Surrogate Approach Research Articles

A machine learning surrogate model for time of flight diffraction measurements of rough defects

Understanding the uncertainty in nondestructive evaluation measurements of rough defects requires a stochastic analysis due to the random variation between the morphology of different defects. In previous studies, large numbers of finite element models of randomly generated rough defects have been run in order to gain an insight into the statistics of the uncertain results. This approach is limited due to the time taken to run each individual model (typically of the order of minutes per model) and so the total number of models run is limited. In this paper, a surrogate model approach is proposed which produces close approximations to an original finite element model of a time-of-flight diffraction measurement, but in a small fraction of the time (<1 ms). The surrogate model is trained on pairs of input (rough defect) and output (A-scan) data from the finite element model; the surrogate then learns the relationship between inputs and outputs and is then able to generate new results. The architecture employed is a machine learning sequence-to-sequence approach similar to those used in natural language algorithms, based on the idea of ‘translating’ between defect to A-scan. In this study, a surrogate model was trained on 2160 finite element results which spanned across a range of ultrasonic incidence angles, rough defect correlation length and root-mean-square roughness. The surrogate model is shown to produce A-scans with close agreement to those produced by the original finite element model; taking approximately 0.425 ms instead of approximately 8 min. Millions of results are then possible in seconds, rather than the decades that would be required for finite element studies; more complete stochastic analysis are therefore now viable.

Robustness of hydrometeorological extremes in surrogated seasonal forecasts

AbstractWater and disaster risk management require accurate information about hydrometeorological extremes. However, estimation of rare events using extreme value analysis is hampered by short observational records, with large resulting uncertainties. Here, we present a surrogate world setup that makes use of data samples from meteorological and hydrological seasonal re‐forecasts to explore extremes for long return periods. The surrogate timeseries allow us to pool the re‐forecasts into 1000‐year‐long timeseries. We can then calculate return values of extremes and explore how they are affected by the size of sub‐samples as method for estimating the uncertainty. The approach relies on the fact that probabilistic seasonal re‐forecasts, initialized with perturbed initial conditions, have limited predictive skill with increasing lead time. At long lead times re‐forecasts will diverge into independent samples. The meteorological seasonal re‐forecasts are taken from the SEAS5 system, and hydrological re‐forecasts are generated with the E‐HYPE process‐based model for the pan‐European domain. Extreme value analysis is applied to annual maxima of precipitation and streamflow for return periods of 100 years. The analysis clearly demonstrates the large uncertainty in long return period estimates with typical available samples of only few decades. The uncertainty is somewhat reduced for 100‐year samples, but several 100 years seem to be necessary to have robust estimates. The bootstrap with replacement approach is applied to shorter timeseries, and is shown to well reproduce the uncertainty range of the longer samples. However, the main estimate of the return value can be significantly offset. Although the method is model based, with the associated uncertainties and bias compared to the real world, the surrogate approach is likely useful to explore rare and compounding extremes.

Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares.

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equationsto compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

Abstract The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. This paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

Species and ecological communities as management surrogates for threatened biodiversity

In the face of the ongoing biodiversity crisis and limited conservation funding, surrogate approaches have become a valuable tool to represent biodiversity. Management surrogates are those that indirectly benefit an ecological system or species by representing the management requirements of co-occurring biodiversity. Recent findings highlight the cost-effective potential of surrogate species in managing threatened species, however, evaluating higher levels of biodiversity as management surrogates remains unexplored. Here, we sought to maximize conservation outcomes for threatened species and threatened ecological communities (TECs) by prioritizing management based on overlapping distributions, threats, and costs. We describe a prioritization framework for identifying TECs that could serve as cost-effective surrogates, and compare it with prioritizing threatened species only or both species and TECs. We show that when the objective is to maximize benefits for threatened species, a community approach performs poorly due to limited geographic overlap and high costs, while prioritizing species returned 7.5 times more benefits delivered to species under the same budget. Yet, if the objective is to maximize benefits across species and TECs simultaneously, a combined approach including both as surrogates delivers the greatest benefit for the same costs as a species-only approach. Range sizes and taxonomic groups significantly influenced the priority list, with threatened invertebrates and TECs of smaller ranges more likely to be selected as surrogates. Overall, this study emphasizes the importance of incorporating accurate data on factors such as threats and costs for identifying effective management surrogates, and highlights the potential benefits of prioritizing across multiple biodiversity features.

