A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems

Area of Science:

• Bioprocess Engineering
• Mathematical Modeling
• Optimization

Background:

• Informative experiments are crucial for parameter estimation in nonlinear dynamic bioprocesses.
• Optimal experiment design techniques systematically create informative experiments.
• The E-criterion, maximizing the smallest eigenvalue of the Fisher information matrix, is key but faces computational hurdles.

Purpose of the Study:

• To address the non-differentiability and computational limitations of the E-criterion in optimal experiment design.
• To reformulate the maximization of the minimum eigenvalue problem for standard optimal control solvers.
• To enable the use of automatic differentiation for improved derivative computation.

Main Methods:

• A reformulation strategy from convex optimization is proposed.
• The method incorporates a matrix inequality constraint for positive semidefiniteness, using Sylvester's criterion.
• This transforms the eigenvalue maximization into a problem solvable by standard optimal control solvers with nonlinear constraints.

Main Results:

• The proposed reformulation successfully addresses the non-differentiability issue of the minimal eigenvalue function.
• The methodology allows for the integration of automatic differentiation within optimal control solvers.
• The approach was validated using a case study in predictive microbiology.

Conclusions:

• The convex optimization reformulation provides an effective solution for optimal experiment design in nonlinear dynamic bioprocesses.
• This approach enhances the systematic design of informative experiments, improving parameter estimation.
• The method offers a computationally tractable alternative for applying the E-criterion in complex bioprocess modeling.