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.
Learning Chaotic Dynamics through Second-Order Geometric Supervision
arXiv:2606. 01596v1 Announce Type: cross 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.
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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
Aug 4
Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Data
arXiv:2507. 09652v2 Announce Type: replace-cross Abstract: Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data.
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 Machine Learning
Jul 22
Attractor Geometry Determines the Identifiability Limits of System Discovery
arXiv:2607. 18490v1 Announce Type: new Abstract: Symbolic discovery of governing equations from data is limited not only by algorithm design and data volume, but by the geometry of the attractor: what the long-run dynamics allow to be recovered.
arXiv Machine Learning
Aug 7
Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles
arXiv:2608. 05522v1 Announce Type: cross Abstract: Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal.
arXiv Machine Learning
Jun 24
Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs
arXiv:2606. 23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics.
Hugging Face Trending Papers
Aug 6
Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles
Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian.
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 Machine Learning
Jun 8
Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series
arXiv:2606. 07385v1 Announce Type: cross Abstract: Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics.
arXiv Machine Learning
Aug 7
Scientific Machine Learning of Chaotic Systems Learns Reduced-Order Equations for Neural Populations
arXiv:2507. 03631v4 Announce Type: replace Abstract: Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data.