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The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially powerful approach for this purpose, but its widespread adoption is prevented by its excessive computational costs. A popular approach to address this computational bottleneck is using surrogate models, which have been used to successfully predict a wide range of constitutive behaviors. However, applications involving microscale damage and fracture remain largely unexplored. This work aims to extend a recent surrogate modeling approach, the Physically Recurrent Neural Network (PRNN), to include the effect of debonding at the fiber-matrix interface while capturing path-dependent behavior. The core idea of the PRNN is to implement the exact material models from the micromodel into one of the layers of the network. In this work, additional material points with a cohesive zone model are integrated within the network, along with the bulk points associated to the fibers and/or matrix. The limitations of the existing architecture are discussed and taken into account for the development of novel architectures that better represent the stress homogenization procedure. In the proposed layout, the history variables of cohesive points act as extra latent features that help determine the local strains of bulk points. Different architectures are evaluated starting with small training datasets. To maximize the predictive accuracy and extrapolation capabilities of the network, various configurations of bulk and cohesive points are explored, along with different training dataset types and sizes.

The power networks are evolving with increased active components such as energy storage and flexibility derived from loads such as electric vehicles, heat pumps, industrial processes, etc. Better models are needed to accurately represent these assets; otherwise, their true capabilities might be over or under-estimated. In this work, we propose a new energy storage and flexibility arbitrage model that accounts for both ramp (power) and capacity (energy) limits, while accurately modelling the ramp rate constraint. The proposed models are linear in structure and efficiently solved using off-the-shelf solvers as a linear programming problem. We also provide an online repository for wider application and benchmarking. Finally, numerical case studies are performed to quantify the sensitivity of ramp rate constraint on the operational goal of profit maximization for energy storage and flexibility. The results are encouraging for assets with a slow ramp rate limit. We observe that for resources with a ramp rate limit of 10% of the maximum ramp limit, the marginal value of performing energy arbitrage using such resources exceeds 65% and up to 90% of the maximum profit compared to the case with no ramp rate limitations.

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the periodic probabilities of states connected by these observed transitions and their time-dependent transition rates can be inferred. Moreover, the smallest number of hidden transitions between accessible ones and some of their transition rates can be extracted. We prove and conjecture lower bounds on the total entropy production for such periodic stationary states. Even though our techniques are based on generalizations of known methods for steady states, we obtain original results for those as well.

The laws of thermodynamics apply to biophysical systems on the nanoscale as described by the framework of stochastic thermodynamics. This theory provides universal, exact relations for quantities like work, which have been verified in experiments where a fully resolved description allows direct access to such quantities. Complementary studies consider partially hidden, coarse-grained descriptions, in which the mean entropy production typically is not directly accessible but can be bounded in terms of observable quantities. Going beyond the mean, we introduce a fluctuating entropy production that applies to individual trajectories in a coarse-grained description under time-dependent driving. Thus, this concept is applicable to the broad and experimentally significant class of driven systems in which not all relevant states can be resolved. We provide a paradigmatic example by studying an experimentally verified protein unfolding process. As a consequence, the entire distribution of the coarse-grained entropy production rather than merely its mean retains spatial and temporal information about the microscopic process. In particular, we obtain a bound on the distribution of the physical entropy production of individual unfolding events.

Modern democracies face a critical issue of declining citizen participation in decision-making. Online discussion forums are an important avenue for enhancing citizen participation. This thesis proposal 1) identifies the challenges involved in facilitating large-scale online discussions with Natural Language Processing (NLP), 2) suggests solutions to these challenges by incorporating hybrid human-AI technologies, and 3) investigates what these technologies can reveal about individual perspectives in online discussions. We propose a three-layered hierarchy for representing perspectives that can be obtained by a mixture of human intelligence and large language models. We illustrate how these representations can draw insights into the diversity of perspectives and allow us to investigate interactions in online discussions., Comment: Accepted at NAACL 2024, Student Research Workshop