A study of stone arch bridge’s flood reliability through a surrogate model approach

Europe’s historic masonry arch bridges are culturally and economically significant, but their long-term safety must be ensured. Scour effects are the most common cause of collapse, so it is necessary to carry out structural assessments to mitigate the risk and prevent potential failures. In this study, a metamodel-based method was used to determine the probability of failure of an existing stone arch bridge in Portugal due to local and contraction scour on the abutments. Non-linear finite element analysis supported the calculation of the reliability index, which took into account the soil-structure interaction and the failure mechanism. The variables with the greatest influence on the load-carrying capacity of the structure were identified and a surrogate model was implemented. Fragility curves were then derived based on the surrogate model, using scour depth as a measure of intensity and load factor as an engineering requirement parameter. The results of the study indicate that the load capacity of the numerical model is compromised when the scour depth of 1.5 m reaches the base of the foundation. As a result, stability problems and settlements are observed in the model. At a depth of 2.5 m, the soil reaches its ultimate bearing capacity.

Physics-infused deep neural network for solution of non-associative Drucker–Prager elastoplastic constitutive model

In the present work, a physics-informed deep learning-based constitutive modeling approach has been introduced, for the first time, to solve non-associative Drucker–Prager elastoplastic solid governed by a linear isotropic hardening rule. A purely data-driven surrogate modeling approach for representing complex and highly non-linear elastoplastic constitutive response prevents accurate predictions due to the absence of prior physical information. To mitigate this, we design an efficient physics-constrained training approach leveraging prior physics-driven optimization procedures. It has been achieved by formulating a highly physics-augmented multi-objective loss function that includes elastoplastic constitutive relations, Drucker–Prager yield criterion, non-associative flow rule, Kuhn–Tucker consistency conditions, and various boundary conditions. Utilizing multiple densely connected independent feed-forward deep neural networks fed with high-fidelity numerical solutions in a data-driven loss function, the model obtains the accurate elastoplastic solution by minimizing the proposed loss function. The strength and robustness of the approach have been demonstrated by accurately solving the benchmark problem where a plastically deformed isotropic shallow stratum has been subjected to compressive pressure under plane strain Drucker–Prager yield condition. To optimize the performance and trainability of the model, extensive experiments on network architecture and various degrees of data-driven estimate shed light on significant improvement in terms of the accuracy of the elastoplastic solution, particularly, that exhibits sharp, or very localized features. Moreover, we propose a transfer learning-based PINNs modeling approach that elucidates the possibility of predicting solutions for different sets of applied stress and material parameters. Requiring significantly less training data, the framework can simultaneously enhance the accuracy of the solution and adaptability of training by demonstrating rapid convergence in critical loss components. The current study highlights a systematic development of a novel physics-informed deep learning approach which is quite generic in nature, yet robust and highly physics-augmented for transferability of known knowledge for vastly accelerated convergence with improved accuracy of predicting an accurate description of non-associative elastoplastic solution in the regime of continuum mechanics.

Use of Artificial Neural Network to Develop Surrogates for Hydrotreated Vegetable Oil with Experimental Validation in Ignition Quality Tester

&lt;div&gt;This article presents surrogate mixtures that simulate the physical and chemical properties in the auto-ignition of hydrotreated vegetable oil (HVO). Experimental investigation was conducted in the Ignition Quality Tester (IQT) to validate the auto-ignition properties with respect to those of the target fuel. The surrogate development approach is assisted by artificial neural network (ANN) embedded in MATLAB optimization function. Aspen HYSYS is used to calculate the key physical and chemical properties of hundreds of mixtures of representative components, mainly alkanes—the dominant components of HVO, to train the learning algorithm. Binary and ternary mixtures are developed and validated in the IQT. The target properties include the derived cetane number (DCN), density, viscosity, surface tension, molecular weight, and volatility represented by the distillation curve. The developed surrogates match the target fuel in terms of ignition delay and DCN within 6% error range. This investigation will be of value to developing high-fidelity models to investigate HVO combustion and spray behavior. This will be beneficial to researchers advancing the design and development of compression ignition engines to efficiently operate on renewable fuels such as HVO.&lt;/div&gt;

