Stochastic Design and Control in Random Heterogeneous Materials

Sternfels, Raphael; Koutsourelakis, Phaedon‐Stelios

doi:10.1615/intjmultcompeng.v9.i4.60

Cited by 7 publications

(6 citation statements)

References 48 publications

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“…Its predictive uncertainty is incorporated and the selfsupervised active learning mechanism can control the number of training data that each particular surrogate would need. While not discussed, it is also possible to assess the optimization error, albeit with additional runs of the high-fidelity model, by using an Importance Sampling step [45]. Lastly we mention further potential of improvement by a fully Bayesian treatment of the surrogate's parameters θ, which would be particularly beneficial in the small-data regime we are operating in.…”

Section: Resultsmentioning

confidence: 99%

“…This is employed so that the resulting SDF integrates to 1 which is the variance of the corresponding Gaussian field. We made use of a spectral representation of the underlying Gaussian field (and therefore of xg) on the basis of its ϕ-controlled SDF and according to the formulations detailed in [47,48,45]. The thresholded Gaussian vector xg gives rise to the binary microstructure x as described above and we denote summarily the corresponding transformation as:…”

Section: Process-structure Linkagementioning

confidence: 99%

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Self-supervised optimization of random material microstructures in the small-data regime

Rixner¹,

Koutsourelakis²

2021

Preprint

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While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources and their quantification and integration in the inversion process are essential in meeting the materials design objectives. The first contribution of this paper is a flexible, fully probabilistic formulation of such optimization problems that accounts for the uncertainty in the process-structure and structure-property linkages and enables the identification of optimal, high-dimensional, process parameters. We employ a probabilistic, data-driven surrogate for the structure-property link which expedites computations and enables handling of non-differential objectives. We couple this with a novel active learning strategy, i.e. a self-supervised collection of data, which significantly improves accuracy while requiring small amounts of training data. We demonstrate its efficacy in optimizing the mechanical and thermal properties of two-phase, random media but envision its applicability encompasses a wide variety of microstructure-sensitive design problems.

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Section: Resultsmentioning

confidence: 99%

Section: Process-structure Linkagementioning

confidence: 99%

Self-supervised optimization of random material microstructures in the small-data regime

Rixner¹,

Koutsourelakis²

2021

Preprint

Self Cite

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“…The calibration problem under uncertainty can then be formulated in two steps [18,19]. First, we naively compose a Bayesian calibration problem in analogy to (1), with the only difference that the model is also dependent on θ. Consequently, the posterior p x|θ, Y obs,C is conditionally dependent on θ, as demonstrated in (3a).…”

Section: Bayesian Calibration Under Uncertaintymentioning

confidence: 99%

Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

Willmann

Nitzler

Brandstaeter

et al. 2022

Adv. Model. and Simul. in Eng. Sci.

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Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We present a Bayesian calibration approach for surface coupled problems in computational mechanics based on measured deformation of an interface when no displacement data of material points is available. The interpretation of such a calibration problem as a statistical inference problem, in contrast to deterministic model calibration, is computationally more robust and allows the analyst to find a posterior distribution over possible solutions rather than a single point estimate. The proposed framework also enables the consideration of unavoidable uncertainties that are present in every experiment and are expected to play an important role in the model calibration process. To mitigate the computational costs of expensive forward model evaluations, we propose to learn the log-likelihood function from a controllable amount of parallel simulation runs using Gaussian process regression. We introduce and specifically study the effect of three different discrepancy measures for deformed interfaces between reference data and simulation. We show that a statistically based discrepancy measure results in the most expressive posterior distribution. We further apply the approach to numerical examples in higher model parameter dimensions and interpret the resulting posterior under uncertainty. In the examples, we investigate coupled multi-physics models of fluid–structure interaction effects in biofilms and find that the model parameters affect the results in a coupled manner.

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“…On the other hand, too few intermediate distributions can adversely affect the overall accuracy of the particulate approximation. To that end we propose an adaptive SMC scheme used in UQ, stochastic design and system identification applications [34][35][36], which determines automatically the number of necessary intermediate distributions based on the effective sample size. The effective sample size is defined as…”

Section: Adaptive Sequential Monte Carlomentioning

confidence: 99%

Reduced-order model tracking and interpolation to solve PDE-based Bayesian inverse problems

Sternfels

Earls

2013

Inverse Problems

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This work presents a computationally efficient probabilistic framework that enables the identification of model parameters from noisy measurements of the response. We consider transient PDE-based models, where the parameters correspond to physical properties. An efficient and reliable procedure for estimation of those unknown parameters is pursued. The proposed framework uses a Bayesian approach, an efficient sequential Monte Carlo sampling scheme, and adaptive reduced-order models (ROMs). The Bayesian approach has several advantages including the ability to provide not only point estimates of the quantities of interest, but also measures of credibility and robustness concerning those estimates. The associated sequential Monte Carlo method sampling scheme is embarrassingly parallelizable, as well as efficient in terms of the number of calls to the forward solver (e.g. a finite element code) used in evaluating the likelihood function. We propose to use a ROM adaptation procedure where projection-based ROMs are seen as points on a certain Riemannian manifold and are 'tracked' and interpolated during the sampling process using a database of precomputed ROMs. This approach ensures that an appropriate ROM is used for the likelihood evaluation in every region of the parameter space, thus leading to computational savings while conserving sufficient accuracy. Using numerical examples, we illustrate the capabilities of the proposed framework, and show that it leads to quality estimates with a quantified predictive uncertainty.

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Stochastic Design and Control in Random Heterogeneous Materials

Cited by 7 publications

References 48 publications

Self-supervised optimization of random material microstructures in the small-data regime

Self-supervised optimization of random material microstructures in the small-data regime

Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

Reduced-order model tracking and interpolation to solve PDE-based Bayesian inverse problems

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