Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion.

Area of Science:

• Statistical modeling
• Machine learning
• Computational mathematics

Background:

• Gaussian process regression enhances prediction accuracy by fusing few high-fidelity data with many low-fidelity data.
• Existing multi-fidelity data fusion methods model the high-fidelity function as dependent on low-fidelity data and additional variables.
• The relationship between high- and low-fidelity models can be complex, not always a direct function.

Purpose of the Study:

• To explore mathematical algorithms for multi-fidelity information fusion.
• To improve the representation of high-fidelity functions using limited training data.
• To investigate the use of additional functions of low-fidelity data in fusion techniques.

Main Methods:

• Modeling the high-fidelity function using multiple variables, including the low-fidelity model and its derivatives.
• Applying Gaussian processes for function approximation.
• Exploring connections with embedology techniques from topology and dynamical systems.

Main Results:

• Demonstrated that incorporating derivatives or shifts of the low-fidelity model significantly improves high-fidelity function approximation.
• Showcased improved representation of the high-fidelity function with fewer training points.
• Validated the approach with examples ranging from simple models to complex computational biology systems like Hodgkin-Huxley neural oscillations.

Conclusions:

• Multi-fidelity information fusion, particularly using derivatives of low-fidelity data, is effective for enhancing Gaussian process regression.
• This approach offers a powerful method for improving predictive accuracy when high-fidelity data is scarce.
• The techniques show promise for applications in computational biology and other scientific domains requiring accurate modeling from limited data.