Pressure changes travel at an infinite sound speed in an incompressible ideal fluid, opposite to what happens in a bubbly liquid, where the presence of bubbles adds compressibility such that the sound speed becomes finite. Here, the transmission of a pressure signal through a confined bubble array is studied numerically. An axisymmetric Boundary Integral (BI) code was used to simulate a horizontal array of spherical bubbles inside a cylindrical container. On one end of the container, a piston is able to move in either a sinusoidal or impulsive way to excite the bubbles, whereas the other end of the cylinder is fixed. A one-dimensional model, hereafter called the Multiple Bagnold Problem (MBP) model, was developed to predict the behavior of the 3D system. A good agreement between the model and the simulations was found for initial excitation times and qualitatively good agreement for later times. The MBP model was subsequently used to obtain an expression for the sound speed in monodisperse systems, which depends on the ratio between the driving and the natural bubble frequency. Two regimes were found, one where the pressure signal travels unattenuated and the other where attenuation is present. Subsequently we turn to more complex, bidisperse systems, where the influence of the presence of bubbles of two different sizes is explored. Analytical expressions to predict the eigenfrequencies were obtained for monodisperse and bidisperse alternating systems. For bidisperse stacked systems the eigenfrequencies were computed numerically giving a good agreement with the MBP simulations. Finally, we discuss the propagation of a pressure signal through a polydisperse system.

The presence of gas or vapour bubbles may strongly influence the forces that occur during the impact of a liquid mass onto a solid. Here, we study this effect numerically, in a well-controlled manner, by simulating the short-time interaction between an impacting droplet and a solid surface, mediated by the gas layer between droplet and solid just before collision, in the presence and absence of bubbles. A boundary integral method is used to simulate the falling droplet, the mediating air layer is modeled using lubrication theory, whereas uniform gas bubbles are added to the droplet that obey a polytropic equation of state. We show that the presence of gas bubbles inside the droplet can have a significant influence on the force exerted on the substrate, even before touchdown. This is due to the transmission of load from the solid, through the gas layer and finally into the bubbly droplet, buffering the impact. We simulate different bubble configurations, modifying their number, size, shape and initial position. It is found that larger bubbles, as well as those close to the impact zone, dampen the collision more as compared to small bubbles or the ones that are far from the droplet's surface. In addition, multiple small bubbles are shown to have a similar or even greater effect as a single large bubble.

Active Learning (AL) addresses the high costs of collecting human annotations by strategically annotating the most informative samples. However, for subjective NLP tasks, incorporating a wide range of perspectives in the annotation process is crucial to capture the variability in human judgments. We introduce Annotator-Centric Active Learning (ACAL), which incorporates an annotator selection strategy following data sampling. Our objective is two-fold: (1) to efficiently approximate the full diversity of human judgments, and (2) to assess model performance using annotator-centric metrics, which emphasize minority perspectives over a majority. We experiment with multiple annotator selection strategies across seven subjective NLP tasks, employing both traditional and novel, human-centered evaluation metrics. Our findings indicate that ACAL improves data efficiency and excels in annotator-centric performance evaluations. However, its success depends on the availability of a sufficiently large and diverse pool of annotators to sample from.

Lunar exploration has become a key focus, driving scientific and technological advances. Ongoing missions are deploying rovers to the surface of the Moon, targeting the far side and south pole. However, these terrains pose challenges, emphasizing the need for precise obstacles and resource detection to avoid mission risks. This work proposes a novel system that integrates eXtended Reality (XR) and Artificial Intelligence (AI) to teleoperate lunar rovers. It is capable of autonomously detecting rocks and recreating an immersive 3D virtual environment of the location of the robot. This system has been validated in a lunar laboratory to observe its advantages over traditional 2D-based teleoperation approaches

