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- W4311431087 abstract "Neural networks with PDEs embedded in their loss functions (physics-informed neural networks) are employed as a function approximators to find solutions to the Ricci flow (a curvature based evolution) of Riemannian metrics. A general method is developed and applied to the real torus. The validity of the solution is verified by comparing the time evolution of scalar curvature with that found using a standard PDE solver, which decreases to a constant value of 0 on the whole manifold. We also consider certain solitonic solutions to the Ricci flow equation in two real dimensions. We create visualisations of the flow by utilising an embedding into $mathbb{R}^3$. Snapshots of highly accurate numerical evolution of the toroidal metric over time are reported. We provide guidelines on applications of this methodology to the problem of determining Ricci flat Calabi--Yau metrics in the context of String theory, a long standing problem in complex geometry." @default.
- W4311431087 created "2022-12-26" @default.
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- W4311431087 date "2022-11-30" @default.
- W4311431087 modified "2023-09-24" @default.
- W4311431087 title "A physics-informed search for metric solutions to Ricci flow, their embeddings, and visualisation" @default.
- W4311431087 doi "https://doi.org/10.48550/arxiv.2212.05892" @default.
- W4311431087 hasPublicationYear "2022" @default.
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