1 citations · 1 across the 8 of their papers we have counts for
8 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…
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…
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…
Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation
Hao Liu, Jiahui Cheng, Wenjing Liao
Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Neverthe…
Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning
Hao Liu, Biraj Dahal, Rongjie Lai +1
Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this co…
Fourier Features for Identifying Differential Equations (FourierIdent)
Mengyi Tang, Hao Liu, Wenjing Liao +1
We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are c…