Learning partial differential equations via data discovery and sparse optimization

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

PDEs with compressed solutions

(2015) Russel E. Caflisch et al.   Communications in Mathematical Sciences

Sparse + low-energy decomposition for viscous conservation laws

(2015) Thomas Y. Hou et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries

(2015) Syuzanna Sargsyan et al.   PHYSICAL REVIEW E

An $L^1$ Penalty Method for General Obstacle Problems

(2015) Giang Tran et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

On the Compressive Spectral Method

(2014) Alan Mackey et al.   MULTISCALE MODELING & SIMULATION

Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator

(2014) Vidvuds Ozoliņš et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems

(2014) Steven L. Brunton et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Compressive sensing as a paradigm for building physics models

(2013) Lance J. Nelson et al.   PHYSICAL REVIEW B

Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements

(2013) Ido Bright et al.   PHYSICS OF FLUIDS

Sparse dynamics for partial differential equations

(2013) H. Schaeffer et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Compressed modes for variational problems in mathematics and physics

(2013) V. Ozolins et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method

(2012) Bingsheng He et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

(2010) Antonin Chambolle et al.   JOURNAL OF MATHEMATICAL IMAGING AND VISION

Distilling Free-Form Natural Laws from Experimental Data

(2009) Michael Schmidt et al.   SCIENCE

The Split Bregman Method for L1-Regularized Problems

(2009) Tom Goldstein et al.   SIAM Journal on Imaging Sciences

A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

(2009) Amir Beck et al.   SIAM Journal on Imaging Sciences