A Markov Chain Surrogate Model for a Two-Dimensional Interacting Particle System with Internal Collisions

Uncertainty quantification in LES of a turbulent bluff-body stabilized flame

The sensitivity of an energetic material is strongly influenced by its microstructure. This work distinguishes the roles played by the microstructure (i.e., the meso-scale) in the macro-scale shock sensitivity of two different materials: TATB and HMX. To quantify sensitivity, we develop a meso-informed energy deposition model for a porous TATB material, following procedures from the previous work on HMX. Simulations of reactive void collapse in TATB are employed to calculate the rate of initiation and growth of hotspots. These rates are expressed as surrogate models, expressing meso-scale (hotspot) quantities of interest as functions of shock strength Ps and void size Dvoid. The hotspot ignition and growth rate surrogates for TATB are compared with those for HMX, providing insights into meso-scale physics underlying shock sensitivity of these two energetic materials. The surrogate models are then used in a meso-informed ignition and growth (MES-IG) model to close macro-scale simulations of the shock response of porous TATB. We also obtain the run-to-detonation distances and generate Pop-plots to quantify macro-scale sensitivity. It is shown that Pop-plots for HMX-based energetic materials accord with behavior observed in experimental studies; however, there is a significant discrepancy between MES-IG predictions and experiments for TATB; the causes for this difference between HMX and TATB are discussed, pointing to areas for future work.

We describe the application of a validation and uncertainty quantification methodology to multiphase computational fluid dynamics modeling, demonstrating the methodology with simulations of a pilot-scale circulating fluidized bed. The overall pressure drop is used as the quantity of interest (QoI); the solids circulation rate and the superficial gas velocity are chosen as the uncertain input quantities. The uncertainty in the QoI, caused by uncertainties in input parameters, surrogate model, spatial discretization, and time averaging, is calculated, and the model form uncertainty is estimated by comparing simulation results with experimental data. The spatial discretization error was determined to be the most dominant source of uncertainty, but the applicability of the method used to calculate that uncertainty needs to be further investigated. The results of the analysis are expressed as a probability box (p-box) plot. A p-box similarly constructed for predictive simulations will give the design engineer information about the confidence in the predicted values.

Factor Fixing (FF) is a common method for reducing the number of model parameters to lower computational cost. FF typically starts with distinguishing the insensitive parameters from the sensitive and pursues uncertainty quantification (UQ) on the resulting reduced‐order model, fixing each insensitive parameter at a fixed value. There is a need, however, to expand such a common approach to consider the effects of decision choices in the FF‐UQ procedure on metrics of interest. Therefore, to guide the use of FF and increase confidence in the resulting dimension‐reduced model, we propose a new adaptive framework consisting of four principles: (a) re‐parameterize the model first to reduce obvious non‐identifiable parameter combinations, (b) focus on decision relevance especially with respect to errors in quantities of interest (QoI), (c) conduct adaptive evaluation and robustness assessment of errors in the QoI across FF choices as sample size increases, and (d) reconsider whether fixing is warranted. The framework is demonstrated on a spatially‐distributed water quality model. The error in estimates of QoI caused by FF can be estimated using a Polynomial Chaos Expansion (PCE) surrogate model. Built with 70 model runs, the surrogate is computationally inexpensive to evaluate and can provide global sensitivity indices for free. For the selected catchment, just two factors may provide an acceptably accurate estimate of model uncertainty in the average annual load of Total Suspended Solids (TSS), suggesting that reducing the uncertainty in these two parameters is a priority for future work before undertaking further formal uncertainty quantification.

