deeponet

The article introduces a rationally enriched Chebyshev trunk for DeepONet surrogate models, enhancing accuracy in simulating high-Péclet transport problems with thin boundary layers.

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.

Proposes a hybrid least squares/gradient descent method for MIONets to accelerate training by using alternating least squares for the last layer parameters of multiple branch networks, leveraging Kronecker and Khatri-Rao products.

Proposes KL-DNN, a scalable operator learning framework that uses Karhunen-Loève expansions to handle large-scale PDE problems, achieving lower errors and two-order-of-magnitude speedup over DeepONet on a 3D carbon storage problem.