Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics

TL;DR

WENDy is a novel method for estimating parameters in nonlinear ODE models that avoids numerical solvers, offering high accuracy and robustness, especially for high-dimensional and stiff systems, with significant speed advantages.

Contribution

The paper introduces WENDy, a weak-form regression approach for parameter estimation in nonlinear ODEs that is faster and more accurate than traditional methods, especially for complex systems.

Findings

WENDy achieves high accuracy in parameter estimation for various biological models.

The method is robust to measurement noise and computationally efficient for high-dimensional systems.

WENDy outperforms conventional solver-based methods in speed and accuracy for stiff and large systems.

Abstract

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support sizes. We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (https://github.com/MathBioCU/WENDy).