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

Area of Science:

• Dynamical Systems and Mathematical Biology
• Computational Science and Engineering

Background:

• Estimating parameters in nonlinear ordinary differential equation (ODE) systems is crucial for scientific modeling.
• Traditional methods often rely on numerical ODE solvers, which can be slow and inaccurate, especially for high-dimensional or stiff systems.
• Measurement noise in biological data further complicates parameter estimation.

Approach:

• Introduced the Weak-form Estimation of Nonlinear Dynamics (WENDy) method, which avoids ODE solvers by converting the system's strong form to its weak form.
• Employs an Errors-In-Variables framework and iteratively reweighted least squares for robust parameter inference.
• Utilizes orthonormal test functions derived from C-infinity bump functions for improved accuracy.

Key Points:

• WENDy provides accurate parameter estimates for nonlinear ODEs, even with significant measurement noise.
• It is computationally efficient, often outperforming traditional methods by orders of magnitude for complex and stiff systems.
• Demonstrated effectiveness across diverse models in population biology, neuroscience, and biochemistry.

Conclusions:

• WENDy offers a robust and computationally efficient alternative for parameter estimation in nonlinear dynamical systems.
• The method's performance is competitive with, and often superior to, conventional approaches.
• Open-source code is available for reproducibility and further application.