Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling

Multi-fidelity surrogate modeling aims to learn an accurate surrogate at the highest fidelity level by combining data from multiple sources. Traditional methods relying on Gaussian processes can hardly scale to high-dimensional data. Deep learning approaches utilize neural network based encoders and decoders to improve scalability. These approaches share encoded representations across fidelities without including corresponding decoder parameters. At the highest fidelity, the representations are decoded with different parameters, making the shared information inherently inaccurate. This hinders inference performance, especially in out-of-distribution scenarios when the highest fidelity data has limited domain coverage. To address these limitations, we propose Multi-fidelity Residual Neural Processes (MFRNP), a novel multi-fidelity surrogate modeling framework. MFRNP optimizes lower fidelity decoders for accurate information sharing by aggregating lower fidelity surrogate outputs and models residual between the aggregation and ground truth on the highest fidelity. We show that MFRNP significantly outperforms current state-of-the-art in learning partial differential equations and a real-world climate modeling task.