A Finite Element Method - Informed Neural Network For Uncertainty Quantification

Sampling approaches for uncertainty quantification for real-world engineering problems are associated with large computational time and cost. This cost comes from the expensive deterministic simulation. Usage of surrogate models is a common way to overcome this issue in engineering applications. A conventional Neural Network (NN) can be used for building such surrogates. However, these neural networks are built based on input-output pairs. It is not possible to verify that the predicted output satisfies underlying physics. In this contribution, a physics-informed neural network based on a hybrid model of machine learning and classical Finite Element Method (FEM) is presented for forward propagation of uncertainty. The method uses FEM during both training and prediction stages. A surrogate model based on neural network for high dimensional problem is constructed by constraining the predictions of the neural network with the discretized partial differential equation of the system. During the training stage, the predicted solution from the FEM informed Neural Network(FEM-NN) is used to compute the residual using stiffness matrices and force vectors. This residual is used as a custom loss function from NN. This makes the whole training unsupervised as it does not require any output values. Hence, the need for expensive FEM solves is circumvented. The FEM-NN hybrid also gives an estimate of the accuracy of prediction by means of the calculated residual along with the prediction. The framework does not require mandatory expensive linear solves of the discretized equation instead substitutes the prediction from the neural network for computing the residual. This reduces the expensive training phase of the problem and can be applicable to real-world FEM simulations. The trained neural network is then sampled in a Monte Carlo (MC) manner to evaluate the statistics of the Quantities of Interest (QoI). The resulting FEM-NN hybrid is physics confirming and data-efficient. The efficacy of the framework is presented by a series of test case examples. The results are compared with classical MC results. The suitability of the method for the uncertainty quantification is studied and presented

D7.4 Final report on Stochastic Optimization results

This deliverable report focuses on the final stochastic optimization results obtained within the EXAscale Quantification of Uncertainties for Technology and Science Simulation (ExaQUte) project. Details on a novel wind inlet generator that is able to incorporate local wind-field data through a deep-learned rapid distortion model and generates the turbulent wind data during run-time is presented in section 2. Section 3 presents the results of the overall stochastic optimization procedure applied to a twisted tapered tower with multiple design parameters within an uncertain synthetic wind field. Thereby, the significance of the developed methods and the obtained results are discussed and their integration in industrial wind-engineering workflows is outlined in section 4

D6.5 Report on stochastic optimisation for wind engineering

This report presents the latest methods of optimisation under uncertainties investigated in the ExaQUte project, and their applications to problems related to civil and wind engineering. The measure of risk throughout the report is the conditional value at risk. First, the reference method is presented: the derivation of sensitivities of the risk measure; their accurate computation; and lastly, a practical optimisation algorithm with adaptive statistical estimation. Second, this method is directly applied to a nonlinear relaxation oscillator (FitzHugh–Nagumo model) with numerical experiments to demonstrate its performance. Third, the optimisation method is adapted to the shape optimisation of an airfoil and illustrated by a large-scale experiment on a computing cluster. Finally, the benchmark of the shape optimisation of a tall building under a turbulent flow is presented, followed by an adaptation of the optimisation method. All numerical experiments showcase the open-source software stack of the ExaQUte project for large-scale computing in a distributed environment

D6.4 Report on stochastic optimisation for unsteady problems

This report brings together methodological research on stochastic optimisation and work on benchmark and target applications of the ExaQute project, with a focus on unsteady problems. A practical, general method for the optimisation of the conditional value at risk is proposed. Three different optimisation problems are described: an oscillator problem selected as a suitable trial and illustration case; the shape optimisation of an airfoil, chosen as a benchmark application in the project; the shape optimisation of a tall building, which is the challenging target application set for ExaQUte. For each problem, the current developments and results are presented, the application of the proposed method is discussed, and the work to be done until the end of the project is laid out.&nbsp

D1.4 Final public Release of the solver

This deliverable presents the final software release of Kratos Multiphysics, together with the XMC library, Hyperloom and PyCOMPSs API definitions [13]. This release also contains the latest developements on MPI parallel remeshing in ParMmg. This report is meant to serve as a supplement to the public release of the software. Kratos is “a framework for building parallel, multi-disciplinary simulation software, aiming at modularity, extensibility, and high performance. Kratos is written in C++, and counts with an extensive Python interface”. XMC is “a Python library for parallel, adaptive, hierarchical Monte Carlo algorithms, aiming at reliability, modularity, extensibility and high performance“. Hyperloom and PyCOMPSs are environments for enabling parallel and distributed computation. ParMmg is an open source software which offers the parallel mesh adaptation of three dimensional volume meshes

