arXiv:2607. 23437v1 Announce Type: cross Abstract: We propose a neural representation for minimal surfaces.
By Jiayin Sun, Albert Chern
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.
By Tancredi Schettini Gherardini, Marco Usula
NeuralSRNF is a new framework that enables efficient statistical shape analysis and generation of genus‑zero 3D and 4D objects undergoing nonrigid deformations. It replaces costly numerical SRNF inversion with a continuous, resolution‑agnostic neural representation that accurately reconstructs shapes and computes inverse SRNF maps in under 3 s, compared to over 10 min for traditional methods. Experiments on multiple datasets show that NeuralSRNF outperforms existing techniques in accuracy and speed across tasks such as geodesic computation, deformation transfer, statistical summarization, and shape generation.
By Awais Nizamani, Hamid Laga, Guanjin Wang, Farid Boussaid, Mohammed Bennamoun, Anuj Srivastava
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.
By Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor
arXiv:2607. 07623v1 Announce Type: new Abstract: Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks.
By Jianing Liu, Dong H. Zhang
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.