👉 Multi-Fidelity Functionals (MLFs) are a sophisticated technique in machine learning and statistics that allow models to leverage information from multiple levels of data fidelity or resolution simultaneously. At their core, MLFs combine predictions from different models trained on data with varying levels of complexity or detail, effectively balancing the trade-off between bias and variance. This is achieved through a weighted sum of these predictions, where each model's contribution is determined by its fidelity to the training data. Higher-fidelity models (those trained on more detailed or complex data) are given greater weight, while lower-fidelity models (trained on simpler or more generalized data) contribute less. This approach not only enhances the robustness and generalization of predictive models but also allows for more efficient use of computational resources by focusing on the most informative aspects of the data. MLFs are particularly useful in scenarios where data comes from heterogeneous sources or when dealing with noisy or incomplete information, as they can effectively integrate diverse insights to produce more accurate and reliable predictions.