Column leaching tests are a common approach for evaluating the leaching behavior of contaminated soil and waste materials, which are often reused for various construction purposes. The observed breakthrough curves of the contaminants are affected by the intricate dynamics of solute transport, inter-phase mass transfer, and dispersion. Disentangling these interactions requires numerical models. However, inverse modeling and parameter sensitivity analysis are often time-consuming, especially when sorption/desorption kinetics are explicitly described by intra-particle diffusion, requiring the discretization along the column axis and inside the grains. To replace such computationally expensive models, we developed a machine-learning based surrogate model employing two disparate ensemble methods (stacking and weighted distance average) within the defined parameter range based on the German standard for column leaching tests. To optimize the surrogate model, adaptive sampling methods based on three distinct infill criteria are employed. These criteria include maximizing expected improvement, the Mahalanobis distance (exploitation), and maximizing standard deviation (exploration).The stacking surrogate model makes use of extremely randomized trees and random forest as base- and meta-model. The model shows a very good performance in emulating the behavior of the original numerical model (Relative Root Mean Squared Error = 0.09). Our proposed surrogate model has been applied to estimate the complete posterior parameter distribution using Markov Chain Monte Carlo simulation. The impact of individual input parameters on the predictions generated by the surrogate model was analyzed using SHapley Additive exPlanations methods.

From a mathematical viewpoint, the frequency domain analysis of vessel motion responses due to wave actions is based on integration of system dynamics idealized in terms of response amplitude operators for six degrees-of-freedom (DOFs) rigid body motions and an input wave spectrum in order to obtain the response spectrum. Various quantities of interest can be deduced from the response spectrum, which are then used for deriving response-based operational limits for marine operations, also including extreme value and fatigue analysis. The variation of such quantities, owing to the uncertainties associated with the vessel system parameters, can be quantified by performing uncertainty propagation and consequent sensitivity analysis. This study emphasizes and proposes a computational-efficient way of assessing the sensitivity of the system model output with respect to the uncertainties residing in the input parameters by operating on a surrogate model representation. In this respect, the global sensitivity analysis was effectively carried out by deploying an efficient nonintrusive polynomial chaos expansion surrogate model built using a point collocation strategy. Successively, Sobol’ indices were obtained from the analytical decomposition of the polynomial coefficients. The indices, eventually, are employed to quantitatively measure the effects of input uncertainties on the output 6DOF vessel root-mean-square responses.

In this paper, we study some strong limit theorems relative to the geometric average of random transition probabilities of nonhomogeneous Markov chains indexed by a tree. This result is an extension of some strong limit theorems relative to the geometric average of random transition probabilities of arbitrary finite nonhomogeneous Markov chains.

In the field of energy system modelling, increasing complexity and optimization analysis are essential for understanding the most effective decarbonization options. However, the growing need for intricate models leads to increased computational time, which can hinder progress in research and policy-making. This study aims to address this issue by integrating machine learning algorithms with EnergyPLAN and EPLANopt, a coupling of EnergyPLAN software and a multi-objective evolutionary algorithm, to expedite the optimization process while maintaining accuracy. By saving computational time, we can increase the number of evaluations, thereby enabling deeper exploration of uncertainty in energy system modelling. Although machine learning models have been widely employed as surrogate models to accelerate optimization problems, their application in energy system modeling at the national scale, while preserving high temporal resolution and extensive sector-coupling, remains scarce. Several machine learning models were evaluated, and an artificial neural network was selected as the most effective surrogate model. The findings demonstrate that incorporating this surrogate model within the optimization process reduces computational time by 64 % compared to the conventional EPLANopt approach, while maintaining an accuracy level close to that obtained by running EPLANopt without the surrogate model.

