Input Parameter Space Research Articles

Boosting Barlow Twins Reduced Order Modeling for Machine Learning‐Based Surrogate Models in Multiphase Flow Problems

AbstractWe present an innovative approach called boosting Barlow Twins reduced order modeling (BBT‐ROM) to enhance the reliability of machine learning surrogate models for multiphase flow problems. BBT‐ROM builds upon Barlow Twins reduced order modeling that leverages self‐supervised learning to effectively handle linear and nonlinear manifolds by constructing well‐structured latent spaces of input parameters and output quantities. To address the challenge of high contrast data in multiphase flow problems due to injection wells and faults, we employ a boosting algorithm within BBT‐ROM. This algorithm sequentially trains a set of weak models (i.e., inaccurate models), improving prediction accuracy through ensemble learning. To evaluate the performance of BBT‐ROM, we conduct three three‐dimensional multiphase flow problems, including waterflooding and geologic carbon storage (GCS), with varying numbers of input parameter cases and model domain features. The results demonstrate that BBT‐ROM excels at predicting non‐wetting phase saturation (e.g., oil or saturation) and fluid pressure, with average relative errors ranging from 0.5% to 3%. Importantly, BBT‐ROM showcases robustness when faced with limited input parameter space during GCS testing.

Prognostic value of clinical and radiomic parameters in patients with liver metastases from uveal melanoma.

Approximately every second patient with uveal melanoma develops distant metastases, with the liver as the predominant target organ. While the median survival after diagnosis of distant metastases is limited to a year, yet-to-be-defined subgroups of patients experience a more favorable outcome. Therefore, prognostic biomarkers could help identify distinct risk groups to guide patient counseling, therapeutic decision-making, and stratification of study populations. To this end, we retrospectively analyzed a cohort of 101 patients with newly diagnosed hepatic metastases from uveal melanoma by using Cox-Lasso regression machine learning, adapted to a high-dimensional input parameter space. We show that substantial binary risk stratification can be performed, based on (i) clinical and laboratory parameters, (ii) measures of quantitative overall hepatic tumor burden, and (iii) radiomic parameters. Yet, combining two or all three domains failed to improve prognostic separation of patients. Additionally, we identified highly relevant clinical parameters (including lactate dehydrogenase, thrombocyte counts, aspartate transaminase, and the metastasis-free interval) at first diagnosis of metastatic disease as predictors for time-to-treatment failure and overall survival. Taken together, the risk stratification models, built by our machine-learning algorithm, identified a comparable and independent prognostic value of clinical, radiological, and radiomic parameters in uveal melanoma patients with hepatic metastases.

Application of factorization machine with quantum annealing to hyperparameter optimization and metamodel‐based optimization in granular flow simulations

AbstractThis study examined the applicability of factorization machines with quantum annealing (FMQA) to the field of landslide risk assessment for two specific black‐box optimization problems, hyperparameter optimization (HPO) for metamodeling and metamodel‐based simulation optimization (MBSO) targeting granular flow simulation using discrete element method (DEM). These two optimization problems are solved successively: HPO is first performed to determine the hyperparameters of the Gaussian process regression (GPR) metamodel, which is then used as a low‐cost, fast approximate solver of granular flow simulations for MBSO. After conducting a series of granular flow simulations using DEM, a metamodel is created that outputs a risk index of interest, the run‐out distance, from its input parameters by employing GPR with two hyperparameters, length‐scale and signal variance. Subsequently, HPO is performed to obtain the optimal set of hyperparameters by applying FMQA and other optimization methods using another set of hyperparameters determined using the gradient‐ascent method as the reference solution. Finally, using the metamodel created by each optimization method as an approximate solver for DEM simulations, MBSO is performed to find the optimal target output, the maximum run‐out distance, in the space of physical input parameters for risk assessment. A comparison of the performance of FMQA with that of other methods shows that FMQA is competitive in terms of efficiency and stability with state‐of‐the‐art algorithms such as Bayesian optimization.

