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Abstract Graphene aerogels (GAs), a special class of 3D graphene assemblies, are well known for their exceptional combination of high strength, lightweightness, and high porosity. However, due to microstructural randomness, the mechanical properties of GAs are also highly stochastic, an issue that has been observed but insufficiently addressed. In this work, we develop Gaussian process metamodels to not only predict important mechanical properties of GAs but also quantify their uncertainties. Using the molecular dynamics simulation technique, GAs are assembled from randomly distributed graphene flakes and spherical inclusions, and are subsequently subject to a quasi-static uniaxial tensile load to deduce mechanical properties. Results show that given the same density, mechanical properties such as the Young’s modulus and the ultimate tensile strength can vary substantially. Treating density, Young’s modulus, and ultimate tensile strength as functions of the inclusion size, and using the simulated GA results as training data, we build Gaussian process metamodels that can efficiently predict the properties of unseen GAs. In addition, statistically valid confidence intervals centered around the predictions are established. This metamodel approach is particularly beneficial when the data acquisition requires expensive experiments or computation, which is the case for GA simulations. The present research quantifies the uncertain mechanical properties of GAs, which may shed light on the statistical analysis of novel nanomaterials of a broad variety.
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Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation
Abstract We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-tobservations; (ii) Student-tprocesses (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.
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- PAR ID:
- 10231134
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Statistics and Computing
- Volume:
- 31
- Issue:
- 4
- ISSN:
- 0960-3174
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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