We propose a set of equations for preliminary risk‐targeted seismic design of structures base‐isolated using single friction pendulum (SFP) bearings. The equations offer statistical estimates of the maximum displacement of the superstructure relative to the base and the maximum displacement of the isolated base response quantities of interest (RQIs), given ground motion intensity measures and the essential dynamic properties of the SFP bearing base‐isolated structure. The set of proposed equations enables preliminary seismic design of SFP base‐isolated structures using the mean annual frequency of exceeding displacement‐defined limit states related to the two RQIs. To develop the design equations, we define and use a two‐degree‐of‐freedom (2DOF) surrogate model that features a few essential dynamic parameters of the SFP bearing base‐isolated structure. We first verify that the 2DOF surrogate model is accurate enough to represent the base and superstructure displacements compared to the complete multiple‐degree‐of‐freedom model of the prototype SFP bearing base‐isolated structure. Next, we perform more than 5 million non‐linear dynamical analyses of 4900 distinct 2DOF surrogates subjected to 210 different recorded ground motions scaled five times. We fit the response data of each 2DOF surrogate to a linear model and use two different modeling techniques to derive the design equations. One model is based on Polynomial Chaos Expansion (PCE), and the other model is based on Linear Regression (LR). The PCE model is more accurate than the LR model, with the trade‐off regarding its simplicity. Nevertheless, both the PCE and the LR models are accurate enough to estimate the design quantities of interest of the SFP bearing base‐isolated structure for preliminary design purposes. Lastly, we exemplify the use of the proposed design equations and we show that the estimate of base displacement is conservative in the cases when the superstructure of the SPF bearing base‐isolated structure yields.

Fast and robust parameter estimation with uncertainty quantification for the cardiac function

Hydrodynamic shape optimization by high fidelity CFD solver and Gaussian process based response surface method

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10−12s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

In the field of multidisciplinary hypersonic vehicle design, striking the balance between the accuracy and efficiency of a predictive aerodynamic response model is a significant challenge. Therefore, the primary objective of this research was to develop guidelines for the construction of Kriging surrogate models for key aerothermodynamic quantities of interest (QoI) applicable to a complex hypersonic vehicle. Kriging models were developed using data points sampled across a broad range of key flight conditions on aerodynamic responses of a Generic Hypersonic Vehicle (GHV) obtained through inviscid Computational Fluid Dynamics (CFD) simulations. These surrogate models were inspected to determine ``best practices'' Kriging correlation and regression functions for each type of aerodynamic response considered. Additionally, the number of training points required to achieve a desired level of surrogate accuracy for each type of response was explored. Trends of the responses with respect to the design space are also discussed.

This work examines the oxidation of a well-characterized, high-octane-number FACE (fuel for advanced combustion engines) F gasoline. Oxidation experiments were performed in a jet-stirred reactor (JSR) for FACE F gasoline under the following conditions: pressure, 10 bar; temperature, 530–1250 K; residence time, 0.7s; equivalence ratios, 0.5, 1.0, and 2.0. Detailed species profiles were achieved by identification and quantification from gas chromatography with mass spectrometry (GC-MS) and Fourier transform infrared spectrometry (FTIR). Four surrogates, with physical and chemical properties that mimic the real fuel properties, were used for simulations, with a detailed gasoline surrogate kinetic model. Fuel and species profiles were well-captured and -predicted by comparisons between experimental results and surrogate simulations. Further analysis was performed using a quantities of interest (QoI) approach to show the differences between experimental and simulation results and to evaluate the gasoline surro...

In our study of dynamic systems, our first goal is to obtain a model. For our purposes, a model consists of mathematical equations which describe the behavior of a system. For example, in Chapter 5 we developed the set of equations (5.7)–(5.12) which describe how the state of a DES evolves as a result of event occurrences over time. Our next goal is to use a model in order to obtain explicit mathematical expressions for quantities of interest. For example, in Chapter 7 our model was a Markov chain and the main quantities of interest were the state probabilities πj(k) = P[X k = j], j= 0, 1, ... In some cases, we can indeed obtain such expressions, as we did with birth-death chains at steady state in Section 7.4.3. In general, however, “real world” systems either do not conform to some assumptions we make in order to simplify a model, or they are just too complex to yield analytical solutions. Our mathematical model may still be valid; the problem is that we often do not have the tools to solve the equations which make up such a model. Simulation is a process through which a system model is evaluated numerically, and the data from this process are used to estimate various quantities of interest. As we have repeatedly pointed out in previous chapters, analytical solutions for DES are particularly hard to come by, making simulation a very attractive tool for their study.KeywordsService TimeQueue LengthSystem TimeBusy PeriodInterarrival TimeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.