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.
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.
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arXiv Machine Learning
Jun 24
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.
arXiv AI
1d ago
Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamics
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.
arXiv AI
1d ago
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 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 Machine Learning
Aug 7
Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
arXiv:2608. 05416v1 Announce Type: new Abstract: Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem?
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 23
Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses
arXiv:2607. 19387v1 Announce Type: cross Abstract: Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields.
arXiv Machine Learning
Jul 31
On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems
arXiv:2607. 28080v1 Announce Type: cross Abstract: We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems.
arXiv Machine Learning
Jun 15
Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems
arXiv:2606. 14079v1 Announce Type: new Abstract: We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces.
arXiv Machine Learning
Aug 3
Structured Neural Chaos: An Adaptive Surrogate Modeling Framework for Functional Uncertainty Quantification and Global Sensitivity Analysis
arXiv:2607. 28903v1 Announce Type: cross Abstract: Variance-based global sensitivity analysis (GSA) plays a key role in uncertainty quantification by identifying the contributions of uncertain inputs to the variability of the model response.
arXiv Machine Learning
Jul 22
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.