In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used in the full-order micromodel by embedding them in a neural network. Following previous developments, this paper extends the applicability of the physically recurrent neural network (PRNN) by introducing an architecture suitable for rate-dependent materials in a finite strain framework. In this model, the homogenized deformation gradient of the micromodel is encoded into a set of deformation gradients serving as input to the embedded constitutive models. These constitutive models compute stresses, which are combined in a decoder to predict the homogenized stress, such that the internal variables of the history-dependent constitutive models naturally provide physics-based memory for the network. To demonstrate the capabilities of the surrogate model, we consider a unidirectional composite micromodel with transversely isotropic elastic fibers and elasto-viscoplastic matrix material. The extrapolation properties of the surrogate model trained to replace such micromodel are tested on loading scenarios unseen during training, ranging from different strain-rates to cyclic loading and relaxation. Speed-ups of three orders of magnitude with respect to the runtime of the original micromodel are obtained., Comment: 28 pages, 26 figures

Large-scale survey tools enable the collection of citizen feedback in opinion corpora. Extracting the key arguments from a large and noisy set of opinions helps in understanding the opinions quickly and accurately. Fully automated methods can extract arguments but (1) require large labeled datasets that induce large annotation costs and (2) work well for known viewpoints, but not for novel points of view. We propose HyEnA, a hybrid (human + AI) method for extracting arguments from opinionated texts, combining the speed of automated processing with the understanding and reasoning capabilities of humans. We evaluate HyEnA on three citizen feedback corpora. We find that, on the one hand, HyEnA achieves higher coverage and precision than a state-of-the-art automated method when compared to a common set of diverse opinions, justifying the need for human insight. On the other hand, HyEnA requires less human effort and does not compromise quality compared to (fully manual) expert analysis, demonstrating the benefit of combining human and artificial intelligence., Comment: Published in JAIR

A numerical framework for simulating progressive failure under high-cycle fatigue loading is validated against experiments of composite quasi-isotropic open-hole laminates. Transverse matrix cracking and delamination are modeled with a mixed-mode fatigue cohesive zone model, covering crack initiation and propagation. Furthermore, XFEM is used for simulating transverse matrix cracks and splits at arbitrary locations. An adaptive cycle jump approach is employed for efficiently simulating high-cycle fatigue while accounting for local stress ratio variations in the presence of thermal residual stresses. The cycle jump scheme is integrated in the XFEM framework, where the local stress ratio is used to determine the insertion of cracks and to propagate fatigue damage. The fatigue cohesive zone model is based on S-N curves and requires static material properties and only a few fatigue parameters, calibrated on simple fracture testing specimens. The simulations demonstrate a good correspondence with experiments in terms of fatigue life and damage evolution., Comment: 31 pages, 15 figures, 1 table

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of this approach. The costs originate from microscale Finite Element (FE) models that must be solved at every macroscopic integration point. A plethora of surrogate modeling strategies attempt to alleviate this cost by learning to predict macroscopic stresses from macroscopic strains, completely replacing the microscale models. In this work, we introduce an alternative surrogate modeling strategy that allows for keeping the multiscale nature of the problem, allowing it to be used interchangeably with an FE solver for any time step. Our surrogate provides all microscopic quantities, which are then homogenized to obtain macroscopic quantities of interest. We achieve this for an elasto-plastic material by predicting full-field microscopic strains using a graph neural network (GNN) while retaining the microscopic constitutive material model to obtain the stresses. This hybrid data-physics graph-based approach avoids the high dimensionality originating from predicting full-field responses while allowing non-locality to arise. By training the GNN on a variety of meshes, it learns to generalize to unseen meshes, allowing a single model to be used for a range of microstructures. The embedded microscopic constitutive model in the GNN implicitly tracks history-dependent variables and leads to improved accuracy. We demonstrate for several challenging scenarios that the surrogate can predict complex macroscopic stress-strain paths. As the computation time of our method scales favorably with the number of elements in the microstructure compared to the FE method, our method can significantly accelerate FE2 simulations.

