3 papers
math.NA2025
Finite Element Representation Network (FERN) for Operator Learning with a Localized Trainable Basis
Zecheng Zhang, Hao Liu, Guosheng Fu +2
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from inp…
cs.LG2025
Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guarantees
Zecheng Zhang, Hao Liu, Wenjing Liao +1
We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different dis…
cs.LG2024
DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuning
Zecheng Zhang, Christian Moya, Lu Lu +2
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning th…