An official website of the United States government
ABSTRACT We introduce MF-Box, an extended version of MFEmulator, designed as a fast surrogate for power spectra, trained using N-body simulation suites from various box sizes and particle loads. To demonstrate MF-Box’s effectiveness, we design simulation suites that include low-fidelity (LF) suites (L1 and L2) at 256 and $$100 \, \rm {Mpc\, ~}h^{-1}$$, each with 1283 particles, and a high-fidelity (HF) suite with 5123 particles at $$256 \, \rm {Mpc\, ~}h^{-1}$$, representing a higher particle load compared to the LF suites. MF-Box acts as a probabilistic resolution correction function, learning most of the cosmological dependencies from L1 and L2 simulations and rectifying resolution differences with just three HF simulations using a Gaussian process. MF-Box successfully emulates power spectra from our HF testing set with a relative error of $$\lt 3~{{\ \rm per\ cent}}$$ up to $$k \simeq 7 \, h\rm {Mpc}{^{-1}}$$ at z ∈ [0, 3], while maintaining a cost similar to our previous multifidelity approach, which was accurate only up to z = 1. The addition of an extra LF node in a smaller box significantly improves emulation accuracy for MF-Box at $$k \gt 2 \, h\rm {Mpc}{^{-1}}$$, increasing it by a factor of 10. We conduct an error analysis of MF-Box based on computational budget, providing guidance for optimizing budget allocation per fidelity node. Our proposed MF-Box enables future surveys to efficiently combine simulation suites of varying quality, effectively expanding the range of emulation capabilities while ensuring cost efficiency.
more »
« less
Mitigating the Effects of Source-Dependent Bias and Noise on Multi-Source Bayesian Optimization: Application to Materials Design
Abstract Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are increasingly used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. Existing multi-fidelity BO (MFBO) methods operate under the following two assumptions: (1) Leveraging global (rather than local) correlation between HF and LF sources, and (2) Associating all the data sources with the same noise process. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. To dispense with these incorrect assumptions, we propose an MF emulation method that (1) learns a noise model for each data source, and (2) enables BO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.
more »
« less
- Award ID(s):
- 2211908
- PAR ID:
- 10520586
- Publisher / Repository:
- American Society of Mechanical Engineers
- Date Published:
- ISBN:
- 978-0-7918-8731-8
- Format(s):
- Medium: X
- Location:
- Boston, Massachusetts, USA
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Resource management in engineering design seeks to optimally allocate while maximizing the performance metrics of the final design. Bayesian optimization (BO) is an efficient design framework that judiciously allocates resources through heuristic-based searches, aiming to identify the optimal design region with minimal experiments. Upon recommending a series of experiments or tasks, the framework anticipates their completion to augment its knowledge repository, subsequently guiding its decisions toward the most favorable next steps. However, when confronted with time constraints or other resource challenges, bottlenecks can hinder the traditional BO’s ability to assimilate knowledge and allocate resources with efficiency. In this work, we introduce an asynchronous learning framework designed to utilize idle periods between experiments. This model adeptly allocates resources, capitalizing on lower fidelity experiments to gather comprehensive insights about the target objective function. Such an approach ensures that the system progresses uninhibited by the outcomes of prior experiments, as it provisionally relies on anticipated results as stand-ins for actual outcomes. We initiate our exploration by addressing a basic problem, contrasting the efficacy of asynchronous learning against traditional synchronous multi-fidelity BO. We then employ this method to a practical challenge: optimizing a specific mechanical characteristic of a dual-phase steel.more » « less
-
Chaudhuri, K (Ed.)How can we efficiently gather information to optimize an unknown function, when presented with multiple, mutually dependent information sources with different costs? For example, when optimizing a physical system, intelligently trading off computer simulations and real-world tests can lead to significant savings. Existing multi-fidelity Bayesian optimization methods, such as multi-fidelity GP-UCB or Entropy Search-based approaches, either make simplistic assumptions on the interaction among different fidelities or use simple heuristics that lack theoretical guarantees. In this paper, we study multifidelity Bayesian optimization with complex structural dependencies among multiple outputs, and propose MF-MI-Greedy, a principled algorithmic framework for addressing this problem. In particular, we model different fidelities using additive Gaussian processes based on shared latent relationships with the target function. Then we use cost-sensitive mutual information gain for efficient Bayesian optimization. We propose a simple notion of regret which incorporates the varying cost of different fidelities, and prove that MF-MI-Greedy achieves low regret. We demonstrate the strong empirical performance of our algorithm on both synthetic and real-world datasets.more » « less
-
null (Ed.)The dynamic stall phenomenon produces adverse aerodynamic loading, which negatively affects the structural strength and life of aerodynamic systems. Aerodynamic shape optimization (ASO) provides a practical approach for delaying and mitigating dynamic stall characteristics without the addition of an auxiliary system. A typical ASO investigation requires multiple evaluations of accurate but time-consuming computational fluid dynamics (CFD) simulations. In the case of dynamic stall, unsteady CFD simulations are required for airfoil shape evaluation; combining it with high-dimensions of airfoil shape parameterization renders the ASO investigation computationally costly. In this study, metamodel-based optimization (MBO) is proposed using the multifidelity modeling (MFM) technique to efficiently conduct ASO investigation for computationally expensive dynamic stall cases. MFM methods combine data from accurate high-fidelity (HF) simulations and fast low-fidelity (LF) simulations to provide accurate and fast predictions. In particular, Cokriging regression is used for approximating the objective and constraint functions. The airfoil shape is parameterized using six PARSEC parameters. The objective and constraint functions are evaluated for a sinusoidally oscillating airfoil with the unsteady Reynolds-averaged Navier-Stokes equations at a Reynolds number of 135,000, Mach number of 0.1, and reduced frequency of 0.05. The initial metamodel is generated using 220 LF and 20 HF samples. The metamodel is then sequentially refined using the expected improvement infill criteria and validated with the normalized root mean square error. The refined metamodel is utilized for finding the optimal design. The optimal airfoil shape shows higher thickness, larger leading-edge radius, and an aft camber compared to baseline (NACA 0012). The optimal shape delays the dynamic stall occurrence by 3 degrees and reduces the peak aerodynamic coefficients. The performance of the MFM method is also compared with the single-fidelity metamodeling method using HF samples. Both the approaches produced similar optimal shapes; however, the optimal shape from MFM achieved a minimum objective function value while more closely satisfying the constraint at a computational cost saving of around 41%.more » « less
-
By querying approximate surrogate models of different fidelity as available information sources, Multi-Fidelity Bayesian Optimization (MFBO) aims at optimizing unknown functions that are costly or infeasible to evaluate. Existing MFBO methods often assume that approximate surrogates have consistently high or low fidelity across the input domain. However, approximate evaluations from the same surrogate can have different fidelity at different input regions due to data availability and model constraints, especially when considering machine learning surrogates. In this work, we investigate MFBO when multi-fidelity approximations have input-dependent fidelity. By explicitly capturing input dependency for multi-fidelity queries in a Gaussian Process (GP), our new input-dependent MFBO (iMFBO) with learnable noise models better captures the fidelity of each information source in an intuitive way. We further design a new acquisition function for iMFBO and prove that the queries selected by iMFBO have higher quality than those by naive MFBO methods, with a derived sub-linear regret bound. Experiments on both synthetic and real-world data demonstrate its superior empirical performance.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/DETC2023-114414
