175 citations · 317 across the 46 of their papers we have counts for
9 papers · 1 filter
Inexact Proximal Point Algorithms for Zeroth-Order Global Optimization
Minxin Zhang, Fuqun Han, Yat Tin Chow +2
This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theo…
Differentially Private Random Feature Model
Chunyang Liao, Deanna Needell, Hayden Schaeffer +1
Designing privacy-preserving machine learning algorithms has received great attention in recent years, especially in the setting when the data contains sensitive information. Diffe…
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…
VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction
Yadi Cao, Yuxuan Liu, Liu Yang +3
In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, ex…
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…
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…
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…