A dynamic data-driven application simulation framework for contaminant transport problems

AbstractWe describe, devise, and augment dynamic data-driven application simulations (DDDAS). DDDAS offers interesting computational and mathematically unsolved problems, such as, how do you analyze, compute, and predict the solution of a generalized PDE when you do not know either where or what the boundary conditions are at any given moment in the simulation in advance? A summary of DDDAS features and why this is a intellectually stimulating new field are included in the paper.We apply the DDDAS methodology to some examples from a contaminant transport problem. We demonstrate that the multiscale interpolation and backward in time error monitoring are useful to long running simulations

Bayesian estimation and reconstruction of marine surface contaminant dispersion

Discharge of hazardous substances into the marine environment poses a substantial risk to both public health and the ecosystem. In such incidents, it is imperative to accurately estimate the release strength of the source and reconstruct the spatio-temporal dispersion of the substances based on the collected measurements. In this study, we propose an integrated estimation framework to tackle this challenge, which can be used in conjunction with a sensor network or a mobile sensor for environment monitoring. We employ the fundamental convection-diffusion partial differential equation (PDE) to represent the general dispersion of a physical quantity in a non-uniform flow field. The PDE model is spatially discretised into a linear state-space model using the dynamic transient finite-element method (FEM) so that the characterisation of time-varying dispersion can be cast into the problem of inferring the model states from sensor measurements. We also consider imperfect sensing phenomena, including miss-detection and signal quantisation, which are frequently encountered when using a sensor network. This complicated sensor process introduces nonlinearity into the Bayesian estimation process. A Rao-Blackwellised particle filter (RBPF) is designed to provide an effective solution by exploiting the linear structure of the state-space model, whereas the nonlinearity of the measurement model can be handled by Monte Carlo approximation with particles. The proposed framework is validated using a simulated oil spill incident in the Baltic sea with real ocean flow data. The results show the efficacy of the developed spatio-temporal dispersion model and estimation schemes in the presence of imperfect measurements. Moreover, the parameter selection process is discussed, along with some comparison studies to illustrate the advantages of the proposed algorithm over existing methods

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of $\mathrm{CO_2}$ sequestration). Here, we present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. We present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of $7 \times 10^{6}$ because our framework is not bound by the Courant-Friedrichs-Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model's accuracy still lies within a mean squared error of 0.07 (two-order of magnitude lower than the maximum value of the finite element results) in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) or t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy

UQ and AI: data fusion, inverse identification, and multiscale uncertainty propagation in aerospace components

A key requirement for engineering designs is that they offer good performance across a range of uncertain conditions while exhibiting an admissibly low probability of failure. In order to design components that offer good performance across a range of uncertain conditions, it is necessary to take account of the effect of the uncertainties associated with a candidate design. Uncertainty Quantification (UQ) methods are statistical methods that may be used to quantify the effect of the uncertainties inherent in a system on its performance. This thesis expands the envelope of UQ methods for the design of aerospace components, supporting the integration of UQ methods in product development by addressing four industrial challenges. Firstly, a method for propagating uncertainty through computational models in a hierachy of scales is described that is based on probabilistic equivalence and Non-Intrusive Polynomial Chaos (NIPC). This problem is relevant to the design of aerospace components as the computational models used to evaluate candidate designs are typically multiscale. This method was then extended to develop a formulation for inverse identification, where the probability distributions for the material properties of a coupon are deduced from measurements of its response. We demonstrate how probabilistic equivalence and the Maximum Entropy Principle (MEP) may be used to leverage data from simulations with scarce experimental data- with the intention of making this stage of product design less expensive and time consuming. The third contribution of this thesis is to develop two novel meta-modelling strategies to promote the wider exploration of the design space during the conceptual design phase. Design Space Exploration (DSE) in this phase is crucial as decisions made at the early, conceptual stages of an aircraft design can restrict the range of alternative designs available at later stages in the design process, despite limited quantitative knowledge of the interaction between requirements being available at this stage. A histogram interpolation algorithm is presented that allows the designer to interactively explore the design space with a model-free formulation, while a meta-model based on Knowledge Based Neural Networks (KBaNNs) is proposed in which the outputs of a high-level, inexpensive computer code are informed by the outputs of a neural network, in this way addressing the criticism of neural networks that they are purely data-driven and operate as black boxes. The final challenge addressed by this thesis is how to iteratively improve a meta-model by expanding the dataset used to train it. Given the reliance of UQ methods on meta-models this is an important challenge. This thesis proposes an adaptive learning algorithm for Support Vector Machine (SVM) metamodels, which are used to approximate an unknown function. In particular, we apply the adaptive learning algorithm to test cases in reliability analysis.Open Acces

OBMeshfree: An optimization-based meshfree solver for nonlocal diffusion and peridynamics models

We present OBMeshfree, an Optimization-Based Meshfree solver for compactly supported nonlocal integro-differential equations (IDEs) that can describe material heterogeneity and brittle fractures. OBMeshfree is developed based on a quadrature rule calculated via an equality constrained least square problem to reproduce exact integrals for polynomials. As such, a meshfree discretization method is obtained, whose solution possesses the asymptotically compatible convergence to the corresponding local solution. Moreover, when fracture occurs, this meshfree formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. As numerical examples, we consider the problem of modeling both homogeneous and heterogeneous materials with nonlocal diffusion and peridynamics models. Convergences to the analytical nonlocal solution and to the local theory are demonstrated. Finally, we verify the applicability of the approach to realistic problems by reproducing high-velocity impact results from the Kalthoff-Winkler experiments. Discussions on possible immediate extensions of the code to other nonlocal diffusion and peridynamics problems are provided. OBMeshfree is freely available on GitHub.Comment: For associated code, see https://github.com/youhq34/meshfree_quadrature_nonloca

The role of advection and dispersion in the rock matrix on the transport of leaking CO2-saturated brine along a fractured zone

CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater motion. Simulations of the reactive transport of leaking CO2aq along a conducting fracture in a clay-rich caprock are conducted to analyze the effect of various physical and geochemical processes. Whilst several modeling transport studies along rock fractures have considered diffusion as the only transport process in the surrounding rock matrix (diffusive transport), this study analyzes the combined role of advection and dispersion in the rock matrix in addition to diffusion (advection-dominated transport) on the migration of CO2aq along a leakage pathway and its conversion in geochemical reactions. A sensitivity analysis is performed to quantify the effect of fluid velocity and dispersivity. Variations in the porosity and permeability of the medium are found in response to calcite dissolution and precipitation along the leakage pathway. We observe that advection and dispersion in the rock matrix play a significant role in the overall transport process. For the parameters that were used in this study, advection-dominated transport increased the leakage of CO2aq from the reservoir by nearly 305%, caused faster transport and increased the mass conversion of CO2aq in geochemical reactions along the transport pathway by approximately 12.20% compared to diffusive transport.Peer ReviewedPostprint (author's final draft