Active-learning Kriging-assisted robust design optimization of tuned mass dampers: Vibration mitigation of a steel-arch footbridge

Many typical footbridges are designed as slender structures to highlight their aesthetic characteristic. As these bridges can be highly susceptible to pedestrian-induced excitations, tuned mass dampers have been adopted as energy absorbers in many applications to mitigate this issue. The design of tuned mass dampers can be formulated as a robust design optimization problem considering various sources of uncertainties related to the bridge state and environment. To alleviate the computational burden of analyzing the statistical moments, surrogate model-based approaches have been introduced to build cheaper-to-evaluate substitutes, and the analytical expression of the robustness has been discussed to facilitate the optimization procedure. Motivated by this, the present paper derives an analytical expression for the robustness index, considering both deterministic and uncertain variables as inputs of the ordinary Kriging surrogate model. An active-learning framework is proposed to streamline the design optimization of tuned mass dampers for the vibration mitigation of slender footbridges. Two numerical examples are firstly investigated to validate the performance of the proposed method; and then, a practical application of a steel-arch footbridge is carefully studied to demonstrate the engineering feasibility and superiority of the proposed method. The results exhibit that the proposed method can efficiently and accurately facilitate the robust design of vibration mitigation devices for practical engineering projects, and showcases the potential to be used in other engineering problems.

Learning the inhomogenous term of a linear ODE

A new method to explain the action of a non-interpretable predictive model correcting the homogeneous solution of a linear ordinary differential equation (ODE) to fit given observations is presented. The prediction correcting a particular solution is ’explained’ by an estimate of the ODE's inhomogeneous term. The method uses the ODE to establish an alternate description of the predicted solution and thus belongs to the surrogate modeling approaches within the explainable AI (XAI) method families. Useful applications include processes which allow fair modeling by a homogeneous linear differential equation but have potential to be improved by including an inhomogeneous term. A study of perturbed heat transfer described by Newton's cooling law illustrates the advantages of explanations given in the form of terms of a differential equation.

Optimization Assisted by Neural Network-Based Machine Learning in Electromagnetic Applications

We introduce an optimization assisted by a neural network (ONN) predictor to the electromagnetic community. ONN belongs to the class of the surrogate model-based optimization approaches, and approximates the objective function using a non-linear approximator – neural network. We provide a comprehensive description of the ONN algorithm and the details of its mathematical formulations. We apply ONN to optimize three popular benchmark functions and compare its performance with some commonly used optimization algorithms, namely particle swarm optimization, genetic algorithm, and Bayesian optimization. For the first time, we demonstrate ONN’s applicability and effectiveness in antenna design problems by optimizing a six-element Yagi-Uda antenna and by solving a challenging ten-dimensional dual-band slotted patch antenna constrained optimization problem. To achieve this, ONN is linked with a full-wave electromagnetic simulation solver through an application user interface. The optimized slotted patch is fabricated and measured to demonstrate how ONN can be part of the full antenna design process. Our empirical results indicate that ONN requires less objective function evaluations to reach the same qualitative point and reaches better optimal points for the same number of iterations for the studied benchmark functions and antenna optimization problems compared to the aforementioned baseline optimization algorithms.

A Hierarchical Surrogate Approach to Biomass Ethanolysis Reaction Kinetic Modelling

The reaction mechanism and kinetics of the sulfuric acid catalysed ethanolysis of glucose, cellulose, xylan, and corncob was investigated using a combination of experiments and empirical reaction mechanism modelling. The...

Surrogate indirect adaptive controller tuning based on polynomial response surface method and bioinspired optimization: Application to the brushless direct current motor controller

