Manifold learning for parameter reduction.

Area of Science:

• Computational Mathematics
• Systems Biology
• Nonlinear Dynamics

Background:

• Large-scale dynamical systems often exhibit reduced complexity through a few state variables, simplifying analysis.
• Manual model reduction is impractical for high-dimensional systems, necessitating automated computational approaches.
• Current computational methods excel at state space reduction but often neglect parameter reduction.

Purpose of the Study:

• To develop systematic, data-driven methods for effective parameter identification in complex models.
• To extend current data-driven state space reduction techniques to include parameter space reduction.
• To accelerate the exploration of high-dimensional parameter spaces in nonlinear dynamical systems.

Main Methods:

• Leveraging nonlinear manifold learning techniques for state space reduction.
• Implementing data-driven parameter reduction through effective parameter identification.
• Integrating state and parameter reduction for comprehensive model simplification.

Main Results:

• Demonstrated a data-driven approach for identifying effective model parameters.
• Extended existing computational reduction frameworks to address parameter dimensionality.
• Enabled more efficient exploration of complex, high-dimensional parameter spaces.

Conclusions:

• Data-driven effective parameter identification is crucial for combating the curse of dimensionality in complex models.
• This approach complements state space reduction, offering a more complete model simplification strategy.
• Accelerated exploration of parameter spaces facilitates optimization of complex input-output relations.