Derivative-Based Global Sensitivity Analysis for Models with High-Dimensional Inputs and Functional Outputs

Cleaves, Helen; Alexanderian, Alen; Guy, Hayley; Smith, Ralph C.; Yu, Meilin

doi:10.1137/19m1243518

Cited by 10 publications

(10 citation statements)

References 43 publications

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“…On the other hand, the corresponding PDE solution is less sensitive to the higher-order KL terms of the parameter, as seen in Figure 1 (right). This behavior is consistent with the analysis in [22], where a global sensitivity analysis formalism is used to quantify the impact of the KL terms of the log-coefficient, in an elliptic PDE, on variability in solution of the PDE.…”

Section: Model 1d Elliptic Equation With Ran-dom Coefficient Functionsupporting

confidence: 85%

“…Advanced dimension reduction methods, such as global sensitivity analysis and active subspace, need to be developed to tackle input dimension reduction. One example is our recent work on functional derivative-base global sensitivity analysis [22]. More progress will be reported in our future work.…”

Section: Discussionmentioning

confidence: 95%

“…A question arises: is there a way to find a subset of the parameter KL terms that are most influential to model output variability? In our previous work [22], a derivative-based global sensitivity approach has been established to identify unimportant input parameters, for functionvalued quantities of interest such as the pressure field. The approach in [22] guides an efficient input dimension reduction strategy, by identifying the KL terms of the input that contribute most to variability of the output field.…”

Section: Application To Biotransport In Tumorsmentioning

confidence: 99%

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Model Input and Output Dimension Reduction Using Karhunen–Loève Expansions With Application to Biotransport

Alexanderian

Reese

Smith

et al. 2019

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg

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We consider biotransport in tumors with uncertain heterogeneous material properties. Specifically, we focus on the elliptic partial differential equation (PDE) modeling the pressure field inside the tumor. The permeability field is modeled as a log-Gaussian random field with a prespecified covariance function. We numerically explore dimension reduction of the input parameter and model output. Truncated Karhunen-Loève (KL) expansions are used to decompose the log-permeability field, as well as the resulting random pressure field. We find that although very high-dimensional representations are needed to accurately represent the permeability field, especially in presence of small correlation lengths, the pressure field is not very sensitive to high-order KL terms of the input parameter. Moreover, we find that the pressure field itself can be represented accurately using a KL expansion with a small number of terms. These observations are used to guide a reduced-order modeling approach to accelerate computational studies of biotransport in tumors.

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Section: Model 1d Elliptic Equation With Ran-dom Coefficient Functionsupporting

confidence: 85%

Section: Discussionmentioning

confidence: 95%

Section: Application To Biotransport In Tumorsmentioning

confidence: 99%

See 1 more Smart Citation

Model Input and Output Dimension Reduction Using Karhunen–Loève Expansions With Application to Biotransport

Alexanderian

Reese

Smith

et al. 2019

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg

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“…These concepts were originally conceived for scalar QoIs. Recent works such as [1,11,41] generalize standard GSA tools to the case of vector-and function-valued QoIs. In particular, [17,1] concern variance-based GSA using Sobol' indices for such QoIs.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, [17,1] concern variance-based GSA using Sobol' indices for such QoIs. The article [11] studies DGSMs for function-valued QoIs. A generalization of active subspace methods for vectorial outputs is presented in [41].…”

Section: Introductionmentioning

confidence: 99%

Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media

2021

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We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-value outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loéve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.

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Adaptive basis sets for practical quantum computing

Kwon

Curtin

Morrow

et al. 2023

Int J of Quantum Chemistry

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Electronic structure calculations on small systems such as H 2 , H 2 O, LiH, and BeH 2 with chemical accuracy are still a challenge for the current generation of noisy intermediate-scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H 2 molecule, in which exponents and contraction coefficients depend on the H H distance, and apply it to the generation of H 2 potential energy surface on IBM-Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double-zeta basis sets, thus allowing one to perform double-zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.

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Derivative-Based Global Sensitivity Analysis for Models with High-Dimensional Inputs and Functional Outputs

Cited by 10 publications

References 43 publications

Model Input and Output Dimension Reduction Using Karhunen–Loève Expansions With Application to Biotransport

Model Input and Output Dimension Reduction Using Karhunen–Loève Expansions With Application to Biotransport

Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media

Adaptive basis sets for practical quantum computing

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