The increment of autonomous systems has stimulated the research of new controller tuning techniques to face the unpredictable disturbances and parametric uncertainties inherent in any autonomous system that affect its performance. The indirect adaptive controller tuning approach based on the general dynamic model (IACTA-GDM) and bioinspired optimization is one of the most successful elections facing parametric uncertainties and disturbances, which are intricate to handle by other controller tuning techniques. However, this controller tuning approach is limited by the complexity of the dynamic model due to the computational burden, restricting its application to relatively small systems or systems with slow responses where the tuning is updated at large time intervals. The present work proposes a novel surrogate indirect adaptive controller tuning approach based on the response surface method (SIACTA-RSM) to address computational burden limitations. The proposal is tested on the speed regulation controller of a brushless direct current motor, with the aim of reducing the speed regulation error and the control system’s power consumption. The closed-loop system performance and the required computational time obtained by the proposed SIACTA-RSM are compared to the ones of a well-established IACTA-GDM. The descriptive and inferential statistics, as well as graphical comparisons, show that the system performance obtained by the SIACTA-RSM proposal is as competitive as the IACTA-GDM approach, keeping a mean difference among the results by up to 3.18% while reducing the computational burden of IACTA-GDM by up to 90%. These outcomes show that the SIACTA-RSM proposal is a reliable alternative to overcome the computational burden limitations that affect the IACTA-GDM approach while maintaining competitive performance.

UDGAN: A new urban design inspiration approach driven by using generative adversarial networks

Abstract The morphological design of urban space affects the quality of the environment. The traditional experience-based design approach was greatly improved by introducing computational design tools. However, the existing urban design tools are mostly developed on pre-set rules or given targets, which have few contributions to enhance creativity or generate inspiring schemes. Therefore, this paper proposes a new computational urban design approach named UDGAN, integrating generative adversarial networks (GANs) and multi-objective optimization algorithms. This model utilizes urban design scheme plans over the past 20 years from a particular designer as training datasets. Four preference models were trained to autonomously generate stylized urban design schemes. Eight morphological parameters were used to analyze the model performance by comparing generated results with the ground truth. This GAN-based surrogate approach is combined with a morphological indicator alignment process using multi-objective optimization model to obtain better results. The result shows that the R2 predicted by the improved Pix2Pix model reaches 0.798, and the similarity of the generated results can be stably distributed between 0.7 and 0.8, so the design scheme of this preferred style can be effectively learned. At the same time, the pre-trained model greatly reduces the time consumption of the design scheme generation, taking 5 min approximately to complete a generation process. This approach quickly generated the design scheme with preferred features, supporting the designer with creativity and greatly saving the time of design creation, transforming computational design into an inspiration-driven process.

Aerodynamic shape optimization of gas turbines: a deep learning surrogate model approach

Aerodynamic shape optimization of gas turbines: a deep learning surrogate model approach

Developing rear-end and side-swipe conflict prediction models for urban signalized intersections under disordered traffic conditions

A Traffic Conflict Technique is a proactive approach that identifies observable critical vehicle interactions (conflict) that could have led to a crash. This paper develops conflict-based safety performance functions (SPFs) to predict the number of traffic conflicts at the signal cycle level in mixed traffic conditions with poor lane discipline (disordered traffic conditions). 9586 vehicle trajectories were extracted from traffic video data collected from 4 signalized intersections in India. Critically interacting vehicle pairs were estimated using Time to Collision (TTC). The conventional surrogate measure is modified into a 2-dimensional surrogate approach which captures the conflicts by incorporating the vehicle dimension, heading direction, position, speed, and acceleration in the longitudinal and lateral direction between vehicles. Rear-end and side-swipe conflicts are identified at varying threshold values to incorporate severity. Rear-end conflict SPFs show that higher conflict occurrence is expected during signal cycles with more traffic volume, higher vehicle arrival speed, more right-turning traffic, and a lower platoon ratio. At severe threshold (TTC ≤ 1 s), one 1 m/s increase in speed of vehicle increases the expected number of rear-end conflicts by 6%. Furthermore, SPFs show that severe side-swipe conflicts are expected during signal cycles with more lane-changing maneuvers and right-turning vehicles. For TTC ≤ 1 s, one unit increase in the number of lane changes would increase the expected number of sides-wipe conflicts by 7.9%. The finding of this study can be most beneficially used for arriving at policy measures and improving the safety of signalized intersections in disordered traffic conditions.

Efficient sensitivity analysis for biomechanical models with correlated inputs.

