Mixing space-time derivatives for video compressive sensing. - Yi Yang 010; Hayden Schaeffer; Wotao Yin; Stanley J. Osher (ACSSC, 2013)

Boundary detection in echocardiography using a Split Bregman edge detector and a topology preserving level set approach. - Nóirín Duggan; Hayden Schaeffer; Carole Le Guyader; Edward Jones; Martin Glavin; Luminita A. Vese (ISBI, 2013)

A Low Patch-Rank Interpretation of Texture. - Hayden Schaeffer; Stanley J. Osher (SIAM J. Imaging Sci., 2013)

Variational Models for Fine Structures. - Hayden Schaeffer (2013)

Active Contours with Free Endpoints. - Hayden Schaeffer; Luminita A. Vese (J. Math. Imaging Vis., 2014)

Variational Dynamics of Free Triple Junctions. - Hayden Schaeffer; Luminita A. Vese (J. Sci. Comput., 2014)

On the Compressive Spectral Method. - Alan Mackey; Hayden Schaeffer; Stanley J. Osher (Multiscale Model. Simul., 2014)

Sparse + low-energy decomposition for viscous conservation laws. - Thomas Y. Hou 001; Qin Li 007; Hayden Schaeffer (J. Comput. Phys., 2015)

An L1 Penalty Method for General Obstacle Problems. - Giang Tran; Hayden Schaeffer; William M. Feldman; Stanley J. Osher (SIAM J. Appl. Math., 2015)

Space-Time Regularization for Video Decompression. - Hayden Schaeffer; Yi Yang 010; Stanley J. Osher (SIAM J. Imaging Sci., 2015)

Real-Time Adaptive Video Compression. - Hayden Schaeffer; Yi Yang 010; Hongkai Zhao; Stanley J. Osher (SIAM J. Sci. Comput., 2015)

An Accelerated Method for Nonlinear Elliptic PDE. - Hayden Schaeffer; Thomas Y. Hou 001 (J. Sci. Comput., 2016)

Recovery guarantees for polynomial approximation from dependent data with outliers. - Lam Si Tung Ho; Hayden Schaeffer; Giang Tran; Rachel A. Ward (CoRR, 2018)

Extracting Sparse High-Dimensional Dynamics from Limited Data. - Hayden Schaeffer; Giang Tran; Rachel A. Ward (SIAM J. Appl. Math., 2018)

On the Convergence of the SINDy Algorithm. - Linan Zhang; Hayden Schaeffer (Multiscale Model. Simul., 2019)

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data. - Yifan Sun; Linan Zhang; Hayden Schaeffer (MSML, 2020)

Recovery guarantees for polynomial coefficients from weakly dependent data with outliers. - Lam Si Tung Ho; Hayden Schaeffer; Giang Tran; Rachel A. Ward (J. Approx. Theory, 2020)

Forward Stability of ResNet and Its Variants. - Linan Zhang; Hayden Schaeffer (J. Math. Imaging Vis., 2020)

Extracting Structured Dynamical Systems Using Sparse Optimization With Very Few Samples. - Hayden Schaeffer; Giang Tran; Rachel A. Ward; Linan Zhang (Multiscale Model. Simul., 2020)

Extending the Step-Size Restriction for Gradient Descent to Avoid Strict Saddle Points. - Hayden Schaeffer; Scott G. McCalla (SIAM J. Math. Data Sci., 2020)

Reduced Order Modeling using Shallow ReLU Networks with Grassmann Layers. - Kayla Bollinger; Hayden Schaeffer (MSML, 2021)

Function Approximation via Sparse Random Features. - Abolfazl Hashemi; Hayden Schaeffer; Robert Shi; Ufuk Topcu; Giang Tran; Rachel A. Ward (CoRR, 2021)

Conditioning of Random Feature Matrices: Double Descent and Generalization Error. - Zhijun Chen; Hayden Schaeffer (CoRR, 2021)

SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruning. - Yuege Xie; Bobby Shi; Hayden Schaeffer; Rachel A. Ward (CoRR, 2021)

Concentration of Random Feature Matrices in High-Dimensions. - Zhijun Chen; Hayden Schaeffer; Rachel A. Ward (MSML, 2022)

SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruning. - Yuege Xie; Robert Shi; Hayden Schaeffer; Rachel A. Ward (MSML, 2022)

HARFE: Hard-Ridge Random Feature Expansion. - Esha Saha; Hayden Schaeffer; Giang Tran (CoRR, 2022)

SRMD: Sparse Random Mode Decomposition. - Nicholas Richardson; Hayden Schaeffer; Giang Tran (CoRR, 2022)

Random Feature Models for Learning Interacting Dynamical Systems. - Yuxuan Liu; Scott G. McCalla; Hayden Schaeffer (CoRR, 2022)

BelNet: Basis enhanced learning, a mesh-free neural operator. - Zecheng Zhang; Wing Tat Leung; Hayden Schaeffer (CoRR, 2022)

PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers. - Yuxuan Liu; Zecheng Zhang; Hayden Schaeffer (CoRR, 2023)

D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators. - Zecheng Zhang; Christian Moya; Lu Lu; Guang Lin 001; Hayden Schaeffer (CoRR, 2023)

Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation. - Jingmin Sun; Yuxuan Liu; Zecheng Zhang; Hayden Schaeffer (CoRR, 2024)

LeMON: Learning to Learn Multi-Operator Networks. - Jingmin Sun; Zecheng Zhang; Hayden Schaeffer (CoRR, 2024)

PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics. - Yuxuan Liu; Jingmin Sun; Xinjie He; Griffin Pinney; Zecheng Zhang; Hayden Schaeffer (CoRR, 2024)

Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model. - Derek Jollie; Jingmin Sun; Zecheng Zhang; Hayden Schaeffer (CoRR, 2024)

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study. - Hao Liu; Zecheng Zhang; Wenjing Liao; Hayden Schaeffer (CoRR, 2024)

DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuning. - Zecheng Zhang; Christian Moya; Lu Lu; Guang Lin 001; Hayden Schaeffer (CoRR, 2024)

VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction. - Yadi Cao; Yuxuan Liu; Liu Yang; Rose Yu; Hayden Schaeffer; Stanley J. Osher (CoRR, 2024)

Bayesian Deep Operator Learning for Homogenized to Fine-Scale Maps for Multiscale PDE. - Zecheng Zhang; Christian Moya; Wing Tat Leung; Guang Lin 001; Hayden Schaeffer (Multiscale Model. Simul., 2024)

PROSE: Predicting Multiple Operators and Symbolic Expressions using multimodal transformers. - Yuxuan Liu; Zecheng Zhang; Hayden Schaeffer (Neural Networks, 2024)

A discretization-invariant extension and analysis of some deep operator networks. - Zecheng Zhang; Wing Tat Leung; Hayden Schaeffer (J. Comput. Appl. Math., 2025)

BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics. - Yuxuan Liu; Jingmin Sun; Hayden Schaeffer (CoRR, 2025)

A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions. - Elisa Negrini; Yuxuan Liu; Liu Yang; Stanley J. Osher; Hayden Schaeffer (CoRR, 2025)

Cauchy Random Features for Operator Learning in Sobolev Space. - Chunyang Liao; Deanna Needell; Hayden Schaeffer (CoRR, 2025)