Combining simulation and experimental data via surrogate modelling of continuum dislocation dynamics simulations

Several computational models have been introduced in recent years to yield comprehensive insights into microstructural evolution analyses. However, the identification of the correct input parameters to a simulation that corresponds to a certain experimental result is a major challenge on this length scale. To complement simulation results with experimental data (and vice versa) is not trivial since, e.g. simulation model parameters might lack a physical understanding or uncertainties in the experimental data are neglected. Computational costs are another challenge mesoscale models always have to face, so comprehensive parameter studies can be costly. In this paper, we introduce a surrogate model to circumvent continuum dislocation dynamics simulation by a data-driven linkage between well-defined input parameters and output data and vice versa. We present meaningful results for a forward surrogate formulation that predicts simulation output based on the input parameter space, as well as for the inverse approach that derives the input parameter space based on simulation as well as experimental output quantities. This enables, e.g. a direct derivation of the input parameter space of a continuum dislocation dynamics simulation based on experimentally provided stress–strain data.

Adaptive design of experiments to fit surrogate Gaussian process regression models allows fast sensitivity analysis of the input waveform for patient-specific 3D CFD models of liver radioembolization

Background and objectivePatient-specific 3D computational fluid dynamics (CFD) models are increasingly being used to understand and predict transarterial radioembolization procedures used for hepatocellular carcinoma treatment. While sensitivity analyses of these CFD models can help to determine the most impactful input parameters, such analyses are computationally costly. Therefore, we aim to use surrogate modelling to allow relatively cheap sensitivity analysis. As an example, we compute Sobol's sensitivity indices for three input waveform shape parameters. MethodsWe extracted three characteristic shape parameters from our input mass flow rate waveform (peak systolic mass flow rate, heart rate, systolic duration) and defined our 3D input parameter space by varying these parameters within 75 %-125 % of their nominal values. To fit our surrogate model with a minimal number of costly CFD simulations, we developed an adaptive design of experiments (ADOE) algorithm. The ADOE uses 100 Latin hypercube sampled points in 3D input space to define the initial design of experiments (DOE). Subsequently, we re-sample input space with 10,000 Latin Hypercube sampled points and cheaply estimate the outputs using the surrogate model. In each of 27 equivolume bins which divide our input space, we determine the most uncertain prediction of the 10,000 points, compute the true outputs using CFD, and add these points to the DOE. For each ADOE iteration, we calculate Sobol's sensitivity indices, and we continue to add batches of 27 samples to the DOE until the Sobol indices have stabilized. ResultsWe tested our ADOE algorithm on the Ishigami function and showed that we can reliably obtain Sobol's indices with an absolute error <0.1. Applying ADOE to our waveform sensitivity problem, we found that the first-order sensitivity indices were 0.0550, 0.0191 and 0.407 for the peak systolic mass flow rate, heart rate, and the systolic duration, respectively. ConclusionsAlthough the current study was an illustrative case, the ADOE allows reliable sensitivity analysis with a limited number of complex model evaluations, and performs well even when the optimal DOE size is a priori unknown. This enables us to identify the highest-impact input parameters of our model, and other novel, costly models in the future.

Deep learning-based predictive models for laser direct drive at the Omega Laser Facility

The rich and complex physics of inertial confinement fusion provides a unique and challenging space for high-fidelity first-principles modeling. Consequently, simulation codes that are used to design experiments are computationally expensive and lack the predictive capability required for extensive parameter exploration in search of a high-performing design for laser direct drive. In this article, we present two deep-learning-based predictive models intended to address these difficulties. The first model (TL DNN) acts as a fast emulator of simulations as well as experiments at the Omega Laser Facility. This model is trained on a simulation database and subsequently calibrated on experimental data using transfer learning. To facilitate the development of this model, an autoencoder is developed to reduce the dimensionality of the input space by compressing the laser pulse input. The model predicts key experimental scalar observables of Omega experiments with high accuracy and minimal computational cost. This deep neural net enables rapid exploration of a high-dimensional input parameter space for an optimal implosion design. The second model (DNN SM+) aims to extend the statistical modeling work of Lees et al. [Phys. Rev. Lett. 127, 105001 (2021)], by increasing the complexity of the model space and allowing for coupling between degradation terms. Since the model capacity of DNN SM+ is higher than the model of Lees et al., DNN SM+ can potentially provide an improvement in predictive capability, and we use this model to provide insight into complicated degradation dependencies.

