5 papers
Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Yahong Yang, Zecheng Zhang, Wei Zhu +2
We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms. In contrast to standard operator-lear…
Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
Hao Liu, Zecheng Zhang, Wenjing Liao +1
Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for un…
Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics
Biraj Dahal, Jiahui Cheng, Hao Liu +2
Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we p…
IDENT Review: Recent Advances in Identification of Differential Equations from Noisy Data
Roy Y. He, Hao Liu, Wenjing Liao +1
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the und…
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…