Presenting high-level arguments is a crucial task for fostering participation in online societal discussions. Current argument summarization approaches miss an important facet of this task -- capturing diversity -- which is important for accommodating multiple perspectives. We introduce three aspects of diversity: those of opinions, annotators, and sources. We evaluate approaches to a popular argument summarization task called Key Point Analysis, which shows how these approaches struggle to (1) represent arguments shared by few people, (2) deal with data from various sources, and (3) align with subjectivity in human-provided annotations. We find that both general-purpose LLMs and dedicated KPA models exhibit this behavior, but have complementary strengths. Further, we observe that diversification of training data may ameliorate generalization. Addressing diversity in argument summarization requires a mix of strategies to deal with subjectivity., Comment: Accepted at EACL2024 (main proceedings)

Purpose: This study aims to enhance the clinical use of automated sleep-scoring algorithms by incorporating an uncertainty estimation approach to efficiently assist clinicians in the manual review of predicted hypnograms, a necessity due to the notable inter-scorer variability inherent in polysomnography (PSG) databases. Our efforts target the extent of review required to achieve predefined agreement levels, examining both in-domain and out-of-domain data, and considering subjects diagnoses. Patients and methods: Total of 19578 PSGs from 13 open-access databases were used to train U-Sleep, a state-of-the-art sleep-scoring algorithm. We leveraged a comprehensive clinical database of additional 8832 PSGs, covering a full spectrum of ages and sleep-disorders, to refine the U-Sleep, and to evaluate different uncertainty-quantification approaches, including our novel confidence network. The ID data consisted of PSGs scored by over 50 physicians, and the two OOD sets comprised recordings each scored by a unique senior physician. Results: U-Sleep demonstrated robust performance, with Cohen's kappa (K) at 76.2% on ID and 73.8-78.8% on OOD data. The confidence network excelled at identifying uncertain predictions, achieving AUROC scores of 85.7% on ID and 82.5-85.6% on OOD data. Independently of sleep-disorder status, statistical evaluations revealed significant differences in confidence scores between aligning vs discording predictions, and significant correlations of confidence scores with classification performance metrics. To achieve K of at least 90% with physician intervention, examining less than 29.0% of uncertain epochs was required, substantially reducing physicians workload, and facilitating near-perfect agreement.

Due to the empirical success of reinforcement learning, an increasing number of students study the subject. However, from our practical teaching experience, we see students entering the field (bachelor, master and early PhD) often struggle. On the one hand, textbooks and (online) lectures provide the fundamentals, but students find it hard to translate between equations and code. On the other hand, public codebases do provide practical examples, but the implemented algorithms tend to be complex, and the underlying test environments contain multiple reinforcement learning challenges at once. Although this is realistic from a research perspective, it often hinders educational conceptual understanding. To solve this issue we introduce EduGym, a set of educational reinforcement learning environments and associated interactive notebooks tailored for education. Each EduGym environment is specifically designed to illustrate a certain aspect/challenge of reinforcement learning (e.g., exploration, partial observability, stochasticity, etc.), while the associated interactive notebook explains the challenge and its possible solution approaches, connecting equations and code in a single document. An evaluation among RL students and researchers shows 86% of them think EduGym is a useful tool for reinforcement learning education. All notebooks are available from https://www.edugym.org/, while the full software package can be installed from https://github.com/RLG-Leiden/edugym.