In most variance-based sensitivity analysis (SA) approaches applied to biomechanical models, statistical independence of the model input is assumed. However, often the model inputs are correlated. This might alter the interpretation of the SA results, which may severely impact the guidance provided during model development and personalization. Potential reasons for the infrequent usage of SA techniques that account for input correlation are the associated high computational costs, especially for models with many parameters, and the fact that the input correlation structure is often unknown. The aim of this study was to propose an efficient correlated global sensitivity analysis method by applying a surrogate model-based approach. Furthermore, this article demonstrates how correlated SA should be interpreted and how the applied method can guide the modeler during model development and personalization, even when the correlation structure is not entirely known beforehand. The proposed methodology was applied to a typical example of a pulse wave propagation model and resulted in accurate SA results that could be obtained at a theoretically 27,000× lower computational cost compared to the correlated SA approach without employing a surrogate model. Furthermore, our results demonstrate that input correlations can significantly affect SA results, which emphasizes the need to thoroughly investigate the effect of input correlations during model development. We conclude that our proposed surrogate-based SA approach allows modelers to efficiently perform correlated SA to complex biomechanical models and allows modelers to focus on input prioritization, input fixing and model reduction, or assessing the dependency structure between parameters.

Evaluation of surrogate flood models for the use in impact-based flood warning systems at national scale

Recent flood events show that gaps in the communication channels from warning services to target groups inhibit mitigation. One approach addressing this issue is impact-based warning. We introduce a library-based surrogate flood model for the use in impact-based warning systems, tested for the main river network of Northern Switzerland. To validate the surrogate model, we compare the impacts to buildings, persons and workplaces with hazard classification, estimated with transient simulations for nine extreme precipitation scenarios. With 78 analyzed model regions, the surrogate approach reaches a Flood Area Index between 0.74 and 0.90 for each scenario (overall 0.84). The Critical Success Index calculated based on exposed persons is 0.77–0.93 (overall 0.89). Our prototype of a library-based flood surrogate model demonstrates the ability of accurately representing a same resolved transient model, bearing the potential to predict flood impacts nationwide in near real-time and the applicability to probabilistic forecasts.

Moving into the modern era of molecular classification for endometrial cancer.

The molecular subtypes of endometrial carcinoma (EC) were first described by The Cancer Genome Atlas (TCGA) a decade ago. Using surrogate approaches, the molecular classification has been demonstrated to be prognostic across EC patients and to have predictive implications. Starting in 2020, the molecular classification has been incorporated into multiple guidelines as part of the risk assessment and most recently into the International Federation of Gynecology and Obstetrics (FIGO) staging. This review article discusses the implementation of the EC molecular classification into clinical practice, the therapeutic implications, and the molecular and clinical heterogeneity of the EC molecular subtypes.

Hemodynamic Failure Staging With Blood Oxygenation Level-Dependent Cerebrovascular Reactivity and Acetazolamide-Challenged (15O-)H2O-Positron Emission Tomography Across Individual Cerebrovascular Territories.

Staging of hemodynamic failure (HF) in symptomatic patients with cerebrovascular steno-occlusive disease is required to assess the risk of ischemic stroke. Since the gold standard positron emission tomography-based perfusion reserve is unsuitable as a routine clinical imaging tool, blood oxygenation level-dependent cerebrovascular reactivity (BOLD-CVR) with CO2 is a promising surrogate imaging approach. We investigated the accuracy of standardized BOLD-CVR to classify the extent of HF. Patients with symptomatic unilateral cerebrovascular steno-occlusive disease, who underwent both an acetazolamide challenge (15O-)H2O-positron emission tomography and BOLD-CVR examination, were included. HF staging of vascular territories was assessed using qualitative inspection of the positron emission tomography perfusion reserve images. The optimum BOLD-CVR cutoff points between HF stages 0-1-2 were determined by comparing the quantitative BOLD-CVR data to the qualitative (15O-)H2O-positron emission tomography classification using the 3-dimensional accuracy index to the randomly assigned training and test data sets with the following determination of a single cutoff for clinical application. In the 2-case scenario, classifying data points as HF 0 or 1-2 and HF 0-1 or 2, BOLD-CVR showed an accuracy of >0.7 for all vascular territories for HF 1 and HF 2 cutoff points. In particular, the middle cerebral artery territory had an accuracy of 0.79 for HF 1 and 0.83 for HF 2, whereas the anterior cerebral artery had an accuracy of 0.78 for HF 1 and 0.82 for HF 2. Standardized and clinically accessible BOLD-CVR examinations harbor sufficient data to provide specific cerebrovascular reactivity cutoff points for HF staging across individual vascular territories in symptomatic patients with unilateral cerebrovascular steno-occlusive disease.