Multi-fidelity Models Research Articles

A physics-embedded deep-learning framework for efficient multi-fidelity modeling applied to guided wave based structural health monitoring

Health monitoring of structures using ultrasonic guided waves is an evolving technology with potential applications in monitoring pipelines, civil bridges, and aircraft components. However, the sensitivity of guided waves to external parameters affects the reliability of monitoring systems based on them. These influencing factors and experimental related factors cannot be perfectly modeled, which give rise to the discrepancy between numerical simulations and experimental measurements. Therefore, it is important to address this inevitable discrepancy and generate close-to-experiment simulations. In this work, we present a deep learning-based Digital Twin framework containing multi-fidelity modeling to reduce the discrepancy between measurements and simulations and a deep generative model to generate close-to-experiment guided wave responses by harnessing the vital characteristics of the two sources. These realistic simulations (close to experiment) can then be used in assessing the reliability of health monitoring system by generating probability of detection curves. Furthermore, they can also be used for augmenting the training data for a machine learning algorithm. We use a measurement dataset corresponding to crack propagation and simulations to validate the proposed framework. The results show that the discrepancy is indeed reduced to a great extent, furthermore, we also show that this framework enables the computation of probability of detection from close-to-experiment data as a direct consequence of rapid generation of realistic simulations.

A Multi-Fidelity Uncertainty Propagation Model for Multi-Dimensional Correlated Flow Field Responses

Given the randomness inherent in fluid dynamics problems and limitations in human cognition, Computational Fluid Dynamics (CFD) modeling and simulation are afflicted with non-negligible uncertainties, casting doubts on the credibility of CFD. Scientifically and rigorously quantifying the uncertainty of CFD is paramount for assessing its credibility and informing engineering decisions. In order to quantify the uncertainty of multidimensional flow field responses stemming from uncertain model parameters, this paper proposes a method based on Gappy Proper Orthogonal Decomposition (POD) for supplementing high-fidelity flow field data within a framework that leverages POD and surrogate models. This approach enables the generation of corresponding high-fidelity flow fields from low-fidelity ones, significantly reducing the cost of high-fidelity flow field computation in uncertainty propagation modeling. Through an analysis of the impact of uncertainty in the coefficients of the Spalart–Allmaras (SA) turbulence model on the distribution of wall friction coefficients for the NACA0012 airfoil and pressure coefficients for the M6 wing, the proposed multi-fidelity modeling approach is demonstrated to offer significant advancements in both accuracy and efficiency compared to single-fidelity methods, providing a robust and efficient prediction model for large-scale random sampling.

Adaptive neural network surrogate model for solving the nonlinear elastic inverse problem via Bayesian inference

Abstract In this paper, we consider a Bayesian method for nonlinear elastic inverse problems. As a working model, we are interested in the inverse problem of restoring elastic properties from measured tissue displacement. In order to reduce the computational cost, we will use the following multi-fidelity model approach. First, we construct a surrogate low-fidelity DNNs-based model in the prior distribution, then use a certain number of simulations of high fidelity model associated with an adaptive strategy online to update the low-fidelity model locally. Numerical examples show that the proposed method can solve nonlinear elastic inverse problems efficiently and accurately.

An efficient parameter-retrieval-based surrogate-assisted optimization of on-platform honeycomb absorbing structures

An electromagnetic parameter-retrieval-based surrogate-assisted optimization (PSAO) algorithm is presented to reduce radar cross section (RCS) by optimizing the on-platform honeycomb absorbing structures. To facilitate the optimization process, the honeycomb structure is transformed to an anisotropic homogeneous slab, and the effective parameters of the slab are extracted by the retrieval algorithm. A multi-fidelity model is employed to reduce the computing-time consumption, in which a Gaussian process (GP) regression model is used as the substitute for the coarse model. The GP model establishes a relationship between the geometry of the honeycomb structure and the RCS response of the target coated with the equivalent slab. Finally, the optimization result of the fine model is achieved through a space mapping strategy. The accuracy of the parameter extraction algorithm is verified by analyzing the honeycomb absorbing structure. Subsequently, the proposed optimization method is applied to a metal plate and a metal cylinder, resulting in a 10 dB reduction of RCS in broadband and wide-angle scenarios. This demonstrates the applicability of the proposed PSAO algorithm to both planar and conformal on-platform honeycomb absorbing structures. Furthermore, an NACA0015 foil is analyzed, showing an average RCS reduction of 10 dB and a minimum RCS reduction of 5 dB in the X-band. These results indicate that the PSAO approach can effectively apply to complicated targets. Additionally, the proposed method exhibits significant advantages in terms of computational accuracy and efficiency compared to the traditional genetic algorithm.

