12 citations · 25 across the 18 of their papers we have counts for
21 papers
Vector- and tensor-meson resonance contributions to decays
Yuan-Guo Xu, Qin-Ze Song, Bo Lan +1
Light vector- and tensor-meson resonance contributions to the three-body decays are studied in a quasi-two-body framework combined with SU(3) flavor relations f…
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…
PI-MFM: Physics-informed multimodal foundation model for solving partial differential equations
Min Zhu, Jingmin Sun, Zecheng Zhang +2
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across…
Deep Neural Operator Learning for Probabilistic Models
Erhan Bayraktar, Qi Feng, Zecheng Zhang +1
We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a b…
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…
A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theory
Adrien Weihs, Jingmin Sun, Zecheng Zhang +1
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces…
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…
CCS: Controllable and Constrained Sampling with Diffusion Models via Initial Noise Perturbation
Bowen Song, Zecheng Zhang, Zhaoxu Luo +6
Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial…
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…
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…
Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model
Derek Jollie, Jingmin Sun, Zecheng Zhang +1
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-depe…
PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
Yuxuan Liu, Jingmin Sun, Xinjie He +3
We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics…
Deep Analysis of Time Series Data for Smart Grid Startup Strategies: A Transformer-LSTM-PSO Model Approach
Zecheng Zhang
Grid startup, an integral component of the power system, holds strategic importance for ensuring the reliability and efficiency of the electrical grid. However, current methodologi…
LeMON: Learning to Learn Multi-Operator Networks
Jingmin Sun, Zecheng Zhang, Hayden Schaeffer
Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure t…
MODNO: Multi Operator Learning With Distributed Neural Operators
Zecheng Zhang
The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, r…
Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation
Jingmin Sun, Yuxuan Liu, Zecheng Zhang +1
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foun…
Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks
Christian Moya, Amirhossein Mollaali, Zecheng Zhang +2
In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for…
D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators
Zecheng Zhang, Christian Moya, Lu Lu +2
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. Ho…
Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensors
Guang Lin, Na Ou, Zecheng Zhang +1
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired fro…
PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers
Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer
Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions,…
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
Guang Lin, Zecheng Zhang, Zhidong Zhang
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from…