Disagreements are common in online discussions. Disagreement may foster collaboration and improve the quality of a discussion under some conditions. Although there exist methods for recognizing disagreement, a deeper understanding of factors that influence disagreement is lacking in the literature. We investigate a hypothesis that differences in personal values are indicative of disagreement in online discussions. We show how state-of-the-art models can be used for estimating values in online discussions and how the estimated values can be aggregated into value profiles. We evaluate the estimated value profiles based on human-annotated agreement labels. We find that the dissimilarity of value profiles correlates with disagreement in specific cases. We also find that including value information in agreement prediction improves performance., Comment: Accepted as main paper at EMNLP 2023

Due to the increased deployment of renewable energy sources and intelligent components the electric power system will exhibit a large degree of heterogeneity, which requires inclusive and multi-disciplinary system assessment. The concept of co-simulation is a very attractive option to achieve this; each domain-specific subsystem can be addressed via its own specialized simulation tool. The applicability, however, depends on aspects like standardised interfaces, automated case creation, initialisation, and the scalability of the co-simulation itself. This work deals with the inclusion of the Functional Mock-up Interface for co-simulation into the DIgSILENT PowerFactory simulator, and tests its accuracy, implementation, and scalability for the grid connection study of a wind power plant. The coupling between the RMS mode of PowerFactory and MATLAB/Simulink in a standardised manner is shown. This approach allows a straightforward inclusion of black-boxed modelling, is easily scalable in size, quantity, and component type., Comment: 2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe)

In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [$\pm$45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure., Comment: 40 pages, 21 figures

Developing algorithms for extra-terrestrial robotic exploration has always been challenging. Along with the complexity associated with these environments, one of the main issues remains the evaluation of said algorithms. With the regained interest in lunar exploration, there is also a demand for quality simulators that will enable the development of lunar robots. % In this paper, we explain how we built a Lunar simulator based on Isaac Sim, Nvidia's robotic simulator. In this paper, we propose Omniverse Lunar Robotic-Sim (OmniLRS) that is a photorealistic Lunar simulator based on Nvidia's robotic simulator. This simulation provides fast procedural environment generation, multi-robot capabilities, along with synthetic data pipeline for machine-learning applications. It comes with ROS1 and ROS2 bindings to control not only the robots, but also the environments. This work also performs sim-to-real rock instance segmentation to show the effectiveness of our simulator for image-based perception. Trained on our synthetic data, a yolov8 model achieves performance close to a model trained on real-world data, with 5% performance gap. When finetuned with real data, the model achieves 14% higher average precision than the model trained on real-world data, demonstrating our simulator's photorealism.% to realize sim-to-real. The code is fully open-source, accessible here: https://github.com/AntoineRichard/LunarSim, and comes with demonstrations., Comment: 7 pages, 4 figures

Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom, some form of effective, coarse-grained dynamics naturally emerges for which the principles of stochastic thermodynamics generally cease to be applicable straightforwardly. Our work unifies the notion of entropy production along an individual trajectory with that of a coarse-grained dynamics by establishing a framework based on snippets and Markovian events as fundamental building blocks. A key asset of a trajectory-based fluctuating entropy production is the ability to localize individual contributions to the total entropy production in time and space. As an illustration and potential application for inference we introduce a method for the detection of hidden driving. The framework applies equally to even and odd variables and, therefore, includes the peculiar case of entropy production in underdamped Langevin dynamics.

When objects are forced to flow through constrictions their transport can be frustrated temporarily or permanently due to the formation of arches in the region of the bottleneck. While such systems have been intensively studied in the case of solid particles in a gas phase being forced by gravitational forces, the case of solid particles suspended in a liquid phase, forced by the liquid itself, has received much less attention. In this case, the influence of the liquid flow on the transport efficiency is not well understood yet, leading to several apparently trivial, but yet unanswered questions, e.g., would an increase of the liquid flow improve the transport of particles or worsen it? Although some experimental data is already available, it lacks enough detail to give a complete answer to such a question. Numerical models would be needed to scrutinize the system deeper. In this paper, we study this system making use of an advanced discrete particle solver (MercuryDPM) and an approximated numerical model for the liquid drag and compare the results with experimental data., Comment: arXiv admin note: text overlap with arXiv:2205.04354