Optimized multifidelity machine learning for quantum chemistry

Machine learning (ML) provides access to fast and accurate quantum chemistry (QC) calculations for various properties of interest such as excitation energies. It is often the case that high accuracy in prediction using a ML model, demands a large and costly training set. Various solutions and procedures have been presented to reduce this cost. These include methods such as Δ-ML, hierarchical-ML, and multifidelity machine learning (MFML). MFML combines various Δ-ML like sub-models for various fidelities according to a fixed scheme derived from the sparse grid combination technique. In this work we implement an optimization procedure to combine multifidelity models in a flexible scheme resulting in optimized MFML (o-MFML) that provides superior prediction capabilities. This hyperparameter optimization is carried out on a holdout validation set of the property of interest. This work benchmarks the o-MFML method in predicting the atomization energies on the QM7b dataset, and again in the prediction of excitation energies for three molecules of growing size. The results indicate that o-MFML is a strong methodological improvement over MFML and provides lower error of prediction. Even in cases of poor data distributions and lack of clear hierarchies among the fidelities, which were previously identified as issues for multifidelity methods, the o-MFML is advantageous for the prediction of quantum chemical properties.

Accelerating defect predictions in semiconductors using graph neural networks

First-principles computations reliably predict the energetics of point defects in semiconductors but are constrained by the expense of using large supercells and advanced levels of theory. Machine learning models trained on computational data, especially ones that sufficiently encode defect coordination environments, can be used to accelerate defect predictions. Here, we develop a framework for the prediction and screening of native defects and functional impurities in a chemical space of group IV, III–V, and II–VI zinc blende semiconductors, powered by crystal Graph-based Neural Networks (GNNs) trained on high-throughput density functional theory (DFT) data. Using an innovative approach of sampling partially optimized defect configurations from DFT calculations, we generate one of the largest computational defect datasets to date, containing many types of vacancies, self-interstitials, anti-site substitutions, impurity interstitials and substitutions, as well as some defect complexes. We applied three types of established GNN techniques, namely crystal graph convolutional neural network, materials graph network, and Atomistic Line Graph Neural Network (ALIGNN), to rigorously train models for predicting defect formation energy (DFE) in multiple charge states and chemical potential conditions. We find that ALIGNN yields the best DFE predictions with root mean square errors around 0.3 eV, which represents a prediction accuracy of 98% given the range of values within the dataset, improving significantly on the state-of-the-art. We further show that GNN-based defective structure optimization can take us close to DFT-optimized geometries at a fraction of the cost of full DFT. The current models are based on the semi-local generalized gradient approximation-Perdew–Burke–Ernzerhof (PBE) functional but are highly promising because of the correlation of computed energetics and defect levels with higher levels of theory and experimental data, the accuracy and necessity of discovering novel metastable and low energy defect structures at the PBE level of theory before advanced methods could be applied, and the ability to train multi-fidelity models in the future with new data from non-local functionals. The DFT-GNN models enable prediction and screening across thousands of hypothetical defects based on both unoptimized and partially optimized defective structures, helping identify electronically active defects in technologically important semiconductors.

Automatic Prediction of Peak Optical Absorption Wavelengths in Molecules Using Convolutional Neural Networks.

Molecular design depends heavily on optical properties for applications such as solar cells and polymer-based batteries. Accurate prediction of these properties is essential, and multiple predictive methods exist, from ab initio to data-driven techniques. Although theoretical methods, such as time-dependent density functional theory (TD-DFT) calculations, have well-established physical relevance and are among the most popular methods in computational physics and chemistry, they exhibit errors that are inherent in their approximate nature. These high-throughput electronic structure calculations also incur a substantial computational cost. With the emergence of big-data initiatives, cost-effective, data-driven methods have gained traction, although their usability is highly contingent on the degree of data quality and sparsity. In this study, we present a workflow that employs deep residual convolutional neural networks (DR-CNN) and gradient boosting feature selection to predict peak optical absorption wavelengths (λmax) exclusively from SMILES representations of dye molecules and solvents; one would normally measure λmax using UV-vis absorption spectroscopy. We use a multifidelity modeling approach, integrating 34,893 DFT calculations and 26,395 experimentally derived λmax data, to deliver more accurate predictions via a Bayesian-optimized gradient boosting machine. Our approach is benchmarked against the state of the art that is reported in the scientific literature; results demonstrate that learnt representations via a DR-CNN workflow that is integrated with other machine learning methods can accelerate the design of molecules for specific optical characteristics.

