PINNs in More General Geometry
Not on the map. Why?
Abstract (arXiv)
Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can be coded as loss functions to align the AI loss-minimisation goal with that of solving the geometric problem. This contribution to the Recent Progress in Computational String Geometry workshop proceedings introduces the PINN architecture defining principles, motivates how they are well suited for problems in differential geometry, and demonstrates their use via summaries of three works at this intersection.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 9 of its 27 references that are in the map. First posted on arXiv 27 Apr 2026.
Builds on
9 of 27 references.
References · 9
- 2015Automatic differentiation in machine learning: a surveycited by 855
- 2021Learning Size and Shape of Calabi-Yau Spacescited by 28
- 2022Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networkscited by 19
- 2022Machine Learned Calabi-Yau Metrics and Curvaturecited by 14
- 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
- 2023Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networkscited by 5
- 2026A Machine Learning Approach to the Nirenberg Problemcited by 5
- 2026Neural and numerical methods for G2-structures on contact Calabi-Yau 7-manifoldscited by 4
- 2026Minimising Willmore Energy via Neural Flowcited by 4
Built on by
Citing papers per year: 2026: 1.
1 paper.