arXiv Machine Learning

Neural Representation of Minimal Surfaces

arXiv:2607. 23437v1 Announce Type: cross Abstract: We propose a neural representation for minimal surfaces.

arXiv Machine Learning

Jun 18

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.

By Sheng-Gwo Chen, Chen-Chang Peng

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.

By Tancredi Schettini Gherardini

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.

By Tancredi Schettini Gherardini, Marco Usula

arXiv Machine Learning

Jul 20

Trainable Spline Representations for Physics-Informed Learning

arXiv:2607. 15751v1 Announce Type: new Abstract: This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning.

By Giovanni Canali, Nicola Demo, Gianluigi Rozza

benchmarks

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.

By Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen

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.

By Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor

rag 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

Jul 31

Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries

arXiv:2605. 00760v2 Announce Type: replace Abstract: This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network, the DeepONet framework.

By Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu

arXiv Machine Learning

Jun 17

INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

arXiv:2606. 18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN).

By Shayan Dodge (DESTeC, University of Pisa, Pisa, Italy), Alessandro Formisano (Department of Engineering, University of Campania Luigi Vanvitelli, Aversa, Italy), Sami Barmada (DESTeC, University of Pisa, Pisa, Italy)

arXiv Machine Learning

Jun 19

Evolutionary Two-Stage Hyperparameter Optimization Strategies for Physics-Informed Neural Networks

arXiv:2606. 20442v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training.

By Fedor Buzaev (HSE University), Dmitry Efremenko (HSE University), Egor Bugaev (HSE University), Andrei Ermakov (HSE University, AXXX), Denis Derkach (HSE University), Daria Pugacheva (HSE University, AXXX), Fedor Ratnikov (HSE University)

rag

arXiv AI

Jun 10

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

arXiv:2602. 02788v2 Announce Type: replace-cross Abstract: We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries.

By Benjamin D. Shaffer, Shawn Koohy, Brooks Kinch, M. Ani Hsieh, Nathaniel Trask

llms benchmarks safety

arXiv Machine Learning

Jun 16

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

arXiv:2606. 16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters.

By Vijay Kumar, Gautam Singh

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