AMFGP: An active learning reliability analysis method based on multi-fidelity Gaussian process surrogate model

Multi-fidelity modeling is widely available in theoretical research and engineering practice. Although high-fidelity models often necessitate substantial computational resources, they yield more accurate and reliable results. Low-fidelity models are less computationally demanding, while their results may be inaccurate or unreliable. For the reliability analysis based on complex limit state functions, a method based on active learning multi-fidelity Gaussian process model, called AMFGP, is proposed by combining surrogate model with adaptive strategy, ensuring a balance between prediction accuracy and computational cost in terms of both surrogate modeling and active learning: A dependent Gaussian process surrogate model using complete statistical characteristics is developed under the multi-fidelity framework, and the surrogate performances of different single-fidelity and multi-fidelity models with different learning functions are investigated; based on the proposed model, an adaptive strategy considering the dependence between predictions, the model correlation, and the sample density is designed, and the adaptive performance of different learning functions in different models is explored. The proposed method is validated for effectiveness and adaptability in three mathematical examples with different dimensions and demonstrated for efficiency and practicality in an engineering application to aero engine gear.

Automatic Prediction of Band Gaps of Inorganic Materials Using a Gradient Boosted and Statistical Feature Selection Workflow.

Machine learning (ML) methods can train a model to predict material properties by exploiting patterns in materials databases that arise from structure-property relationships. However, the importance of ML-based feature analysis and selection is often neglected when creating such models. Such analysis and selection are especially important when dealing with multifidelity data because they afford a complex feature space. This work shows how a gradient-boosted statistical feature-selection workflow can be used to train predictive models that classify materials by their metallicity and predict their band gap against experimental measurements, as well as computational data that are derived from electronic-structure calculations. These models are fine-tuned via Bayesian optimization, using solely the features that are derived from chemical compositions of the materials data. We test these models against experimental, computational, and a combination of experimental and computational data. We find that the multifidelity modeling option can reduce the number of features required to train a model. The performance of our workflow is benchmarked against state-of-the-art algorithms, the results of which demonstrate that our approach is either comparable to or superior to them. The classification model realized an accuracy score of 0.943, a macro-averaged F1-score of 0.940, area under the curve of the receiver operating characteristic curve of 0.985, and an average precision of 0.977, while the regression model achieved a mean absolute error of 0.246, a root-mean squared error of 0.402, and R2 of 0.937. This illustrates the efficacy of our modeling approach and highlights the importance of thorough feature analysis and judicious selection over a "black-box" approach to feature engineering in ML-based modeling.

Development of a novel multi-fidelity meta modeling approach for robust multi-objective optimization of a natural gas-hydrogen/diesel dual fuel engine

Multi-fidelity modeling (MFM) is an evolving field that matches low-fidelity models (LFM) and high-fidelity models (HFM) to get better solutions with low computational cost. However, improving the duality between accuracy and computational cost remain challenging, particularly for complex problems such as dual fuel engines. This paper contributes to the MF modeling cost-effectiveness improvement by proposing a new approach to solve large-dimensional multi-objective optimization problems. The first step is to build a meta-model based on the LF model, which will be subjected to a comet-governed analysis to detect potential areas where the uncertainty on the LF model is relatively high. Then, a design of experiment (DOE) will be developed based on the results of this analysis to construct an initial HF model. Finally, an iterative loop will be activated to improve the accuracy of the MF model using a well-weighed combination of the details delivered by the LF model correction via the HF model and the HF meta-model. The developed approach is validated on four different mathematical benchmarks with different difficulties, compared with four different MF modeling strategies. This validation shows that the proposed MF modeling is competitive and can produce solutions as accurate as the HF model while reducing significantly the overall computation time by up to 50%. As an engineering application, the operating conditions in a natural gas-hydrogen/diesel dual fuel engine in terms of compression ratio, pilot injection timing, and EGR are optimized. A reduction of 46%, 68%, and 96% was achieved for HC, NOx, and the knocking index, respectively, while an increase in thermal efficiency of about 5% was obtained.

