|
Abstract:
|
In many scientific disciplines, time-evolving phenomena are frequently modeled by nonlinear ordinary differential equations (ODEs). We present an approach to learning ODEs with rigorous statistical inference from time series data. Our methodology builds on a popular technique for this task in which the ODEs to be estimated are assumed to be sparse linear combinations of several candidate functions, such as polynomials. In addition to producing point estimates of the nonzero terms in the estimated equations, we propose leveraging recent advances in high-dimensional statistical inference to quantify the uncertainty in the estimate of each term. We use both frequentist and Bayesian versions of regularized regression to estimate ODE systems as sparse combinations of terms that are statistically significant or have high posterior probabilities, respectively. We demonstrate through simulations that this approach allows us to recover the correct terms in the dynamics more often than existing methods that do not account for uncertainty.
|