Assessing input parameter hyperspace and parameter identifiability in a cardiovascular system model via sensitivity analysis

We aim to clarify our understanding of the process of state-space model input parameter identification, known, within the clinical context, as model personalisation. To do so, we apply reference sensitivity and identifiability techniques to a lumped parameter, single ventricle representation of the systemic circulation, chosen in view of its relative simplicity and prior art. We attempt to quantify the reliability of input parameter identifiability through the lens of 4 clinically relevant measurements and the attendant difficulty in personalising the model. In turn, this that we extend existing methods which combine both parameter influence and orthogonality, to global sensitivities. By examining different parameter sensitivity evaluation methodologies, we investigate the stability of optimal parameter subsets which are commonly used to aid clinical investigations. In order to perform the personalisation process, one must understand the complexity of the high dimensional input parameter hyperspace associated with this class of model. By utilising Sobol indices, we propose a domain-agnostic and intuitive approach. This involves varying the bounds of the input parameter space relative to the model’s base state. These investigations yield a pseudo-mapping of the input hyperspace, cementing our understanding of the role of identifiable input parameters in the state-space model. Our findings suggest a novel global methodology for input parameter identifiability and input hyperspace mapping, providing valuable insights into solving the personalisation process.

Autocalibration of the E3SM Version 2 Atmosphere Model Using a PCA‐Based Surrogate for Spatial Fields

AbstractGlobal Climate Model tuning (calibration) is a tedious and time‐consuming process, with high‐dimensional input and output fields. Experts typically tune by iteratively running climate simulations with hand‐picked values of tuning parameters. Many, in both the statistical and climate literature, have proposed alternative calibration methods, but most are impractical or difficult to implement. We present a practical, robust, and rigorous calibration approach on the atmosphere‐only model of the Department of Energy's Energy Exascale Earth System Model (E3SM) version 2. Our approach can be summarized into two main parts: (a) the training of a surrogate that predicts E3SM output in a fraction of the time compared to running E3SM, and (b) gradient‐based parameter optimization. To train the surrogate, we generate a set of designed ensemble runs that span our input parameter space and use polynomial chaos expansions on a reduced output space to fit the E3SM output. We use this surrogate in an optimization scheme to identify values of the input parameters for which our model best matches gridded spatial fields of climate observations. To validate our choice of parameters, we run E3SMv2 with the optimal parameter values and compare prediction results to expertly‐tuned simulations across 45 different output fields. This flexible, robust, and automated approach is straightforward to implement, and we demonstrate that the resulting model output matches present day climate observations as well or better than the corresponding output from expert tuned parameter values, while considering high‐dimensional output and operating in a fraction of the time.

Galaxy clustering multi-scale emulation

Simulation-based inference has seen increasing interest in the past few years as a promising approach to modelling the non-linear scales of galaxy clustering. The common approach, using the Gaussian process, is to train an emulator over the cosmological and galaxy–halo connection parameters independently for every scale. We present a new Gaussian process model that allows the user to extend the input parameter space dimensions and to use a non-diagonal noise covariance matrix. We use our new framework to simultaneously emulate every scale of the non-linear clustering of galaxies in redshift space from the ABACUSSUMMITN-body simulations at redshift z = 0.2. The model includes nine cosmological parameters, five halo occupation distribution (HOD) parameters, and one scale dimension. Accounting for the limited resolution of the simulations, we train our emulator on scales from 0.3 h−1 Mpc to 60 h−1 Mpc and compare its performance with the standard approach of building one independent emulator for each scale. The new model yields more accurate and precise constraints on cosmological parameters compared to the standard approach. As our new model is able to interpolate over the scale space, we are also able to account for the Alcock-Paczynski distortion effect, leading to more accurate constraints on the cosmological parameters.

Constraining the carbon cycle in JULES-ES-1.0

Abstract. Land surface models are an important tool in the study of climate change and its impacts, but their use can be hampered by uncertainties in input parameter settings and by errors in the models. We apply uncertainty quantification (UQ) techniques to constrain the input parameter space and corresponding historical simulations of JULES-ES-1.0 (Joint UK Land Environment Simulator Earth System), the land surface component of the UK Earth System Model, UKESM1.0. We use an ensemble of historical simulations of the land surface model to rule out ensemble members and corresponding input parameter settings that do not match modern observations of the land surface and carbon cycle. As JULES-ES-1.0 is computationally expensive, we use a cheap statistical proxy termed an emulator, trained on the ensemble of model runs, to rule out parts of the parameter space where the simulator has not yet been run. We use history matching, an iterated approach to constraining JULES-ES-1.0, running an initial ensemble and training the emulator, before choosing a second wave of ensemble members consistent with historical land surface observations. We successfully rule out 88 % of the initial input parameter space as being statistically inconsistent with observed land surface behaviour. The result is a set of historical simulations and a constrained input space that are statistically consistent with observations. Furthermore, we use sensitivity analysis to identify the most (and least) important input parameters for controlling the global output of JULES-ES-1.0 and provide information on how parameters might be varied to improve the performance of the model and eliminate model biases.