Multi-fidelity Fourier neural operator for fast modeling of large-scale geological carbon storage

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical simulators are required to train a model to accurately predict the complex physical behaviors associated with this process. In practice, the available training data are always limited in large-scale 3D problems due to the high computational cost. Therefore, we propose to use a multi-fidelity Fourier neural operator (FNO) to solve large-scale GCS problems with more affordable multi-fidelity training datasets. FNO has a desirable grid-invariant property, which simplifies the transfer learning procedure between datasets with different discretization. We first test the model efficacy on a GCS reservoir model being discretized into 110 k grid cells. The multi-fidelity model can predict with accuracy comparable to a high-fidelity model trained with the same amount of high-fidelity data with 81 % less data generation costs. We further test the generalizability of the multi-fidelity model on a same reservoir model with a finer discretization of 1 million grid cells. This case was made more challenging by employing high-fidelity and low-fidelity datasets generated by different geostatistical models and reservoir simulators. We observe that the multi-fidelity FNO model can predict pressure fields with reasonable accuracy even when the high-fidelity data are extremely limited. The findings of this study can help for better understanding of the transferability of multi-fidelity deep learning surrogate models.

Multifidelity aerodynamic shape optimization for airfoil dynamic stall mitigation using manifold mapping

Aerodynamic shape optimization for dynamic stall mitigation is computationally challenging, requiring multiple costly CFD evaluations. This work proposes a multifidelity modeling technique to efficiently mitigate dynamic stall over an airfoil, particularly manifold mapping (MM) within a trust-region-based optimization framework to find an optimal shape defined by six PARSEC parameters. The high-fidelity (HF) responses are modeled using the unsteady Reynolds-averaged Navier–Stokes equations with Menter’s shear stress transport turbulence model at a Reynolds number of 135,000, Mach number of 0.1, and reduced frequency of 0.05. The low-fidelity responses are acquired from the Kriging regression (KR) trained over the design space. The MM with the pattern-search algorithm is utilized to find optimal designs in two different test cases. The result yields two distinct optimal shapes with a higher thickness, larger leading-edge radius, and more aft camber than the baseline airfoil (NACA 0012), indicating the presence of multiple valid designs. Both designs delay the dynamic stall angle over 3 deg while mitigating peak lift and pitching moment magnitudes. The current approach delivers a computational saving of over 70% compared to HF-KR and Cokriging regression techniques. These findings present an efficient multifidelity strategy with potential application to other computationally expensive optimization problems.

DESIGN OF EXPERIMENTS VIA MULTI-FIDELITY SURROGATES AND STATISTICAL SENSITIVITY MEASURES

Parameter estimation and optimal experimental design problems have been widely studied across science and engineering. The two are inextricably linked, with optimally designed experiments leading to better-estimated parameters. This link becomes even more crucial when available experiments produce minimal data due to practical constraints of limited experimental budgets. This work presents a novel framework that allows for the identification of optimal experimental arrangement, from a finite set of possibilities, for precise parameter estimation. The proposed framework relies on two pillars. First, we use multi-fidelity modeling to create reliable surrogates that relate unknown parameters to a measurable quantity of interest for a multitude of available choices defined through a set of candidate control vectors. Secondly, we quantify the "estimation potential" of an arrangement from the set of control vectors through the examination of statistical sensitivity measures calculated from the constructed surrogates. The measures of sensitivity are defined using analysis of variance as well as directional statistics. Two numerical examples are provided, where we demonstrate how the correlation between the estimation potential and the frequency of precise parameter estimation can inform the choice of optimal arrangement.

