arXiv:2608. 08091v1 Announce Type: cross Abstract: Dynamical systems model trajectory data generated by fixed underlying dynamics, with applications ranging from biology to physics.
arXiv:2609.07031v1 Announce Type: new Abstract: Learning with group invariances is central to many scientific and geometric learning problems, yet its computational foundations remain poorly understo...
arXiv:2608. 01582v1 Announce Type: cross Abstract: Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling.
arXiv:2512. 20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning.
arXiv:2509. 03340v4 Announce Type: replace-cross Abstract: Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking.
The paper introduces a diagnostic tool that measures how neural emulators of partial differential equations capture physical symmetries by evaluating the overlap of loss gradients along symmetry-related states. This metric probes the local geometry of the learned loss landscape and goes beyond traditional equivariance tests by directly assessing learning dynamics. Applied to autoregressive fluid flow emulators, the study shows that orbit-wise gradient coherence enables generalization over symmetry transformations and reveals when training selects a symmetry-compatible basin.
arXiv:2412. 12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods.
arXiv:2608.24700v1 Announce Type: new Abstract: When a network has learned a function with a known symmetry, can that symmetry be moved through the parametrisation---is there a motion in parameter sp...
The paper presents a variational learning framework that simultaneously infers non‑parametric interaction kernels and environmental or intra‑agent forces in collective dynamics. It extends existing methods to handle both interaction and environmental components, validating the approach on benchmark models such as synchronization, alignment, and attraction‑repulsion systems. A model‑selection procedure is also introduced to identify the best explanatory framework from trajectory data, enabling direct recovery of mechanistic interaction mechanisms.
arXiv:2512. 05337v2 Announce Type: replace-cross Abstract: We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$.
arXiv:2410. 11894v3 Announce Type: replace-cross Abstract: Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum.
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv:2605.06140v3 Announce Type: replace-cross Abstract: Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such...