Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling.

Area of Science:

• Computational Science
• Data Science
• Engineering

Background:

• Multi-fidelity modeling combines low-cost and high-fidelity data for accurate predictions.
• Existing methods rely on strong correlations, but low-fidelity models can be inaccurate outside specific parameter ranges.

Purpose of the Study:

• To develop a probabilistic framework for multi-fidelity modeling that learns complex, nonlinear cross-correlations.
• To safeguard against erroneous predictions from low-fidelity models outside their validity regime.
• To extend existing linear autoregressive methodologies with enhanced capabilities.

Main Methods:

• Utilizes Gaussian process regression and nonlinear autoregressive schemes.
• Learns space-dependent cross-correlations between models of variable fidelity.
• Integrates low-fidelity model outputs with high-fidelity observations.

Main Results:

• Demonstrates effective learning of complex nonlinear and space-dependent cross-correlations.
• Successfully safeguards against low-fidelity models providing wrong trends.
• Achieves significant computational gains compared to high-fidelity-only approaches.

Conclusions:

• The proposed framework offers a fundamental extension to multi-fidelity information fusion algorithms.
• Maintains algorithmic complexity and computational cost similar to existing linear methods.
• Validated on synthetic and real-world computational fluid dynamics datasets.