Sources Of Epistemic Uncertainty Research Articles

Forests high on CO2: A glimpse into how scientists study the biochemical machinery of forest ecosystems

Are forests across the planet storing more carbon as a result of rising atmospheric carbon dioxide (CO2) concentration? In this text, I propose to reflect on the work of researchers who are asking that very question. The focus is on a particular approach called free-air CO2 enrichment (FACE) experiments, in which forests in their local environment are subjected to a CO2 concentration higher than in the ambient air, to test the CO2 fertilization hypothesis. This hypothesis predicts that forests store more carbon in those conditions. FACE studies held the promise of establishing cause–effect relations and transcending the here and now. They emerged in the United States in the late 1980s, at a time when ecology scaled up to make itself relevant to the then nascent Earth System science. FACE experiments in forests are now conducted in Australia, the United Kingdom, and Brazil, and their results are closely scrutinized by a small research community. The text, first, presents the engineering feat that underpins FACE experiments in forests and discuss two problems highlighted by scientists because they impede hasty generalization from the data: the timescale needed to witness forests change and the spatial heterogeneity of forest soils. It then shows how scientists contend with their incomplete understanding of forest ecosystems as they bring together computer models and empirical data to build consensus around the sources of epistemic uncertainty. To conclude, I propose to rework the idea of “the macroscope” to conceptualize what scientists do when they seek to study forests as complex, layered, multi-scale systems. I wish to capture how researchers, who willingly endorse a planetary gaze, problematize their own predicament. This, as I suggest, has to do with the immanence of forests in the world.

Dynamic Knowledge Injection for AIXI Agents

Prior approximations of AIXI, a Bayesian optimality notion for general reinforcement learning, can only approximate AIXI's Bayesian environment model using an a-priori defined set of models. This is a fundamental source of epistemic uncertainty for the agent in settings where the existence of systematic bias in the predefined model class cannot be resolved by simply collecting more data from the environment. We address this issue in the context of Human-AI teaming by considering a setup where additional knowledge for the agent in the form of new candidate models arrives from a human operator in an online fashion. We introduce a new agent called DynamicHedgeAIXI that maintains an exact Bayesian mixture over dynamically changing sets of models via a time-adaptive prior constructed from a variant of the Hedge algorithm. The DynamicHedgeAIXI agent is the richest direct approximation of AIXI known to date and comes with good performance guarantees. Experimental results on epidemic control on contact networks validates the agent's practical utility.

Drift-based fragility assessment of nonductile reinforced concrete columns failing in shear under cyclic loading

The paper presents drift-based fragility functions for nonductile reinforced concrete (RC) columns having light transverse reinforcement steel ratio which predominantly fail in shear. These fragilities were developed for four key damage states (i.e., light cracking, severe cracking, shear failure, and loss of axial load carrying capacity) associated with their structural performance observed in laboratory tests and repairability. For this purpose, experimental results of 71 column specimens tested under cyclic lateral loading were collected from 22 research programs; particularly, drift ratios associated to the column specimens tested to reach axial collapse. It is shown that the shear span-to-depth ratio and level of axial load ratio have influence on the drift-based fragilities associated to the damage states considered in this investigation. Additionally, several sources of epistemic uncertainty due to specimen-to-specimen, finite-sample, column shear span-to-depth aspect ratio, and level of axial compression load were quantified from the experimental database. The introduced drift-based fragilities are a very useful tool to assess the expected damage of existing buildings, such as school buildings that might exhibit the short captive column effect.

Likelihood of Primary Surface Faulting: Updating of Empirical Regressions

Abstract Surface faulting is a common phenomenon for crustal earthquakes and is an important source of localized hazard to buildings and infrastructure. Nevertheless, not all earthquakes of a given magnitude generate surface faulting. To correctly assess the hazard posed by surface fault displacement, it is critical to use reliable regressions of the likelihood of surface faulting. Such regressions are derived from empirical data and the ones currently used in engineering practice are based on datasets acquired several years ago. The aim of this work is to update the regressions characterizing the likelihood of primary surface faulting (i.e., P(Slip|m)). We systematically analyze Mw≥5.5 earthquakes that occurred in 1992–2018, with hypocentral depths lower than 20 km and epicenter onshore. We obtain information on the occurrence or non-occurrence of primary surface faulting for 363 earthquakes (87 with primary surface faulting and 276 without). We derive empirical regressions of P(Slip|m) from the entire dataset as well as for normal, strike-slip, and reverse earthquakes, and discuss the potential sources of aleatory and epistemic uncertainty. A sensitivity analysis shows that the P(Slip|m) term has a significant impact on the hazard curve expressed as the annual frequency of exceeding a given displacement value. We argue that the regressions presented in this work can be incorporated in models for probabilistic fault displacement hazard assessment, ultimately providing a better evaluation of the hazard.

