Multi-Fidelity Modeling
Definition
Training with a mix of cheap low-fidelity data and expensive high-fidelity data: a small number of high-fidelity samples corrects a large pool of low-fidelity samples, maximizing accuracy under a fixed budget.
What it is
Low-fidelity data (coarse mesh, simplified physics, potential flow / Euler) is cheap and can be generated in bulk; high-fidelity data (fine mesh, RANS/LES, fully coupled) is expensive and scarce. Multi-fidelity methods use the low-fidelity model to capture the overall trend and learn a correction from the high-fidelity samples (additive or multiplicative bridging, or a multi-level Gaussian process), then combine the two.
Key points
- Budget allocation is the central question: high-fidelity samples are typically 1%-10% of the total, and where you place them matters more than the model architecture.
- Correlation is a prerequisite: if low- and high-fidelity trends disagree (e.g. the low-fidelity model misses separation or turbulence), the correction fails or even hurts.
- Common implementations: co-Kriging / multi-level Gaussian processes, transfer-learning style neural networks, residual correction networks.
- It pairs naturally with uncertainty quantification: uncertainty in low-fidelity regions is calibrated by high-fidelity samples.
Common pitfalls / boundaries
- The low-fidelity model must not miss the governing physics; otherwise the correction itself is strongly nonlinear and unlearnable.
- Never report only the total sample count — state the low/high-fidelity ratio and each one's cost.