用物理信息神经网络解决微分几何问题，让AI自动学习几何函数。
PINNs in More General Geometry
- 将微分几何中的泛函最小化转化为神经网络损失函数
- 通过三个案例展示在复杂几何结构上的求解能力
- 适合对几何建模与深度学习交叉研究的学者
基于微分条件设计损失函数的神经架构是物理信息神经网络（PINN）模型的基础。由于许多微分几何问题可表述为某类微分泛函的最小化，这些泛函可被编码为损失函数，使人工智能的损失最小化目标与几何问题求解目标对齐。本文在近期计算弦几何研讨会论文集中，阐述了定义PINN架构的原则，论证其在微分几何问题中的适用性，并通过三篇该交叉领域的研究成果予以演示。
原文摘要 · Abstract (English)
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.
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