Multivariate Uncertainty in Deep Learning.

Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes filters are typically assumed to be a fixed covariance matrix. This assumption is risky, particularly for "black box" deep learning models, in which uncertainty can vary dramatically and unexpectedly. Accurate quantification of multivariate uncertainty will allow for the full potential of deep learning to be used more safely and reliably in these applications. We show how to model multivariate uncertainty for regression problems with neural networks, incorporating both aleatoric and epistemic sources of heteroscedastic uncertainty. We train a deep uncertainty covariance matrix model in two ways: directly using a multivariate Gaussian density loss function and indirectly using end-to-end training through a Kalman filter. We experimentally show in a visual tracking problem the large impact that accurate multivariate uncertainty quantification can have on the Kalman filter performance for both in-domain and out-of-domain evaluation data. We additionally show, in a challenging visual odometry problem, how end-to-end filter training can allow uncertainty predictions to compensate for filter weaknesses.

Uncertainty Of Ship Hull Girder Ultimate Strength in Longitudinal Bending

The engineering modelling of ship hull girder strength usually consists of global and local levels. The Smith-type progressive collapse method is a typical example of this kind, in which the global model requires input from the local model with the underpinning local structural behaviour, i.e., load-shortening curve (LSC). However, the modelling is prone to uncertainty due to the statistical variability of the basic variables (aleatoric uncertainty) and the inadequacy of engineering models in both global and local levels (epistemic uncertainty). The former can be well tackled by a probabilistic sampling, whereas dealing with the latter for ship hull girder strength lacks an established approach. There can be different sources of epistemic uncertainty. In the modelling of ship hull girder strength, this may be partially manifested as that caused by different choices of local engineering models for predicting the LSC. In the light of this, a probabilistic method is applied in this research to investigate and quantify the uncertainty related to the local models. The adopted approach is a hybrid method incorporating the Smith-type progressive collapse method with Monte-Carlo Simulation and an adaptable LSC algorithm. Case studies on four merchant ships show that the ultimate strength in sagging is subjected to the most significant computational uncertainty as compared with those in hogging and horizontal bending. In a bi-axial load case, the computational uncertainty estimated for vertical bending will be counteracted as the horizontal bending increases. Nevertheless, this change is not directly proportional to the bi-axial load component ratio and appreciably varies between different ship types. The insights and data provided by this study may eventually resolve the epistemic uncertainty in the modelling of ship hull girder strength. It would also be useful to improve the ultimate limit state-based reliability analysis with regards to the strength model uncertainty evaluation.

Enriching stochastic model updating metrics: An efficient Bayesian approach using Bray-Curtis distance and an adaptive binning algorithm

In practical engineering, experimental data is not fully in line with the true system response due to various uncertain factors, e.g., parameter imprecision, model uncertainty, and measurement errors. In the presence of mixed sources of aleatory and epistemic uncertainty, stochastic model updating is a powerful tool for model validation and parameter calibration. This paper investigates the use of Bray-Curtis (B-C) distance in stochastic model updating and proposes a Bayesian approach addressing a scenario where the dataset contains multiple outliers. In the proposed method, a B-C distance-based uncertainty quantification metric is employed, that rewards models for which the discrepancy between observations and simulated samples is small while penalizing those which exhibit large differences. To improve the computational efficiency, an adaptive binning algorithm is developed and embedded into the Bayesian approximate computation framework. The merit of this algorithm is that the number of bins is automatically selected according to the difference between the experimental data and the simulated data. The effectiveness and efficiency of the proposed method is verified via two numerical cases and an engineering case from the NASA 2020 UQ challenge. Both static and dynamic cases with explicit and implicit propagation models are considered.