Parallel Processing of Image Databases for Accelerated Morphological Analysis

Nuclear forensics relies on different signatures to identify the source of nuclear material. Such signatures include crystalline structure, chemical composition, and particle morphology. One way to quantify morphology in electron microscope imagery is through image segmentation, where pixels are assigned to several partitions (or groups) that correspond to particles, grains, and other objects of interest within the image. Once pixels are assigned to segments, it is relatively straightforward to quantify other quantities of interest, such as grain size, circularity, etc. However, the range and diversity of microscope images make it difficult to obtain an accurate segmentation automatically. The accuracy of segmentation can be improved through supervised learning, but this requires many images to be manually segmented. Another way to improve the accuracy is to use interactive segmentation. Interactive segmentation requires a human to provide image-specific user input to improve performance. However, the amount of user input (effort) is generally far less than is required for supervised learning. In this paper, we investigate several parallelization strategies to automatically explore the user input parameter space of interactive segmentation algorithms across a large number of images. Specifically, we investigate four different parallelization mechanisms in a high-performance computing (HPC) environment and use the Amdahl fraction to evaluate efficiency on multiple processor cores across multiple nodes. Ultimately, the parallelization strategy that was most efficient utilized the message passing interface integrated with the segmentation and quantification code. This strategy had an Amdahl fraction of 0.985 and a performance of about 0.251 s/image. These results indicate that the parameter space of interactive segmentation algorithms can be efficiently explored using HPC. This opens the door to future work where user input is reduced and where interactive image segmentation algorithms are automatically applied to large image sets.

Development of an Artificial Intelligence Model to Predict Combustion Properties, With a Focus on Auto-Ignition Delay

Abstract Hydrogen-compatible gas turbines are one way to decarbonize electricity production. However, burning and handling hydrogen is not trivial because of its high reactivity and tendency to detonate. Mandatory safety parameters, such as auto-ignition delay times, can be estimated thanks to predictive detailed kinetic models, but with significant calculation times that limit coupling with fluid mechanic codes. An auto-ignition prediction tool was developed based on an artificial intelligence (AI) model for fast computations and an implementation into an explosion model. A dataset of ignition delay times (IDTs) was generated automatically using a recent detailed kinetic model from National University of Galway (NUIG) selected from the literature. Generated data cover a wide operating range and different compositions of fuels. Clustering problems in sample points were avoided by a quasi-random Sobol sequence, which covers uniformly the entire input parameter space. The different algorithms were trained, cross-validated, and tested using a database of more than 70,000 ignitions cases of natural gas/hydrogen blends calculated with the full kinetic model by using a common split of 70/30 for training, testing. The AI model shows a high degree of robustness. For both the training and testing datasets, the average value of the correlation coefficient was above 99.91%, and the mean absolute error (MAE) and the mean square error (MSE) were around 0.03 and lower than 0.04, respectively. Tests showed the robustness of the AI model outside the ranges of pressure, temperature, and equivalence ratio of the dataset. A deterioration is, however, observed with increasing amounts of large alkanes in the natural gas.

IPSAL: Implementation of the module to generate the Sobol sequence and indices

Sensitivity and uncertainty analysis hold significant importance across a range of applications, spanning from industrial problems to climate change, financial risk assessment, as well as mathematical and computational models. These analyses involve identifying influential input parameters in models to comprehend their impact on the output. Sensitivity analysis can be performed locally, examining parameter effects at a fixed value, or globally, evaluating the model across a range of parameter values. The Sobol method stands as a robust approach for global sensitivity analysis, employing a Sobol sequence to create samples more uniformly within the input parameter space, thus enabling efficient exploration of model inputs. This paper aims to introduce a computational implementation in Scilab to generate the Sobol sequence for utilization in sensitivity analysis through the Sobol method. A test case was applied to generate Sobol sequences and discuss the obtained results.