This paper discusses our approaches for task-oriented conversational modelling using subjective knowledge, with a particular emphasis on response generation. Our methodology was shaped by an extensive data analysis that evaluated key factors such as response length, sentiment, and dialogue acts present in the provided dataset. We used few-shot learning to augment the data with newly generated subjective knowledge items and present three approaches for DSTC11: (1) task-specific model exploration, (2) incorporation of the most frequent question into all generated responses, and (3) a waterfall prompting technique using a combination of both GPT-3 and ChatGPT., Comment: DSTC11

Open-access optical microcavities are Fabry-Perot type cavities consisting of two micrometer-size mirrors, separated by an air (or vacuum) gap typically of a few micrometers. Compared to integrated microcavities, this configuration is more flexible as the relative position of the two mirrors can be tuned, allowing to change on demand parameters such as cavity length and mode volume, and to select specific transverse cavity modes. These advantages come at the expense of mechanical stability of the cavity itself, which is particularly relevant in noisy closed-cycle cryostats. Here we show an open-access optical microcavity based on scanning-probe microscope design principles. When operated at 4 K in a tabletop optical closed-cycle cryostat without any dedicated low-pass filter, we obtain stabilities of 5.7 and 10.6 pm rms in the quiet and full period of the cryocooler cycle, respectively. Our device has free-space optical access, essential for instance for full polarization control., Comment: 10 pages, 7 figures

When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. Contrary to this intuition, due to thermal Marangoni contraction the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. We describe and quantify this self-propulsion of the volatile drop. It arises due to spontaneous symmetry breaking of thermal-Marangoni convection, which is induced by the non-uniform evaporation of the droplet. Using infra-red imaging, we reveal the characteristic interfacial flow patterns associated with the Marangoni convection in the evaporating drop. A scaling relation describes the correlation between the moving velocity of the drop and the apparent contact angle, both of which increase with the substrate temperature.

The dissolution and subsequent mass transfer of carbon dioxide gas into liquid barriers plays a vital role in many environmental and industrial applications. In this work, we study the downward dissolution and propagation dynamics of CO2 into a vertical water barrier confined to a narrow vertical glass cylinder, using both experiments and direct numerical simulations. Initially, the dissolution of CO2 results in the formation of a CO2-rich water layer, which is denser in comparison to pure water, at the top gas-liquid interface. Continued dissolution of CO2 into the water barrier results in the layer becoming gravitationally unstable, leading to the onset of buoyancy driven convection and, consequently, the shedding of a buoyant plume. By adding sodium fluorescein, a pH-sensitive fluorophore, we directly visualise the dissolution and propagation of the CO2 across the liquid barrier. Tracking the CO2 front propagation in time results in the discovery of two distinct transport regimes, a purely diffusive regime and an enhanced diffusive regime. Using direct numerical simulations, we are able to successfully explain the propagation dynamics of these two transport regimes in this laterally strongly confined geometry, namely by disentangling the contributions of diffusion and convection to the propagation of the CO2 front., Comment: Submitted to Physical Review Fluids

In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated based on observations from a finite element discretization. To avoid the computation of intractable integrals, a second, finer, discretization is introduced that is assumed sufficiently dense to represent the true solution field. A prior distribution is assumed over the fine discretization, which is then updated based on observations from the coarse discretization. This yields a posterior distribution with a mean that serves as an estimate of the solution, and a covariance that models the uncertainty associated with this estimate. Two particular choices of prior are investigated: a prior defined implicitly by assigning a white noise distribution to the right-hand side term, and a prior whose covariance function is equal to the Green's function of the partial differential equation. The former yields a posterior distribution with a mean close to the reference solution, but a covariance that contains little information regarding the finite element discretization error. The latter, on the other hand, yields posterior distribution with a mean equal to the coarse finite element solution, and a covariance with a close connection to the discretization error. For both choices of prior a contradiction arises, since the discretization error depends on the right-hand side term, but the posterior covariance does not. We demonstrate how, by rescaling the eigenvalues of the posterior covariance, this independence can be avoided.