Probabilistic electric load forecasting through Bayesian Mixture Density Networks

This work presents a novel approach to address a challenging and still unsolved problem of neural network based load forecasting systems, that despite the significant results reached in terms of prediction error reduction, still lack suitable indications regarding sample-wise trustworthiness of their predictions. The present approach is framed on Bayesian Mixture Density Networks, enhancing the mapping capabilities of neural networks by integrated predictive distributions, and encompassing both aleatoric and epistemic uncertainty sources. An end-to-end training method is developed, aimed to discover the latent functional relation to conditioning variables, characterize the inherent load stochasticity, and convey parameters uncertainty in a unique framework. To achieve reliable and computationally scalable estimators, both Mean Field variational inference and deep ensembles are integrated. Experiments have been performed on short-term load forecasting tasks at both regional and fine-grained household scale, to investigate heterogeneous operating conditions. Different architectural configurations are compared, showing by Continuous Ranked Probability Score based tests that significant performance improvements are achieved by integrating flexible aleatoric uncertainty patterns and multi-modalities in the parameters posterior space.

Modeling Epistemic Uncertainty in Offshore Wind Farm Production Capacity to Reduce Risk.

Financial stakeholders in offshore wind farm projects require predictions of energy production capacity to better manage the risk associated with investment decisions prior to construction. Predictions for early operating life are particularly important due to the dual effects of cash flow discounting and the anticipated performance growth due to experiential learning. We develop a general marked point process model for the times to failure and restoration events of farm subassemblies to capture key uncertainties affecting performance. Sources of epistemic uncertainty are identified in design and manufacturing effectiveness. The model then captures the temporal effects of epistemic and aleatory uncertainties across subassemblies to predict the farm availability-informed relative capacity (maximum generating capacity given the technical state of the equipment). This performance measure enables technical performance uncertainties to be linked to the cost of energy generation. The general modeling approach is contextualized and illustrated for a prospective offshore wind farm. The production capacity uncertainties can be decomposed to assess the contribution of epistemic uncertainty allowing the value of gathering information to reduce risk to beexamined.

Variance-based sensitivity analysis of dynamic systems with both input and model uncertainty

This paper develops a methodology to compute variance-based sensitivity indices for dynamic systems with time series inputs and outputs, while accounting for both aleatory and epistemic uncertainty sources, and both random process and random variable inputs. We present semi-analytical methods for computing sensitivity indices for linear systems with Gaussian random process inputs, and for the general case of nonlinear systems with non-Gaussian random process inputs. The novel elements in this approach are the treatment of model form error, quantifying the cumulative effects of uncertainty sources over time, and evaluating sensitivity indices for multi-physics models. Bayesian state and parameter estimation methods are incorporated to quantify the model uncertainty arising from unknown model parameters and model form errors, and sensitivity indices are computed before and after model updating. The proposed methods are illustrated for (a) a linear Timoshenko beam erroneously modeled as an Euler-Bernoulli beam, and (b) hypersonic flow behavior of a flexible panel represented by a coupled multi-physics nonlinear model.

Hierarchical multiscale quantification of material uncertainty

The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material behavior across scales is a source of epistemic uncertainty of the overall material behavior. However, assessing this uncertainty is difficult due to the complex nature of material response and the prohibitive computational cost of integral calculations. In this paper, we exploit the multiscale and hierarchical nature of material response to develop an approach to quantify the overall uncertainty of material response without the need for integral calculations. Specifically, we bound the uncertainty at each scale and then combine the partial uncertainties in a way that provides a bound on the overall or integral uncertainty. The bound provides a conservative estimate on the uncertainty. Importantly, this approach does not require integral calculations that are prohibitively expensive. We demonstrate the framework on the problem of ballistic impact of a polycrystalline magnesium plate. Magnesium and its alloys are of current interest as promising light-weight structural and protective materials. Finally, we remark that the approach can also be used to study the sensitivity of the overall response to particular mechanisms at lower scales in a materials-by-design approach.

