arXiv Machine Learning
Jul 28
Neural Representation of Minimal Surfaces
arXiv:2607. 23437v1 Announce Type: cross Abstract: We propose a neural representation for minimal surfaces.
A Neural Network Framework for Geodesic-Like Curve Computation on Parametric Surfaces
arXiv:2606. 18759v1 Announce Type: cross Abstract: The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically.
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arXiv Machine Learning
Jun 11
Minimal surfaces, Knots, and Neural Networks
arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.
arXiv AI
Jun 4
Curvature-aware dynamic precision approach for physics-informed neural networks
arXiv:2606. 04736v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training.
arXiv Machine Learning
Jul 9
Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
arXiv:2607. 07623v1 Announce Type: new Abstract: Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks.
Hugging Face Trending Papers
Jul 8
Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects curvature that becomes a dominant source of nonlinearity.
arXiv AI
Jul 22
Riemannian Deep Learning:Modules, Networks, and Geometries
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv AI
Aug 3
A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem
arXiv:2607. 28733v1 Announce Type: cross Abstract: This proceedings contribution elaborates on the findings of arXiv:2605.
arXiv AI
Jul 24
Riemannian Deep Learning: Modules, Networks, and Geometries
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv Machine Learning
Jun 18
TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
arXiv:2601. 20361v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time.
arXiv Machine Learning
Jul 30
Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces
arXiv:2505. 16035v3 Announce Type: replace Abstract: We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers.
arXiv Machine Learning
22h ago
Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements
arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.
arXiv Machine Learning
Jun 19
Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.