Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models

• URL: http://arxiv.org/abs/2407.15110v1
• Date: Sun, 21 Jul 2024 10:40:50 GMT
• Title: Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models
• Authors: Jiaxiang Yi, Ji Cheng, Miguel A. Bessa,
• Abstract summary: Multi-fidelity machine learning methods integrate scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy for problems spanning low- and high-dimensional domains.
• Score: 0.34592277400656235
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy for problems spanning low- and high-dimensional domains, integrating a non-probabilistic regression model for the low-fidelity with a Bayesian model for the high-fidelity. The models are trained in a staggered scheme, where the low-fidelity model is transfer-learned to the high-fidelity data and a Bayesian model is trained for the residual. This three-model strategy -- deterministic low-fidelity, transfer learning, and Bayesian residual -- leads to a prediction that includes uncertainty quantification both for noisy and noiseless multi-fidelity data. The strategy is general and unifies the topic, highlighting the expressivity trade-off between the transfer-learning and Bayesian models (a complex transfer-learning model leads to a simpler Bayesian model, and vice versa). We propose modeling choices for two scenarios, and argue in favor of using a linear transfer-learning model that fuses 1) kernel ridge regression for low-fidelity with Gaussian processes for high-fidelity; or 2) deep neural network for low-fidelity with a Bayesian neural network for high-fidelity. We demonstrate the effectiveness and efficiency of the proposed strategies and contrast them with the state-of-the-art based on various numerical examples. The simplicity of these formulations makes them practical for a broad scope of future engineering applications.

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