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.

Disentangled Multi-Fidelity Deep Bayesian Active Learning

To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Other deep learning-based methods use the hierarchical structure, which only supports passing information from low-fidelity to high-fidelity. This approach also leads to the undesirable propagation of errors from low-fidelity representations to high-fidelity ones. We propose a novel disentangled deep Bayesian learning framework for multi-fidelity active learning, that learns the surrogate models conditioned on the distribution of functions at multiple fidelities.