Augmenting Deep Residual Surrogates with Fourier Neural Operators for Rapid Two-Phase Flow and Transport Simulations

Summary Accurate numerical modeling of multiphase flow and transport mechanisms is essential to study varied, complex physical phenomena including flow in subsurface oil and gas reservoirs and subsurface aquifers subject to CO2 sequestration. State-of-the-art complete physics-based solvers suffer from many computational challenges. High-fidelity data-driven surrogate models that solve the governing partial differential equations (PDEs) have the potential to optimize the time to solution and increase confidence in critical business and engineering decisions through better quantification of solution statistics. We leverage the recently proposed Fourier neural operators (FNOs) with quasilinear time complexity to capture the spectral information from feature maps to solve the coupled porous flow and transport PDEs. Embedding Fourier layers within the residual blocks results in a highly effective structure that, while achieving competitive accuracy, also enables efficient training of deeper networks with a dramatically reduced number of trainable parameters. The resulting novel deep-learning (DL) architecture is coined as FResNet++. FResNet++ uses squeeze and excitation blocks, atrous spatial pyramid pooling (ASPP), and attention blocks to increase its sensitivity to the relevant features and capture multiscale information, and it is specifically tuned to operate optimally to learn from and predict numerically simulated flow (pressure and saturation) fields. We demonstrate the ability of FResNet++ to generalize over multiple high-dimensional input parameter spaces that describe subsurface permeability and porosity heterogeneity. The resulting DL architecture accurately captures the complex interplay between viscous forces and highly heterogeneous permeability and porosity fields. We investigate two-phase flow in porous media, which is the archetypal problem for reservoir simulation giving rise to a system of nonlinearly coupled PDEs with highly heterogeneous coefficients. We show in blind tests that FResNet++ predicts saturation fields more accurately compared to ResU-Net and original FNO with fully connected linear layers. We additionally investigate the effects of using alternative loss functions and an alternative way of utilizing FResNet++ to increase its effectiveness. For the first time in the literature, we show that the spatiotemporal evolution of pressure and saturation fields can be jointly predicted with good accuracy using a single FResNet++ network over long time horizons in response to previously unseen permeability and porosity fields. After a moderate training investment on graphics processing units (GPUs), FResNet++ yields a speedup of at least four orders of magnitude compared to a conventional numerical PDE solver and operates with notably fewer trainable parameters compared to the original FNO. Our numerical experiments validate that FNOs can be utilized in various convolutional neural network-based architectures and can effectively substitute for repetitive physics-based forward simulations for scenario testing.

A Predictive Model for Weld Properties in AA-7075-FSW: A Heterogeneous AMIS-Ensemble Machine Learning Approach

This study addresses the research gap in materials science by developing an integrated predictive model for Ultimate Tensile Strength (UTS), Maximum Hardness (MH), and Heat Input (HI) in AA-7075 Friction Stir Welding (FSW). The aim is to enhance welding procedures, particularly in high-precision industries like aerospace and automotive. By incorporating four control parameters (Tilt Angle, Rotation Speed, Welding Speed, and Shoulder Diameter) and utilizing a Long Short-Term Memory (LSTM) machine learning model, a Heterogeneous Ensemble Machine Learning (He-EM) approach is developed. The Artificial Multiple Intelligence System (AMIS) optimizes the decision fusion strategy of each technique, ensuring the model's effectiveness. Validated using diverse experimental design methods and three datasets, the proposed AMIS He-EM model outperforms existing techniques (GPR, SVM, HE-UWE, and HE-WEDE) by significant margins (35.12%, 24.92%, 22.31%, and 15.48% respectively). The model's robustness is demonstrated, as its performance remains consistent across different experimental design methods. The key finding of this research is the remarkable improvement in accuracy for predicting UTS, MH, and HI in AA7075 FSW. This study highlights the importance of incorporating four control parameters and utilizing the D-optimal design for efficient exploration of the input parameter space. The implications of this research are profound, offering opportunities to optimize welding procedures, improve product performance, and streamline manufacturing processes in industries relying on AA7075 FSW.

