Deep Multi-Fidelity Active Learning of High-dimensional Outputs
This work aims to improve the efficiency of data collection for high-dimensional output functions, which is relevant for researchers and practitioners in computational physics and engineering design.
This paper addresses the challenge of efficiently estimating high-dimensional output functions in applications like physical simulation and engineering design by proposing a deep multi-fidelity active learning approach. It identifies optimal fidelity and input for new training examples to maximize the benefit-cost ratio, demonstrating its advantages in computational physics and engineering design.
Many applications, such as in physical simulation and engineering design, demand we estimate functions with high-dimensional outputs. The training examples can be collected with different fidelities to allow a cost/accuracy trade-off. In this paper, we consider the active learning task that identifies both the fidelity and input to query new training examples so as to achieve the best benefit-cost ratio. To this end, we propose DMFAL, a Deep Multi-Fidelity Active Learning approach. We first develop a deep neural network-based multi-fidelity model for learning with high-dimensional outputs, which can flexibly, efficiently capture all kinds of complex relationships across the outputs and fidelities to improve prediction. We then propose a mutual information-based acquisition function that extends the predictive entropy principle. To overcome the computational challenges caused by large output dimensions, we use multi-variate Delta's method and moment-matching to estimate the output posterior, and Weinstein-Aronszajn identity to calculate and optimize the acquisition function. The computation is tractable, reliable and efficient. We show the advantage of our method in several applications of computational physics and engineering design.