arXiv Machine Learning
Jun 4
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
arXiv:2407. 06312v2 Announce Type: replace-cross Abstract: Many systems resist analytical modeling, making data-driven inference of dynamics important.
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arXiv Machine Learning
Jun 30
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
arXiv:2606. 29083v1 Announce Type: cross Abstract: Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust.
arXiv Machine Learning
Jul 21
fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture
arXiv:2607. 17990v1 Announce Type: new Abstract: Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency.
arXiv Machine Learning
Sep 10
Geometric Dictionary Learning of Dynamical Systems with Optimal Transport
The paper introduces DOODL, a framework that learns a dictionary of spectral dynamics to represent related dynamical systems as points on a low‑dimensional manifold in operator space. By constraining operator estimation to this learned manifold, DOODL provides compact, interpretable embeddings and enables fast, accurate operator estimation from short, partially observed trajectories. Experiments on metastable Langevin dynamics and turbulent plasma simulations show that DOODL achieves one to two orders of magnitude lower errors than independent estimation methods, especially in low‑data regimes.
arXiv AI
Aug 5
A neural operator framework for data-driven discovery of stability and receptivity in physical systems
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv AI
Jun 17
KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting
arXiv:2606. 17070v1 Announce Type: cross Abstract: Accurate oceanic forecasting is critical for climate monitoring and disaster early warning.
arXiv Machine Learning
Jun 19
Learning to Emulate Chaos: Adversarial Optimal Transport Regularization
arXiv:2604. 21097v2 Announce Type: replace-cross Abstract: Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model with data-driven methods such as machine learning emulators.
arXiv Machine Learning
Jul 17
A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
arXiv:2511. 06609v4 Announce Type: replace Abstract: The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines.
arXiv AI
Jul 7
When is a System Discoverable from Data? Discovery Requires Chaos
arXiv:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
arXiv AI
Jul 22
Incomplete Observations Boost Evolutionary Performance in Ocean Modeling
arXiv:2607. 19147v1 Announce Type: cross Abstract: Data-driven methods have revolutionized ocean modeling, yet current approaches rely heavily on complete reanalysis datasets, imposing computational constraints and limiting model performance to that of the training data.
arXiv AI
Aug 18
PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Models
arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.
arXiv Machine Learning
Jun 5
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.