Uncertainties in dynamic response of buildings with non-linear base-isolators

Dynamic response of base-isolated buildings under uni-directional sinusoidal base excitation is numerically investigated considering uncertainties in the isolation and excitation parameters. The buildings are idealized as single degree of freedom (SDOF) system and multi-degrees of freedom (MDOF) system with one lateral degree of freedom at each floor level. The isolation system is modeled using two different mathematical models such as: (i) code-recommended equivalent linear elastic-viscous damping model and (ii) bi-linear hysteretic model. The uncertain parameters of the isolator considered are time period, damping ratio, and yield displacement. Moreover, the amplitude and frequency of the sinusoidal base excitation function are considered uncertain. The uncertainty propagation is investigated using generalized polynomial chaos (gPC) expansion technique. The unknown gPC expansion coefficients are obtained by non-intrusive sparse grid collocation scheme. Efficiency of the technique is compared with the sampling method of Monte Carlo (MC) simulation. The stochastic response quantities of interest considered are bearing displacement and top floor acceleration of the building. Effects of individual uncertain parameters on the building response are quantified using sensitivity analyses. Effect of various uncertainty levels of the input parameters on the dynamic response of the building is also investigated. The peak bearing displacement and top floor acceleration are more influenced by the amplitude and frequency of the sinusoidal base excitation function. The effective time period of the isolation system also produces a considerable influence. However, in the presence of similar uncertainty level in the time period, amplitude and frequency of the sinusoidal forcing function, the effect of uncertainties in the other parameters of the isolator (e.g., damping ratio and yield displacement) is comparatively less. Interestingly, the mean values of the response quantities are found to be higher than the deterministic values in several instances, indicating the need of conducting stochastic analysis. The gPC expansion technique presented here is found to be a computationally efficient yet accurate alternative to the MC simulation for numerically modeling the uncertainty propagation in the dynamic response analyses of the base-isolated buildings

ExaQUte: D2.3. Adjoint-based error estimation routines

This document presents a simple and ecient strategy for adaptive mesh refinement (AMR) and a posteriori error estimation for the transient incompressible Navier{Stokes equations. This strategy is informed by the work of Prudhomme and Oden [22, 23] as well as modern goal-oriented methods such as [5]. The methods described in this document have been implemented in the Kratos Multiphysics software and uploaded to https://zenodo.org [27].1 This document includes: A review of the state-of-the-art in solution-oriented and goal-oriented AMR. The description of a 2D benchmark model problem of immediate relevance to the objectives of the ExaQUte project. The definition and a brief mathematical summary of the error estimator(s). The results obtained. A description of the API.Preprin

Risk-averse design of tall buildings for uncertain wind conditions

Reducing the intensity of wind excitation via aerodynamic shape modification is a major strategy to mitigate the reaction forces on supertall buildings, reduce construction and maintenance costs, and improve the comfort of future occupants. To this end, computational fluid dynamics (CFD) combined with state-of-the-art stochastic optimization algorithms is more promising than the trial and error approach adopted by the industry. The present study proposes and investigates a novel approach to risk-averse shape optimization of tall building structures that incorporates site-specific uncertainties in the wind velocity, terrain conditions, and wind flow direction. A body-fitted finite element approximation is used for the CFD with different wind directions incorporated by re-meshing the fluid domain. The bending moment at the base of the building is minimized, resulting in a building with reduced cost, material, and hence, a reduced carbon footprint. Both risk-neutral and risk-averse optimization of the twist and tapering of a representative building are presented under uncertain inflow wind conditions that have been calibrated to fit freely-available site-specific data from Basel, Switzerland. The risk-averse strategy uses the conditional value-at-risk to optimize for the low-probability high-consequence events appearing in the worst 10% of loading conditions. Adaptive sampling is used to accelerate the gradient-based stochastic optimization pipeline. The adaptive method is easy to implement and particularly helpful for compute-intensive simulations because the number of gradient samples grows only as the optimal design algorithm converges. The performance of the final risk-averse building geometry is exceptionally favorable when compared to the risk-neutral optimized geometry, thus, demonstrating the effectiveness of the risk-averse design approach in computational wind engineering

ExaQUte: D6.4 Report on stochastic optimisation for unsteady problems

This report brings together methodological research on stochastic optimisation and work on benchmark and target applications of the ExaQute project, with a focus on unsteady problems. A practical, general method for the optimisation of the conditional value at risk is proposed. Three different optimisation problems are described: an oscillator problem selected as a suitable trial and illustration case; the shape optimisation of an airfoil, chosen as a benchmark application in the project; the shape optimisation of a tall building, which is the challenging target application set for ExaQUte. For each problem, the current developments and results are presented, the application of the proposed method is discussed, and the work to be done until the end of the project is laid out.Preprin

ExaQUte: D1.4 Final public release of the solver

This deliverable presents the final software release of Kratos Multiphysics, together with the XMC library, Hyperloom and PyCOMPSs API definitions [13]. This release also contains the latest developements on MPI parallel remeshing in ParMmg. This report is meant to serve as a supplement to the public release of the software. Kratos is “a framework for building parallel, multi-disciplinary simulation software, aiming at modularity, extensibility, and high performance. Kratos is written in C++, and counts with an extensive Python interface”. XMC is “a Python library for parallel, adaptive, hierarchical Monte Carlo algorithms, aiming at reliability, modularity, extensibility and high performance“. Hyperloom and PyCOMPSs are environments for enabling parallel and distributed computation. ParMmg is an open source software which offers the parallel mesh adaptation of three dimensional volume meshes.Preprin