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Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many more evaluations of the forward model. Replacing computationally expensive forward models by fast surrogate models is an attractive option. However, computing the simulated training data for building a sufficiently accurate surrogate model can be computationally expensive in itself, leading to the design of computer experiments problem of finding evaluation points and accuracies such that the highest accuracy is obtained given a fixed computational budget. Here, we consider a fully adaptive greedy approach to this problem. Using Gaussian process regression as surrogate, samples are drawn from the available posterior approximation while designs are incrementally defined by solving a sequence of optimization problems for evaluation accuracy and positions. The selection of training designs is tailored towards representing the posterior to be sampled as good as possible, while the interleaved sampling steps discard old inaccurate samples in favor of new, more accurate ones. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs., Comment: 23 pages, 10 figures

The use of computer simulations to model physical systems has gained significant traction in recent years. A key factor in ensuring the accuracy of these models is the proper calibration of model parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. However, predictions can become inaccurate if model errors are neglected. A promising approach to address this issue involves embedding a bias term in the inference parameters, allowing the quantified bias to influence non-observed Quantities of Interest (QoIs). This paper introduces a more interpretable framework for bias embedding compared to existing methods. Current likelihood formulations that incorporate embedded bias often fail when measurement noise is present. To overcome these limitations, we adapt the existing likelihood models to properly account for noise and propose two new formulations designed to address the shortcomings of the previous approaches. Moreover, we evaluate the performance of this bias-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the bias term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction reliability. Finally, the proposed embedded bias model is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation, using temperature observations to illustrate its effectiveness., Comment: 37 pages, 24 figures, 5 tables

Designing civil structures such as bridges, dams or buildings is a complex task requiring many synergies from several experts. Each is responsible for different parts of the process. This is often done in a sequential manner, e.g. the structural engineer makes a design under the assumption of certain material properties (e.g. the strength class of the concrete), and then the material engineer optimizes the material with these restrictions. This paper proposes a holistic optimization procedure, which combines the concrete mixture design and structural simulations in a joint, forward workflow that we ultimately seek to invert. In this manner, new mixtures beyond standard ranges can be considered. Any design effort should account for the presence of uncertainties which can be aleatoric or epistemic as when data is used to calibrate physical models or identify models that fill missing links in the workflow. Inverting the causal relations established poses several challenges especially when these involve physics-based models which most often than not do not provide derivatives/sensitivities or when design constraints are present. To this end, we advocate Variational Optimization, with proposed extensions and appropriately chosen heuristics to overcome the aforementioned challenges. The proposed methodology is illustrated using the design of a precast concrete beam with the objective to minimize the global warming potential while satisfying a number of constraints associated with its load-bearing capacity after 28days according to the Eurocode, the demoulding time as computed by a complex nonlinear Finite Element model, and the maximum temperature during the hydration.

Simulation-based digital twins must provide accurate, robust and reliable digital representations of their physical counterparts. Quantifying the uncertainty in their predictions plays, therefore, a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must be then carefully implemented. When applied to complex standing structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aiming to infer the model parameters often fail at compensating for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for such models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of such approaches in the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error and provides further insight into the system by including additional pre-existing information without modifying the computational model., Comment: 32 pages, 21 figures, 9 tables. Submitted for consideration to Applied Stochastic Models in Business and Industry

In the field of computational science and engineering, workflows often entail the application of various software, for instance, for simulation or pre- and postprocessing. Typically, these components have to be combined in arbitrarily complex workflows to address a specific research question. In order for peer researchers to understand, reproduce and (re)use the findings of a scientific publication, several challenges have to be addressed. For instance, the employed workflow has to be automated and information on all used software must be available for a reproduction of the results. Moreover, the results must be traceable and the workflow documented and readable to allow for external verification and greater trust. In this paper, existing workflow management systems (WfMSs) are discussed regarding their suitability for describing, reproducing and reusing scientific workflows. To this end, a set of general requirements for WfMSswere deduced from user stories that we deem relevant in the domain of computational science and engineering. On the basis of an exemplary workflow implementation, publicly hosted at GitHub (https:// github.com/BAMresearch/NFDI4IngScientificWorkflowRequirements), a selection of different WfMSs is compared with respect to these requirements, to support fellow scientists in identifying the WfMSs that best suit their requirements.

In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modelled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed by solving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling.