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

Area of Science:

• Computational Biology
• Mathematical Modeling
• Systems Biology

Background:

• Estimating parameters in nonlinear systems of ordinary differential equations (ODEs) is crucial for understanding complex biological processes.
• Traditional methods often rely on numerical ODE solvers, which can be computationally expensive and sensitive to measurement noise.

Purpose of the Study:

• To introduce a novel method, Weak-form Estimation of Nonlinear Dynamics (WENDy), for robust and efficient parameter estimation in nonlinear ODE systems.
• To demonstrate the method's accuracy and computational advantages over existing techniques, particularly for high-dimensional and stiff systems.

Main Methods:

• WENDy converts the strong form of ODEs to their weak form, enabling parameter inference via regression.
• It utilizes an Errors-In-Variables framework and iteratively reweighted least squares for statistical robustness.
• Orthonormal test functions derived from bump functions enhance accuracy.

Main Results:

• WENDy provides accurate parameter estimates even with high levels of measurement noise.
• It is competitive with traditional methods for low-dimensional systems but significantly faster and more accurate for higher-dimensional and stiff systems.
• The method was successfully applied to diverse models in population biology, neuroscience, and biochemistry.

Conclusions:

• WENDy offers a computationally efficient and robust alternative for parameter estimation in nonlinear dynamical systems.
• Its performance advantages make it suitable for complex biological modeling, including population dynamics, neural activity, and biochemical pathways.
• The availability of open-source code facilitates reproducibility and adoption of the WENDy method.