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.
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.
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.
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.
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.
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).
arXiv:2609.13194v1 Announce Type: cross Abstract: A large literature builds physical structure into learned dynamics on the premise that models respecting the underlying physics predict better. We te...
arXiv:2606. 21828v2 Announce Type: replace-cross Abstract: Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction.
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.
arXiv:2609.09904v1 Announce Type: cross Abstract: Federated clients that perform several local optimization steps can return parameter displacements with widely different magnitudes. The quadratic re...
arXiv:2606. 11431v1 Announce Type: new Abstract: Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training.
arXiv:2606. 01122v1 Announce Type: new Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss.
arXiv:2606. 03003v1 Announce Type: cross Abstract: A latent world model built from an equivariant encoder $E$ and an equivariant predictor $f$ inherits a provable symmetry of its training loss: when the world's dynamics genuinely carries a group $G$ acting on latents by an orthogonal representation $\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting the dynamics on a restricted slice of orientations mathematically determines it on the entire orbit (j\v{u} y\=i f\v{a}n s\=an).