Adaptive Multi-Fidelity (AMF) modelling of damage in composites under Low-Velocity impact and compression after impact

In this paper, the recently developed adaptive multi-fidelity (AMF) approach is extended for progressive damage analysis of composite laminate subjected to low-velocity impact (LVI) and compression after impact (CAI). This approach is more computationally efficient by utilizing a combination of low-fidelity shell elements and high-fidelity brick elements in a single concurrent model. A general set of criteria has been proposed to govern the transition of shell and brick elements from one to the other and vice versa, as dictated by the mechanics of damage evolution. When matrix cracks or interfacial delamination initiates, shell elements transit to brick elements and cohesive elements are inserted to capture the damage growth. The brick elements partitioned by non-critical cracks are reverted to smeared shell elements when the numerical crack density becomes saturated in a laminate. Geometrical non-linearity is adopted here to predict large deformation in the composite laminate for both implicit quasi-static and dynamic analyses. The performance of AMF models is benchmarked with high-fidelity models and experimental data reported in literature. The predicted results show reasonable agreement with experimental observation and high-fidelity models, and up to 51% improvement in computational efficiency is achievable.

Time-averaged flow field reconstruction based on a multifidelity model using physics-informed neural network (PINN) and nonlinear information fusion

PurposeCurrent methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods.Design/methodology/approachA multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data.FindingsTwo experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction.Originality/valueIn this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.

A 5M Synchronization Mechanism for Digital Twin Shop-Floor

In recent years, as a promising way to realize digital transformation, digital twin shop-floor (DTS) plays an important role in smart manufacturing. The core feature of DTS is the synchronization. How to implement and maintain the synchronization is critical for DTS. However, there is still a lack of a common definition for synchronization in DTS. Besides, a systematic synchronization mechanism for DTS is strongly needed. This paper first summarizes the definition and requirements of synchronization in DTS, to clarify the understanding of synchronization in DTS. Then, a 5M synchronization mechanism for DTS is proposed, where 5M refers to multi-system data, multi-fidelity model, multi-resource state, multi-level state, and multi-stage operation. As a bottom-up synchronization mechanism, 5M synchronization mechanism for DTS has the potential to support DTS to achieve and maintain physical-virtual state synchronization, and to realize operation synchronization of DTS. The implementation methods of 5M synchronization mechanism for DTS are also introduced. Finally, the proposed synchronization mechanism is validated in a digital twin satellite assembly shop-floor, which proves the effectiveness and feasibility of the mechanism.

Multi-fidelity modeling using Gaussian processes for the frequency dependent Helmholtz equation

In scientific and engineering problems, accurate model predictions are generally accompanied with high resource and time expenses. In most applications, the data generation process can only be performed for a limited number of forward evaluations leading to insufficient model results. The concept of multi-fidelity modeling is to holistically evaluate data from different sources with varying complexity and costs. Ideally, the predictive quality of models with a high-fidelity can be combined with the efficiency of low-fidelity models. Usually, physical experiments and numerical simulations at large-scale are attributed to high-fidelity models, while analytical solutions or small-scale numerical models and experiments are considered as low-fidelity models. This contribution aims to develop a multi-fidelity model for an interior sound propagation problem. More specifically, a vehicle interior noise problem is investigated by using two boundary element models of different fidelity levels. The finer mesh corresponds to the high-fidelity model, whereas the coarser mesh is adopted as the low-fidelity model. As such, the multi-fidelity model is realized as a vector-valued Gaussian process.

Optimal decision-making in high-throughput virtual screening pipelines

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the enormous search space containing the candidates and the substantial computational cost of high-fidelity property prediction models make screening practically challenging. In this work, we propose a general framework for constructing and optimizing a high-throughput virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return on computational investment. Based on both simulated and real-world data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate virtual screening without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.

Partial-physics-informed multi-fidelity modeling of manufacturing processes

Partial-physics-informed multi-fidelity modeling of manufacturing processes

Efficient multi-fidelity computation of blood coagulation under flow.

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, [Formula: see text], and provide the governing PDEs for [Formula: see text]. This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order (p) allows balancing accuracy and computational cost providing a speedup of over N/p compared to high-fidelity models. Moreover, this cost becomes independent of the number of chemical species in the large computational meshes typical of the arterial and cardiac chamber simulations. Using a coagulation network with N = 9 and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. The thrombin concentration in these models departs from the high-fidelity solution by under 20% (p = 1) and 2% (p = 2) after 20 cardiac cycles. These multi-fidelity models could enable new coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it could be generalized to advance our understanding of other reacting systems affected by flow.