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.
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.
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arXiv Machine Learning
Jun 2
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.
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
Sep 7
Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
The paper introduces a method called model‑constrained randomized Jacobian matching to enforce second‑order consistency when learning chaotic dynamical systems. By comparing Jacobians at randomly perturbed inputs, the approach implicitly penalises Hessian mismatch without computing full Hessian tensors, achieving $O(d^2)$ memory cost. Experiments on Lorenz 63 and Lorenz 96 show that this second‑order supervision reduces invariant‑measure error, improves Lyapunov‑spectrum accuracy, and avoids spurious attractors that plague first‑order methods.
arXiv Machine Learning
Aug 27
DAW: Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems
arXiv:2608. 22277v2 Announce Type: replace Abstract: Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts.
arXiv Machine Learning
Sep 15
Algorithmic Information Dynamics of Learning: A Certified, Differentiable Complexity Controller for Grokking
arXiv:2609.13197v1 Announce Type: new Abstract: Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the...
arXiv Machine Learning
Jul 17
An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications
arXiv:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
arXiv Machine Learning
Jun 5
PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability
arXiv:2606. 05191v1 Announce Type: new Abstract: Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements.
arXiv AI
Jul 31
Shared Symbolic Backbones for Physically Consistent Multi-Output Symbolic Regression
arXiv:2607. 26528v1 Announce Type: cross Abstract: Symbolic regression provides analytical expressions, but it is usually applied one output at a time.
arXiv Machine Learning
Aug 11
Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates
arXiv:2608. 08103v1 Announce Type: new Abstract: Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made.
arXiv AI
Jun 10
Between Amnesia and Chaos: A Memory Stability Expressivity Trilemma for Trainable Dissipative Oscillator Networks
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
arXiv Statistics ML
Aug 25
Symbolic Neural ODEs: Learning interpretable models from time-series data
arXiv:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...