Data-driven discovery of partial differential equations
University of Washington Applied Physics Laboratory · University of Washington · +1 more institution
Abstract
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with…
Citation impact
- FWCI
- 57.96
- Percentile
- 100%
- References
- 52
Authors
4Topics & keywords
- Partial differential equation
- Computer science
- Stochastic partial differential equation
- Regression
- Differential (mechanical device)
- Data mining
- Mathematics
- Statistics