On Transfer Learning of Neural Networks Using Bi-Fidelity Data for Uncertainty Propagation

De, Subhayan; Britton, Jolene; Reynolds, Matthew; Skinner, Ryan; Jansen, Kenneth E.; Doostan, Alireza

doi:10.1615/int.j.uncertaintyquantification.2020033267

Cited by 50 publications

(19 citation statements)

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“…In essence, if a LF estimate provides satisfactory results then there is little to be gained through HF samples and a BF approximation. As the number of HF samples increases, we observe crossover points where the the HF estimate is better than the BF estimate, which is typical of multi-fidelity approximations [11]. There is also a notable improvement in the BF estimates when the approximation rank is raised from r = 3 to 8.…”

Section: Resultsmentioning

confidence: 73%

“…, n, denotes n columns of H H H that make up the randomly selected HF samples used for the BF estimate, and the reduced basis measurement matrix η η η n ∈ R r×n is such that η η η n ( j, i) := η j (ξ ξ ξ i ). For ease of notation, we continue to denote the full N sample HF matrix as H H H. We note that, following [29], the regression problem (11) requires n ∼ r log(r) HF samples, which is considerably smaller than what is needed in (4) when r P. At this stage, useful statistics such as the expected value and variance of the QoI can be easily retrieved from the coefficients.…”

Section: Bf Approximation Via Lf Reduced Basis Liftingmentioning

confidence: 99%

“…The second theorem that we build upon concerns the number of samples needed to accurately recover coefficients C C C B from (11). From [30,29], we recall the coherence parameter µ of that provides a bound on the realized spectral radius of η η η as…”

Section: Error Estimatesmentioning

confidence: 99%

“…where C C C B is the least squares solution to (11). It follows that for E , which is independent of i, and is a sampling event that occurs with probability…”

Section: Error Estimatesmentioning

confidence: 99%

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Bi-fidelity Reduced Polynomial Chaos Expansion for Uncertainty Quantification

Newberry¹,

Hampton²,

Jansen³

et al. 2021

Preprint

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A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This work considers a stochastic model reduction method (SMR), in the context of polynomial chaos (PC) expansions, where low-fidelity (LF) samples are leveraged to form a stochastic reduced basis. The reduced basis enables the construction of a bi-fidelity (BF) estimate of a quantity of interest from a small number of high-fidelity (HF) samples. A successful BF estimate approximates the quantity of interest with accuracy comparable to the HF model and computational expense close to the LF model. We develop new error bounds for the SMR approach and present a procedure to practically utilize these bounds in order to assess the appropriateness of a given pair of LF and HF models for BF estimation. The effectiveness of the SMR approach, and the utility of the error bound are presented in three numerical examples.

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Section: Resultsmentioning

confidence: 73%

Section: Bf Approximation Via Lf Reduced Basis Liftingmentioning

confidence: 99%

Section: Error Estimatesmentioning

confidence: 99%

“…where C C C B is the least squares solution to (11). It follows that for E , which is independent of i, and is a sampling event that occurs with probability…”

Section: Error Estimatesmentioning

confidence: 99%

See 2 more Smart Citations

Bi-fidelity Reduced Polynomial Chaos Expansion for Uncertainty Quantification

Newberry¹,

Hampton²,

Jansen³

et al. 2021

Preprint

Self Cite

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“…In uncertainty quantification of physical systems, [51] used the dropout strategy [52], which ignores some of the connections in the networks with a probability for model and parametric uncertainty. Recently, [53] and [54] used transfer learning techniques and convolutional neural networks for uncertainty quantification of physical systems. However, these studies do not address the prediction of UGW patterns when uncertainty is present in a WpFSI problem.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Ultrasonic Guided Wave Propagation in Solid-fluid and their Interface under Uncertainty using Machine Learning

De,

Hai,

Doostan

et al. 2021

Preprint

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Structural health monitoring (SHM) systems use non-destructive testing principle for damage identification. As part of SHM, the propagation of ultrasonic guided waves (UGWs) is tracked and analyzed for the changes in the associated wave pattern. These changes help identify the location of a structural damage, if any. We advance existing research by accounting for uncertainty in the material and geometric properties of a structure. The physics model used in this study comprises of a monolithically coupled system of acoustic and elastic wave equations, known as the wave propagation in fluid-solid and their interface (WpFSI) problem. As the UGWs propagate in the solid, fluid, and their interface, the wave signal displacement measurements are contrasted against the benchmark pattern. For the numerical solution, we develop an efficient algorithm that successfully addresses the inherent complexity of solving the multiphysics problem under uncertainty. We present a procedure that uses Gaussian process regression and convolutional neural network for predicting the UGW propagation in a solid-fluid and their interface under uncertainty. First, a set of training images for different realizations of the uncertain parameters of the inclusion inside the structure is generated using a monolithically-coupled system of acoustic and elastic wave equations. Next, Gaussian processes trained with these images are used for predicting the propagated wave with convolutional neural networks for further enhancement to produce high-quality images of the wave patterns for new realizations of the uncertainty. The results indicate that the proposed approach provides an accurate prediction for the WpFSI problem in the presence of uncertainty.

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