Fast surrogate modeling using dimensionality reduction in model inputs and field output: Application to additive manufacturing

Vohra, Manav; Nath, Paromita; Mahadevan, Sankaran; Lee, Yung-Tsun Tina

doi:10.1016/j.ress.2020.106986

Cited by 42 publications

(20 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Introductionmentioning

confidence: 99%

“…However, accuracy is mostly dependent on the data used to train neural networks. Hence, its applicability is limited in situations involving sparse and noisy training data (Vohra et al, 2020). The parametric method mainly include the high-order response surface method (HRSM) (Gavin and Yau, 2008), polynomial chaos expansion (PCE) (Ghanem and Spanos, 1992;Xiu and Karniadakis, 2002;Zhang and Xu, 2021;SalehiA et al, 2018;Xu et al, 2017;Wang and Matthies, 2018), polynomial dimensional decomposition (PDD) (Rahman, 2008(Rahman, , 2009(Rahman, , 2011(Rahman, , 2015Yadav and Rahman, 2013;Ren et al, 2016;Tang et al, 2016Tang et al, , 2019Lu, 2018), etc.…”

mentioning

confidence: 99%

See 1 more Smart Citation

An adaptive polynomial dimensional decomposition method and its application in reliability analysis

Sheng

Fan

Zhang

et al. 2022

View full text Add to dashboard Cite

PurposeThe polynomial dimensional decomposition (PDD) method is a popular tool to establish a surrogate model in several scientific areas and engineering disciplines. The selection of appropriate truncated polynomials is the main topic in the PDD. In this paper, an easy-to-implement adaptive PDD method with a better balance between precision and efficiency is proposed.Design/methodology/approachFirst, the original random variables are transformed into corresponding independent reference variables according to the statistical information of variables. Second, the performance function is decomposed as a summation of component functions that can be approximated through a series of orthogonal polynomials. Third, the truncated maximum order of the orthogonal polynomial functions is determined through the nonlinear judgment method. The corresponding expansion coefficients are calculated through the point estimation method. Subsequently, the performance function is reconstructed through appropriate orthogonal polynomials and known expansion coefficients.FindingsSeveral examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.Originality/valueThe number of unknown coefficients is significantly reduced, and the computational burden for reliability analysis is eased accordingly. The coefficient evaluation for the multivariate component function is decoupled with the order judgment of the variable. The proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.

show abstract

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

An adaptive polynomial dimensional decomposition method and its application in reliability analysis

Sheng

Fan

Zhang

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Similarly, proper orthogonal decomposition (POD) or the Karhunen-Loeve expansion (KLE) has been widely used for reduced-order model construction [17,18,19,20]. Active subspaces, a dimension reduction technique which discovers linear manifolds of the data, has been proposed as an in-built technique for the construction of Gaussian process (GP) surrogates [21,22,23,24]. Furthermore, multiple gradient-based techniques can be found in the literature for identifying subspaces in situations involving multivariate outputs and high-dimensional input parameter spaces [25,26,27,18,19].…”

Section: Introductionmentioning

confidence: 99%

Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models

Kontolati,

Loukrezis,

Santos

et al. 2021

Preprint

View full text Add to dashboard Cite

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pre-trained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

show abstract

“…Reliability assessment and optimization of engineered systems have received growing attention in a broad range of sectors, such as power grid [1,2], transportation systems [3,4,5], computing systems [6,7], electrical and mechanical systems [8,9,10,11]. Over the last few years, the increasing occurrences of extreme events have posed more than ever pressing needs for highly reliable infrastructure systems so that they can still operate at a desirable performance under extreme natural conditions.…”

Section: Introductionmentioning

confidence: 99%

A generic physics-informed neural network-based framework for reliability assessment of multi-state systems

Zhou¹,

Droguett²,

Mosleh³

2021

Preprint

View full text Add to dashboard Cite

In this paper, we leverage the recent advances in physics-informed neural network (PINN) and develop a generic PINN-based framework to assess the reliability of multi-state systems (MSSs). The proposed methodology consists of two major steps. In the first step, we recast the reliability assessment of MSS as a machine learning problem using the framework of PINN. A feedforward neural network with two individual loss groups are constructed to encode the initial condition and state transitions governed by ordinary differential equations (ODEs) in MSS. Next, we tackle the problem of high imbalance in the magnitude of the back-propagated gradients in PINN from a multi-task learning perspective. Particularly, we treat each element in the loss function as an individual task, and adopt a gradient surgery approach named projecting conflicting gradients (PCGrad), where a task's gradient is projected onto the norm plane of any other task that has a conflicting gradient. The gradient projection operation significantly mitigates the detrimental effects caused by the gradient interference when training PINN, thus accelerating the convergence speed of PINN to high-precision solutions to MSS reliability assessment. With the proposed PINN-based framework, we investigate its applications for MSS reliability assessment in several different contexts in terms of time-independent or dependent state transitions and system scales varying from small to medium. The results demonstrate that the proposed PINN-based framework shows generic and remarkable performance in MSS reliability assessment, and the incorporation of PCGrad in PINN leads to substantial improvement in solution quality and convergence speed.

show abstract

Fast surrogate modeling using dimensionality reduction in model inputs and field output: Application to additive manufacturing

Cited by 42 publications

References 42 publications

An adaptive polynomial dimensional decomposition method and its application in reliability analysis

An adaptive polynomial dimensional decomposition method and its application in reliability analysis

Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models

A generic physics-informed neural network-based framework for reliability assessment of multi-state systems

Contact Info

Product

Resources

About