deeponet

本文介绍了一种用于DeepONet代理模型的有理增强Chebyshev主干，提高了模拟具有薄边界层的高Péclet输运问题的准确性。

This paper extends Topological DeepONets to handle functional measurements on Hausdorff locally convex spaces, replacing point samples with continuous linear functionals and introducing fixed and adaptive measurement systems. The framework is validated on several benchmarks including a non-normable input space, and demonstrates compact, discretization-portable coordinates for operator learning.

This paper introduces feature interaction modules based on factorization machines into physics-informed neural networks and neural operators (FM-PINN, FM-Operator, FM-DeepONet) to better capture spatio-temporal variable couplings for solving parameterized PDEs, showing accuracy gains particularly on shock-dominated equations.

提出了一种用于MIONet的混合最小二乘/梯度下降方法，通过利用交替最小二乘法优化多个分支网络的最后一层参数，并借助Kronecker和Khatri-Rao乘积，从而加速训练。

提出KL-DNN，一种可扩展的算子学习框架，利用Karhunen-Loève展开处理大规模PDE问题，在三维碳封存问题上实现了比DeepONet更低的误差和两个数量级的加速。