Cost-effective search for lower-error region in material parameter space using multifidelity Gaussian process modeling

Information regarding precipitate shapes is critical for estimating material parameters. Hence, we considered estimating a region of material parameter space in which a computational model produces precipitates having shapes similar to those observed in the experimental images. This region, called the lower-error region (LER), reflects intrinsic information of the material contained in the precipitate shapes. However, the computational cost of LER estimation can be high because the accurate computation of the model is required many times to better explore parameters. To overcome this difficulty, we used a Gaussian-process-based multifidelity modeling, in which training data can be sampled from multiple computations with different accuracy levels (fidelity). Lower-fidelity samples may have lower accuracy, but the computational cost is lower than that for higher-fidelity samples. Our proposed sampling procedure iteratively determines the most cost-effective pair of a point and a fidelity level for enhancing the accuracy of LER estimation. We demonstrated the efficiency of our method through estimation of the interface energy and lattice mismatch between MgZn2 and {alpha}-Mg phases in an Mg-based alloy. The results showed that the sampling cost required to obtain accurate LER estimation could be drastically reduced.

Multi-objective Bayesian Optimization using Pareto-frontier Entropy

This paper studies an entropy-based multi-objective Bayesian optimization (MBO). The entropy search is successful approach to Bayesian optimization. However, for MBO, existing entropy-based methods ignore trade-off among objectives or introduce unreliable approximations. We propose a novel entropy-based MBO called Pareto-frontier entropy search (PFES) by considering the entropy of Pareto-frontier, which is an essential notion of the optimality of the multi-objective problem. Our entropy can incorporate the trade-off relation of the optimal values, and further, we derive an analytical formula without introducing additional approximations or simplifications to the standard entropy search setting. We also show that our entropy computation is practically feasible by using a recursive decomposition technique which has been known in studies of the Pareto hyper-volume computation. Besides the usual MBO setting, in which all the objectives are simultaneously observed, we also consider the decoupled setting, in which the objective functions can be observed separately. PFES can easily adapt to the decoupled setting by considering the entropy of the marginal density for each output dimension. This approach incorporates dependency among objectives conditioned on Pareto-frontier, which is ignored by the existing method. Our numerical experiments show effectiveness of PFES through several benchmark datasets.

Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization

In a standard setting of Bayesian optimization (BO), the objective function evaluation is assumed to be highly expensive. Multi-fidelity Bayesian optimization (MFBO) accelerates BO by incorporating lower fidelity observations available with a lower sampling cost. In this paper, we focus on the information-based approach, which is a popular and empirically successful approach in BO. For MFBO, however, existing information-based methods are plagued by difficulty in estimating the information gain. We propose an approach based on max-value entropy search (MES), which greatly facilitates computations by considering the entropy of the optimal function value instead of the optimal input point. We show that, in our multi-fidelity MES (MF-MES), most of additional computations, compared with usual MES, is reduced to analytical computations. Although an additional numerical integration is necessary for the information across different fidelities, this is only in one dimensional space, which can be performed efficiently and accurately. Further, we also propose parallelization of MF-MES. Since there exist a variety of different sampling costs, queries typically occur asynchronously in MFBO. We show that similar simple computations can be derived for asynchronous parallel MFBO. We demonstrate effectiveness of our approach by using benchmark datasets and a real-world application to materials science data.