184 citations · 270 across the 14 of their papers we have counts for
17 papers
MOSAIC-SR: Transformer-Guided Symbolic Regression for Scientific Equation Recovery
Peiyi Zheng, Yanming Kang, Hans De Sterck +1
Symbolic regression aims to recover closed-form equations from observations, providing interpretable models for scientific discovery. Existing approaches struggle to combine flexib…
Stable Mesh-Free Variational Radial Basis Function Approximation for Elliptic PDEs and Obstacle Problems
Tan Phuong Dong Le, Giang Tran, Hans De Sterck
We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is…
2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited
Jerome Gilles, Giang Tran, Stanley Osher
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present se…
Fast Multipole Attention: A Scalable Multilevel Attention Mechanism for Text and Images
Yanming Kang, Giang Tran, Hans De Sterck
While Transformer networks benefit from a global receptive field, their quadratic cost relative to sequence length restricts their application to long sequences and high-resolution…
Generalization Bound for Diffusion Models using Random Features
Esha Saha, Giang Tran
Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with…
SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemics
Esha Saha, Lam Si Tung Ho, Giang Tran
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious…
SRMD: Sparse Random Mode Decomposition
Nicholas Richardson, Hayden Schaeffer, Giang Tran
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by con…
HARFE: Hard-Ridge Random Feature Expansion
Esha Saha, Hayden Schaeffer, Giang Tran
We propose a random feature model for approximating high-dimensional sparse additive functions called the hard-ridge random feature expansion method (HARFE). This method utilizes a…
Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Data
Lam Si Tung Ho, Nicholas Richardson, Giang Tran
In this paper, we propose an adaptive group Lasso deep neural network for high-dimensional function approximation where input data are generated from a dynamical system and the tar…
Generalization Bounds for Sparse Random Feature Expansions
Abolfazl Hashemi, Hayden Schaeffer, Robert Shi +3
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach…
Recovery guarantees for polynomial approximation from dependent data with outliers
Lam Si Tung Ho, Hayden Schaeffer, Giang Tran +1
Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, ma…
Extracting structured dynamical systems using sparse optimization with very few samples
Hayden Schaeffer, Giang Tran, Rachel Ward +1
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems fr…
Learning Dynamical Systems and Bifurcation via Group Sparsity
Hayden Schaeffer, Giang Tran, Rachel Ward
Learning governing equations from a family of data sets which share the same physical laws but differ in bifurcation parameters is challenging. This is due, in part, to the wide ra…
Extracting Sparse High-Dimensional Dynamics from Limited Data
Hayden Schaeffer, Giang Tran, Rachel Ward
Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; howe…
Exact Recovery of Chaotic Systems from Highly Corrupted Data
Giang Tran, Rachel Ward
Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields. This task becomes prohibitive when suc…
An L1 Penalty Method for General Obstacle Problems
Giang Tran, Hayden Schaeffer, William M. Feldman +1
We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like…
PDEs with Compressed Solutions
Russel E. Caflisch, Stanley J. Osher, Hayden Schaeffer +1
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted t…