The MS focuses on the process of modeling, quantifying and estimating the effects of uncertainties that characterize irreversible/dissipative material behavior in quasi-static and dynamic conditions. Particular examples of great significance include metal fatigue and concrete fracture analysis, as well as material aging of bone tissues. Moreover, special attention will be paid to the multi-scale and multi-fidelity nature of these problems, as well as to Bayesian analysis and corresponding design of experiments. Numerical tools to be discussed are low-rank functional approximations, Bayesian learning, optimization, stochastic Galerkin, polynomial chaos expansion, and stochastic homogenization, to name just a few.
14:00
The effect of epistemic uncertainties on the seismic fragility assessment of existing concrete gravity dams
Giacomo Sevieri | University College London | United Kingdom
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Giacomo Sevieri | University College London | United Kingdom
The quantification of the seismic risk of concrete gravity dams is a challenging task of primary importance for the scientific community, due to the key role played by such structures for the sustainability of a country. Particularly problematic is the calculation of the structural fragility due to lack of case histories and the too general definition of Limit States.
In this context, numerical models assume great importance for the prediction of the seismic behaviour of the complex dam-soil-reservoir interacting system, nevertheless they are affected by different sources of uncertainty. Particularly important is the effect of epistemic uncertainties related to the mechanical parameters of materials, usually neglected in civil engineering applications.
In this research work, an explanatory example is used to show the effect of epistemic uncertainties on the seismic fragility analysis of existing concrete gravity dams. Special emphasis is placed on the parametrization of the probabilistic problem and the definition of the numerical model. The general Polynomial Chaos Expansion is applied in order to reduce the computational burden thus solving the forward problem even without High Performance Computing.
14:30
A low-rank surogate for a gradient-extended damage-plasticity model
Dieter Moser | RWTH Aachen | Germany
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Dieter Moser | RWTH Aachen | Germany
In most cases damage appears as a local effect, e.g. in the form of a crack. This leads to the fact that discretizations in these local areas need a high resolution, which may be solved with an adaptive schemes or as in our case by adaption of the damage model. In our case the model is based on a ‘two-surface’ approach where damage and plasticity are treated as independent physical mechanisms. Such a model is especially appealing from a practical point of view since it can naturally account for various situations in which the model’s behavior is either (quasi-)brittle-like, ductile-like or possibly anything in between. This behavior is controlled by up to 12 parameters, additional material properties are described by KL-decomposed random fields with possibly hundreds of terms. Therefore, the uncertainty stemming from the damage model and material properties pose a high-dimensional problem, which we will tackle with hierarchical low-rank surrogate models. We will show that using this type of surrogate not only facilitates the generation of samples but also allows for a very elegant way to perform a sensitivity analysis.
15:00
Physics-informed deep learning of divergence-free flows
Dmitry Kabanov | RWTH Aachen University | Germany
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Dmitry Kabanov | RWTH Aachen University | Germany
Luis Espath | RWTH Aachen University | Germany
Raul F. Tempone | RWTH Aachen University | Germany
We apply deep learning technique to solve inverse problems of reconstruction of wind flow from given observations, which are usually sparse. This is solved by constructing a neural network that matches the observations. Following the current trend of physics-informed machine learning, we require that the network must satisfy the physical constraints of the flow. In this case, under the assumption of low flow velocity, we require that the flow is incompressible, hence, the network is constrained to reconstruct divergence-free flow. The above constraint is infeasible to satisfy exactly. To overcome this hurdle, network training is reduced to an unconstrained optimization problem via Lagrange relaxation, where the objective function consists of two terms: one is responsible for matching the observations and another one approximately satisfies the constraint of flow incompressibility. The balance between these two terms is found through a cross-validation procedure.
We apply this approach to the dataset from windmills in Sweden and compare its effectiveness with a more traditional technique of flow reconstruction via Fourier expansions.
15:30
Importance Sampling for a Robust and Efficient Multilevel Monte Carlo Estimator for Stochastic Biological Systems
Nadhir Ben Rached | RWTH Aachen University | Germany
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Raul F. Tempone | RWTH Aachen and KAUST | Germany
Chiheb Ben Hammouda | KAUST | Saudi Arabia
Nadhir Ben Rached | RWTH Aachen University | Germany
The multilevel Monte Carlo (MLMC) method for continuous time Markov chains is a highly efficient simulation technique that can be used to estimate various statistical quantities for stochastic biological systems, and in particular for stochastic reaction networks (SRNs). Unfortunately, the robustness and performance of the multilevel method can be deteriorated due to the well known issue of high kurtosis, observed at the deep levels of MLMC and leading to poor estimates for the sample variance. In this work, we address cases where the high kurtosis issue is due to catastrophic coupling (characteristic of pure jump processes where coupled consecutive paths are identical in most of the simulations, while differences only observed in a very small proportion), and introduce an importance sampling technique that improves the robustness and efficiency of the multilevel method by decreasing significantly the kurtosis, and also increasing the strong convergence rate which results in an improvement of the complexity of the MLMC from $O{TOL^{-2} \log\left(TOL\right)^2}$ to $\O{TOL^{-2}}$, with $TOL$ being a prescribed tolerance. Our analysis along with the numerical experiments highlight the great advantage brought by our novel method for efficiently estimating statistical quantities related to SRNs.