arXiv Machine Learning July 23, 2026 By Abhishek Shankar

Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics

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arXiv:2607. 20235v1 Announce Type: cross Abstract: Classical regularization removes the binary-collision singularity from the Kepler problem, but its value as a representation for learned Hamiltonian dynamics has not been systematically isolated.

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arXiv Machine Learning

Aug 11

Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

arXiv:2608. 08322v1 Announce Type: cross Abstract: Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity.

By Muhammad Akbar Khan

benchmarks

arXiv Machine Learning

Jul 3

An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.

By Joseph Webb, Sadok Jerad, Coralia Cartis

arXiv Machine Learning

Aug 12

A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

arXiv:2608. 10235v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks.

By Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim Tewe

arXiv Machine Learning

Jul 28

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem

arXiv:2607. 23501v1 Announce Type: new Abstract: Locating periodic solutions of chaotic dynamical systems normally requires an initial guess close enough to the target orbit for numerical continuation or gradient-based search to converge.

By Nikolaos Kollias, Nikolaos Matzakos

arXiv Machine Learning

Jul 27

Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations

arXiv:2607. 21644v1 Announce Type: new Abstract: We present a goal-agnostic control framework for partial differential equations (PDEs) built around a joint-embedding predictive architecture (JEPA).

By Jonathan Gallagher, Roberto Guglielmi

rag diffusion benchmarks

arXiv Machine Learning

Jul 27

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.

By Zhangyong Liang, Huanhuan Gao

benchmarks

Related stories

Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem

Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers