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.
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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...
arXiv:2602. 18084v2 Announce Type: replace Abstract: Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs.
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
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:2512. 20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...