Uncertainties in the Seismic Assessment of Historical Masonry Buildings

Seismic assessments of historical masonry buildings are affected by several sources of epistemic uncertainty. These are mainly the material and the modelling parameters and the displacement capacity of the elements. Additional sources of uncertainty lie in the non-linear connections, such as wall-to-wall and floor-to-wall connections. Latin Hypercube Sampling was performed to create 400 sets of 11 material and modelling parameters. The proposed approach is applied to historical stone masonry buildings with timber floors, which are modelled by an equivalent frame approach using a newly developed macroelement accounting for both in-plane and out-of-plane failure. Each building is modelled first with out-of-plane behaviour enabled and non-linear connections, and then with out-of-plane behaviour disabled and rigid connections. For each model and set of parameters, incremental dynamic analyses are performed until building failure and seismic fragility curves derived. The key material and modelling parameters influencing the performance of the buildings are determined based on the peak ground acceleration at failure, type of failure and failure location. This study finds that the predicted PGA at failure and the failure mode and location is as sensitive to the properties of the non-linear connections as to the material and displacement capacity parameters, indicating that analyses must account for this uncertainty to accurately assess the in-plane and out-of-plane failure modes of historical masonry buildings. It also shows that modelling the out-of-plane behaviour produces a significant impact on the seismic fragility curves.

Exposure forecasting for seismic risk estimation: Application to Costa Rica

This study proposes a framework to forecast the spatial distribution of population and residential buildings for the assessment of future disaster risk. The approach accounts for the number, location, and characteristics of future assets considering sources of aleatory and epistemic uncertainty in several time-dependent variables. The value of the methodology is demonstrated at the urban scale using an earthquake scenario for the Great Metropolitan Area of Costa Rica. Hundreds of trajectories representing future urban growth were generated using geographically weighted regression and multiple-agent systems. These were converted into exposure models featuring the spatial correlation of urban expansion and the densification of the built environment. The forecasted earthquake losses indicate a mean increase in the absolute human and economic losses by 2030. However, the trajectory of relative risk is reducing, suggesting that the long-term enforcement of seismic regulations and urban planning are effectively lowering seismic risk in the case of Costa Rica.

A Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Greece

ABSTRACT Using a recently completed database of uniformly processed strong-motion data recorded in Greece, we derive a ground-motion prediction model (GMPM) for horizontal-component peak ground velocity, peak ground acceleration, and 5% damped pseudoacceleration response spectra, at 105 periods ranging from 0.01 to 10 s. The equations were developed by modifying a global GMPM, to account for more rapid attenuation and weaker magnitude scaling in the Greek ground motions than in the global GMPM. Our GMPM is calibrated using the Greek data for distances up to 300 km, magnitudes from 4.0 to 7.0, and time-averaged 30 m shear-wave velocities from 150 to 1200 m/s. The GMPM has important attributes for hazard applications including magnitude scaling that extends the range of applicability to M 8.0 and nonlinear site response. These features are possible because they are well constrained by data in the global GMPM from which our model is derived. An interesting feature of the Greek data, also observed previously in studies of mid-magnitude events (6.1–6.5) in Italy, is that they are substantially overpredicted by the global GMPM, which may be a repeatable regional feature, but may also be influenced by soil–structure interaction. This bias is an important source of epistemic uncertainty that should be considered in hazard analysis.

Uncertainty Reduction Through Data Management in the Development, Validation, Calibration, and Operation of a Hurricane Vulnerability Model

Catastrophe models estimate risk at the intersection of hazard, exposure, and vulnerability. Each of these areas requires diverse sources of data, which are very often incomplete, inconsistent, or missing altogether. The poor quality of the data is a source of epistemic uncertainty, which affects the vulnerability models as well as the output of the catastrophe models. This article identifies the different sources of epistemic uncertainty in the data, and elaborates on strategies to reduce this uncertainty, in particular through identification, augmentation, and integration of the different types of data. The challenges are illustrated through the Florida Public Hurricane Loss Model (FPHLM), which estimates insured losses on residential buildings caused by hurricane events in Florida. To define the input exposure, and for model development, calibration, and validation purposes, the FPHLM teams accessed three main sources of data: county tax appraiser databases, National Flood Insurance Protection (NFIP) portfolios, and wind insurance portfolios. The data from these different sources were reformatted and processed, and the insurance databases were separately cross-referenced at the county level with tax appraiser databases. The FPHLM hazard teams assigned estimates of natural hazard intensity measure to each insurance claim. These efforts produced an integrated and more complete set of building descriptors for each policy in the NFIP and wind portfolios. The article describes the impact of these uncertainty reductions on the development and validation of the vulnerability models, and suggests avenues for data improvement. Lessons learned should be of interest to professionals involved in disaster risk assessment and management.