Evaluation of compliant walking locomotion models for civil engineering applications

This study aims to evaluate the suitability of the spring-loaded inverted pendulum (SLIP) model and three of its upgrades for modelling pedestrians in civil engineering applications. Model equations in Cartesian coordinates have been derived for the four SLIP-based models and they have been presented in ready-to-use format. The input parameter space that produces the stable periodic gait has been identified and relevant gait parameters (step frequency, average speed, and dynamic load factor) have then been evaluated against the measured parameter space characterising the pedestrian population. The results indicate that the original SLIP model has multiple drawbacks. Adding roller feet was found to increase the estimates of average walking speed when compared with the SLIP model. Adding damping brings more substantial benefits of improved coverage of the step frequency and dynamic load factor parameter space. Dimensional analysis was found to be a useful means of modelling a new pedestrian having either a new body mass or leg length. In summary, the analysis suggests that inclusion of leg damping in the model is crucial for achieving realistic estimates of the step frequency and dynamic load factor, while modelling foot geometry brings improved estimates of the walking speed.

Two‐step clustering for data reduction combining DBSCAN and k‐means clustering

AbstractA novel combination of two widely‐used clustering algorithms is proposed here for the detection and reduction of high data density regions. The density‐based spatial clustering of applications with noise (DBSCAN) algorithm is used for the detection of high data density regions and the k‐means algorithm for reduction. The proposed algorithm iterates while successively decrementing the DBSCAN search radius, allowing for an adaptive reduction factor based on the effective data density. The algorithm is demonstrated for a physics simulation application, where a surrogate model for fusion reactor plasma turbulence is generated with neural networks. A training dataset for the surrogate model is created with a quasilinear gyrokinetics code for turbulent transport calculations in fusion plasmas. The training set consists of model inputs derived from a repository of experimental measurements, meaning there is a potential risk of over‐representing specific regions of this input parameter space. By applying the proposed reduction algorithm to this dataset, this study demonstrates that the training dataset can be reduced by a factor ˜20 using the proposed algorithm, without a noticeable loss in the surrogate model accuracy. This reduction also provides a way of analyzing existing high‐dimensional datasets for biases and consequently reducing them, which lowers the cost of re‐populating that parameter space with higher quality data.

Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network

We deploy a supervised machine-learning model based on a neural network to predict the temporal and spectral reshaping of a simple sinusoidal modulation into a pulse train having a comb structure in the frequency domain, which occurs upon nonlinear propagation in an optical fibre. Both normal and anomalous second-order dispersion regimes of the fibre are studied, and the speed of the neural network is leveraged to probe the space of input parameters for the generation of custom combs or the occurrence of significant temporal or spectral focusing.

TCAD-Enabled Machine Learning—An Efficient Framework to Build Highly Accurate and Reliable Models for Semiconductor Technology Development and Fabrication

The requirements on data-driven Machine Learning models for industrial applications are often stricter, compared to those used for academic purposes, as model reliability is critical in industrial environments. Herein is introduced a framework which enables automated data generation with the goal of efficiently providing a data set sufficient to build a reliable and actionable model. Essential to this framework is the placement of the model training/testing data points, which need to be well distributed across the defined input parameter space. The framework is applied to semiconductor fabrication, wherein TCAD, a set of simulation tools that reproduce the physical processing and the final electrical performance of semiconductor devices, is a well-established capability. Transistor-level processing data is reproduced with TCAD simulations, from which the Machine Learning model is built. The framework described here assures that the resulting Machine Learning model fulfills the accuracy requirements across the parameter space. As an example application, the final Machine Learning model is then used to modify the process for a transistor, to obtain both better electrical performance and reduced variability.

Parameter sensitivity of the excessive acceleration failure mode in second-generation intact stability

In this study, the parameter sensitivity of the level 1 and 2 assessments of the excessive acceleration failure mode in the International Maritime Organization second-generation intact stability was analyzed. Monte-Carlo simulations were conducted using the input parameter space, which was generated using a Gaussian distribution, and a variance-based sensitivity analysis was performed using the Monte-Carlo simulation results. The longitudinal and vertical positions of the check point, natural roll period, and roll decay coefficient were selected as input parameters for the level 1 assessment, whereas the roll damping coefficient and effective wave slope coefficient replaced the roll decay coefficient for the level 2 assessment. The results revealed that the highest total sensitivity index for the level 1 assessment was the natural roll period, which was 0.8, and the effective wave slope had a total sensitivity index of 0.5 for the level 2 assessment. This indicated that the uncertainty of the natural roll period was dominantly propagated to the resultant value of the level 1 assessment, while the effective wave slope coefficient was the most sensitive parameter in the level 2 assessment. The uncertainty in the input variable was found to cause the opposite decision if the resultant value was close to the criterion value under a given loading condition.