeling Hamiltonian systems over long temporal intervals remains a significant challenge due to intrinsic multiscale structures and rapid nonlinear transitions. While Hamiltonian Neural Networks (HNNs) incorporate geometric invariants to improve stability, they typically rely on a fixed, externally prescribed temporal structure. This lack of adaptability often leads to accumulated phase errors and degraded accuracy in systems with heterogeneous temporal scales.