@article{coleman_lewis_smith_williams_morris_khuwaileh_2019, title={Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics}, volume={7}, ISSN={["2166-2525"]}, DOI={10.1137/16M1075119}, abstractNote={Recent developments in the field of reduced-order modeling---and, in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this paper, we discuss a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. This analysis extends the gradient-free algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 1603--1615] in two significant ways: (i) we introduce an initialization algorithm to identify lower-dimensional subspaces of influential directions to seed the gradient-free algorithm for high-dimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. We illustrate the initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1 for input dimensions up to 7700.}, number={1}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Coleman, Kayla D. and Lewis, Allison and Smith, Ralph C. and Williams, Brian and Morris, Max and Khuwaileh, Bassam}, year={2019}, pages={117–142} }
@article{lewis_smith_williams_figueroa_2016, title={An information theoretic approach to use high-fidelity codes to calibrate low-fidelity codes}, volume={324}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2016.08.001}, abstractNote={For many simulation models, it can be prohibitively expensive or physically infeasible to obtain a complete set of experimental data to calibrate model parameters. In such cases, one can alternatively employ validated higher-fidelity codes to generate simulated data, which can be used to calibrate the lower-fidelity code. In this paper, we employ an information-theoretic framework to determine the reduction in parameter uncertainty that is obtained by evaluating the high-fidelity code at a specific set of design conditions. These conditions are chosen sequentially, based on the amount of information that they contribute to the low-fidelity model parameters. The goal is to employ Bayesian experimental design techniques to minimize the number of high-fidelity code evaluations required to accurately calibrate the low-fidelity model. We illustrate the performance of this framework using heat and diffusion examples, a 1-D kinetic neutron diffusion equation, and a particle transport model, and include initial results from the integration of the high-fidelity thermal-hydraulics code Hydra-TH with a low-fidelity exponential model for the friction correlation factor.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Lewis, Allison and Smith, Ralph and Williams, Brian and Figueroa, Victor}, year={2016}, month={Nov}, pages={24–43} }
@article{lewis_smith_williams_2016, title={Gradient free active subspace construction using Morris screening elementary effects}, volume={72}, ISSN={["1873-7668"]}, DOI={10.1016/j.camwa.2016.07.022}, abstractNote={Among multivariate functions with high-dimensional input spaces, it is common for functions to vary more strongly in a few dominant directions related to a small number of highly influential parameters. In such cases, the input dimension may be greatly reduced by constructing a low-dimensional response space that is aligned with the directions of strongest dominance; this is the basis behind active subspace methods. Until recently, gradient-based methods have been employed to construct the active subspace. We introduce a gradient-free active subspace construction method that avoids the need to sample from the gradient, which may not be available, via construction of a coarse approximation to the gradient matrix by employing the concept of “elementary effects” from Morris screening procedures. In addition, we introduce the use of adaptive step sizes and directions, when constructing these elementary effects, to allow for more accuracy in locally sensitive regions while still covering a substantial amount of the input space. This increases algorithmic efficiency by avoiding function evaluations in directions in which the gradient is relatively flat. To demonstrate the method, we use an elliptic PDE example with two correlation lengths to illustrate the effects of differing rates of singular value decay. The gradient-free active subspace method is compared to a local sensitivity analysis using coordinate reduction. This problem is then modified to contain a clearly defined 10-dimensional active subspace for verification of our method on a more complex example.}, number={6}, journal={COMPUTERS & MATHEMATICS WITH APPLICATIONS}, author={Lewis, Allison and Smith, Ralph and Williams, Brian}, year={2016}, month={Sep}, pages={1603–1615} }
@inproceedings{lewis_mcmahan_smith_2014, title={Model calibration for beam models in the presence of model discrepancy}, DOI={10.1115/smasis2014-7722}, abstractNote={Piezoelectric, magnetic and shape memory alloy (SMA) materials offer unique capabilities for energy harvesting and reduced energy requirements in aerospace, aeronautic, automotive, industrial and biomedical applications. However, all of these materials exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities that must be incorporated in models and model-based control designs to achieve their full potential. Furthermore, models and control designs must be constructed in a manner that incorporates parameter and model uncertainties and permits predictions with quantified uncertainties. In this presentation, we compare the Euler-Bernoulli and Timoshenko beam models for a cantilever beam with an applied PZT patch to illustrate parameter estimation in the presence of model discrepancy.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2014, vol 1}, author={Lewis, A. L. and McMahan, J. A. and Smith, Ralph}, year={2014} }