Rapid design centering of multi-band antennas using knowledge-based inverse models and response features

In this paper, surrogate models are built iteratively using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the va...

Uncertainty Quantification (UQ) is an increasingly important area of research. As components and systems become more efficient and optimized, the impact of uncertain parameters (such as boundary and operating conditions, geometrical variations due to manufacturing or in-service deterioration, etc.) is likely to become critical. It is therefore fundamental to consider the impact of these uncertainties as early as possible during the design process, with the aim of producing more robust designs (less sensitive to the presence of uncertainties). The cost of UQ with high-fidelity simulations becomes therefore of fundamental importance. The companion part I paper presented an efficient approach for UQ based on Polynomial Chaos expansions, demonstrating its applicability to multi-fimensional uncertainty quantification problems. This paper focuses on the application of this approach to quantify the variability in the performance of two large bypass-ratio jet engine fans in the presence of shape uncertainty due to possible manufacturing processes. The impacts of shape uncertainty on the two geometries are compared, and sensitivities to the location of the blade shape variability are extracted. The mechanisms at the origin of the change in performance are analyzed in detail, as well as the differences between the two configurations. These results provide important information both for controling the manufacturing process, and for designing blades that are less sensitive to the presence of manufacturing uncertainties.

Purpose – The purpose of this paper is to investigate strategies for expedited dimension scaling of electromagnetic (EM)-simulated microwave and antenna structures, exploiting the concept of variable-fidelity inverse surrogate modeling. Design/methodology/approach – A fast inverse surrogate modeling technique is described for dimension scaling of microwave and antenna structures. The model is established using reference designs obtained for cheap underlying low-fidelity model and corrected to allow structure scaling at high accuracy level. Numerical and experimental case studies are provided demonstrating feasibility of the proposed approach. Findings – It is possible, by appropriate combination of surrogate modeling techniques, to establish an inverse model for explicit determination of geometry dimensions of the structure at hand so as to re-design it for various operating frequencies. The scaling process can be concluded at a low computational cost corresponding to just a few evaluations of the high-fidelity computational model of the structure. Research limitations/implications – The present study is a step toward development of procedures for rapid dimension scaling of microwave and antenna structures at high-fidelity EM-simulation accuracy. Originality/value – The proposed modeling framework proved useful for fast geometry scaling of microwave and antenna structures, which is very laborious when using conventional methods. To the authors’ knowledge, this is one of the first attempts to surrogate-assisted dimension scaling of microwave components at the EM-simulation level.

Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

Although the learning‐based surrogate model could achieve fast prediction, the model uncertainty in data and predictions remains a significant challenge. To alleviate the uncertainty problems for the surrogate model, a learning‐based uncertainty analysis method for improving the stability of the inverse model of RF devices is proposed. The inherent uncertainty in the inverse model is analyzed by leveraging ensemble adversarial learning, enabling the prediction of confidence intervals for the inverse surrogate model output without changing the original neural network structure. Subsequently, the differential evolution (DE) algorithm is employed to optimize the geometric parameters of the inverse model output within the predicted interval. To validate feasibility and effectiveness of the method, RF hairpin filter is used for the design example via the neural networks. RF filters with multiple center frequencies and bandwidths are simulated, fabricated and measured. Both simulated and measured results demonstrate a notable enhancement, with a 37.22% predicted accuracy improvement in the degree of fitting between the optimized response and the label of the input network, compared to the circuit response (S‐parameter) pre‐optimization. The proposed method exhibits much better performance in terms of the predicted accuracy and computational time compared to direct optimization without inverse model. The learning‐based method could also be applicable to the other RF devices, affirming the practical applicability and robustness of the approach.

