  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 at the highest fidelity by actively acquiring data from multiple
fidelity levels. However, existing approaches based on Gaussian processes are
hardly scalable to high-dimensional data. Deep learning-based methods often
impose a hierarchical structure in hidden representations, which only supports
passing information from low-fidelity to high-fidelity. These approaches can
lead to the undesirable propagation of errors from low-fidelity representations
to high-fidelity ones. We propose a novel framework called Disentangled
Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), which learns the
surrogate models conditioned on the distribution of functions at multiple
fidelities. On benchmark tasks of learning deep surrogates of partial
differential equations including heat equation, Poisson's equation and fluid
simulations, our approach significantly outperforms state-of-the-art in
prediction accuracy and sample efficiency.