Surrogate model based uncertainty quantification of CFD simulations of the viscous flow around a ship advancing in shallow water

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

Abstract. The 2004 Indian Ocean tsunami caused significant economic losses and a large number of fatalities in the coastal areas. The estimation of tsunami flow conditions using inverse models has become a fundamental aspect of disaster mitigation and management. Here, a case study involving the Phra Thong island, which was affected by the 2004 Indian Ocean tsunami, in Thailand was conducted using inverse modeling that incorporates a deep neural network (DNN). The DNN inverse analysis reconstructed the values of flow conditions such as maximum inundation distance, flow velocity and maximum flow depth, as well as the sediment concentration of five grain-size classes using the thickness and grain-size distribution of the tsunami deposit from the post-tsunami survey around Phra Thong island. The quantification of uncertainty was also reported using the jackknife method. Using other previous models applied to areas in and around Phra Thong island, the predicted flow conditions were compared with the reported observed values and simulated results. The estimated depositional characteristics such as volume per unit area and grain-size distribution were in line with the measured values from the field survey. These qualitative and quantitative comparisons demonstrated that the DNN inverse model is a potential tool for estimating the physical characteristics of modern tsunamis.

Uncertainty quantification of separation control with synthetic jet actuator over a NACA0025 airfoil

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

Here, we examine the suitability of truncated Polynomial Chaos Expansions (PCE) and truncated Gram-Charlier Expansions (GrChE) as possible methods for uncertainty quantification (UQ) in nonlinear systems with intermittency and positive Lyapunov exponents.These two methods rely on truncated Galerkin projections of either the system variables in a fixed polynomial basis spanning the 'uncertain' subspace (PCE) or a suitable eigenfunction expansion of the joint probability distribution associated with the uncertain evolution of the system (GrChE).Based on a simple, statistically exactly solvable non-linear and non-Gaussian test model, we show in detail that methods exploiting truncated spectral expansions, be it PCE or GrChE, have significant limitations for uncertainty quantification in systems with intermittent instabilities or parametric uncertainties in the damping.Intermittency and fat-tailed probability densities are hallmark features of the inertial and dissipation ranges of turbulence and we show that in such important dynamical regimes PCE performs, at best, similarly to the vastly simpler Gaussian moment closure technique utilized earlier by the authors in a different context for UQ within a framework of Empirical Information Theory.Moreover, we show that the non-realizability of the GrChE approximations is linked to the onset of intermittency in the dynamics and it is frequently accompanied by an erroneous blow-up of the second-order statistics at short times.These limitations of the two types of truncated spectral expansions arise from the following: (i) Non-uniform convergence in time of PCE and GrChE resulting in a rapidly increasing number of terms necessary for a good approximation of the random process as time evolves, (ii) Fundamental problems with capturing the constant flux of randomness due to white Gaussian noise forcing via finite truncations of the spectral representation of the associated Wiener process, (iii) Slow decay of PCE and GrChE coefficients in the presence of intermittency, hampering implementation of sparse truncation methods which have been widely used in nearly elliptic problems or in low Reynolds number flows.Rigorous justification of these limitations is richly illustrated by straightforward tests exploiting a simple nonlinear and non-Gaussian but statistically exactly solvable test model which is proposed here as a challenging benchmark for algorithms for UQ in systems with intermittency.

Nondiffusive phonon transport presents significant challenges in micro/nanoscale thermal characterization, compounded by the limitations of experimental-numerical techniques and the presence of measurement noise. Additionally, inverse modeling and uncertainty quantification (UQ) for submicron thermal transport remain under-explored. In this study, we introduce a physics-informed Bayesian deep learning framework designed to address phonon Boltzmann transport equation (BTE)-based forward and inverse problems leveraging limited and noisy data. Our approach combines Bayesian neural networks with a nonparametric variational inference method, formulating the BTE-constrained training in a Bayesian manner. This enables the estimation of the posterior distribution of neural network parameters and unknown equation parameters based on a likelihood function that incorporates uncertainties from both the measurement data and the BTE model. Through numerical experiments on various phonon transport scenarios, we demonstrate that our method can accurately reconstruct temperature and heat flux profiles, infer critical quantities of interest (e.g., Knudsen number), and provide robust uncertainty quantification, even when data is sparse and noisy. This framework enhances our capability to conduct nondiffusive thermal simulations and inverse modeling with quantified uncertainty, offering a powerful tool for advancing thermal transport research and optimization in micro/nanoscale devices.

Generative inverse modeling for improved geological CO2 storage prediction via conditional diffusion models

Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square