Understanding uncertainty in the Impact Classification for Alien Taxa (ICAT) assessments

The Environmental Impact Classification for Alien Taxa (EICAT) and the Socio-Economic Impact Classification of Alien Taxa (SEICAT) have been proposed to provide unified methods for classifying alien species according to their magnitude of impacts. EICAT and SEICAT (herein “ICAT” when refered together) were designed to facilitate the comparison between taxa and invasion contexts by using a standardised, semi-quantitative scoring scheme. The ICAT scores are assigned after conducting a literature review to evaluate all impact observations against the protocols’ criteria. EICAT classifies impacts on the native biota of the recipient environments, whereas SEICAT classifies impacts on human activities. A key component of the process is to assign a level of confidence (high, medium or low) to account for uncertainty. Assessors assign confidence scores to each impact record depending on how confident they are that the assigned impact magnitude reflects the true situation. All possible sources of epistemic uncertainty are expected to be captured by one overall confidence score, neglecting linguistic uncertainties that assessors should be aware of. The current way of handling uncertainty is prone to subjectivity and therefore might lead to inconsistencies amongst assessors. This paper identifies the major sources of uncertainty for impacts classified under the ICAT frameworks, where they emerge in the assessment process and how they are likely to be contributing to biases and inconsistency in assessments. In addition, as the current procedures only capture uncertainty at the individual impact report, interspecific comparisons may be limited by various factors, including data availability. Therefore, ranking species, based on impact magnitude under the present systems, does not account for such uncertainty. We identify three types of biases occurring beyond the individual impact report level (and not captured by the confidence score): biases in the existing data, data collection and data assessment. These biases should be recognised when comparing alien species based on their impacts. Clarifying uncertainty concepts relevant to the ICAT frameworks will lead to more consistent impact assessments and more robust intra- and inter-specific comparisons of impact magnitudes.

Long-Term Probabilistic Volcanic Hazard Assessment Using Open and Non-open Data: Observations and Current Issues

Probabilistic volcanic hazard assessment (PVHA) has become the paradigm to quantify volcanic hazard over the last decades. Substantial aleatory and epistemic uncertainties in PVHA arise from complexity of physico-chemical processes, impossibility of their direct observation and, importantly, a severe scarcity of observables from past eruptions. One factor responsible for data scarcity is the infrequency of moderate/large eruptions; other factors include lack of discoverability and accessibility to volcanological data. Open-access databases can help alleviate data scarcity and have significantly contributed to long-term PVHA of eruption onset and size, while are less common for data required in other PVHA components (e.g. vent opening). Making datasets open is complicated by economical, technological, ethical and/or policy-related challenges. International synergies (e.g. Global Volcanism Program, WOVOdat, Global Volcano Model, EPOS) will be key to facilitate the creation and maintenance of open-access databases that support Next-Generation PVHA. Additionally, clarification of some misconceptions about PVHA can also help progress. Firstly, PVHA should be understood as an expansion of deterministic, scenario-based hazard assessments. Secondly, a successful PVHA should sometimes be evaluated by its ability to deliver useful and usable hazard-related messages that help mitigate volcanic risk. Thirdly, PVHA is not simply an end product but a driver for research: identifying the most relevant sources of epistemic uncertainty can guide future efforts to reduce the overall uncertainty. Broadening of the volcanological community expertise to statistics or engineering has already brought major breakthroughs in long-term PVHA. A vital next step is developing and maintaining more open-access datasets that support PVHA worldwide.

Quantifying & analysing mixed aleatoric and structural uncertainty in complex turbulent flow simulations

Reynolds Averaged Navier Stokes models are the most popular approach for Computational Fluid Dynamics simulations of turbulent flows. Despite their popularity, these numerical models still need an appropriate quantification of margins and uncertainty for reliable engineering practice. In turbulent flow simulations, there are two kinds of uncertainties: aleatoric (those arising due to errors in initial conditions, material parameters, etc.) and structural or epistemic (those arising due to the turbulence model used). While these uncertainties have been explored in isolation, there are no studies that properly consider both types of uncertainty together as is the case in real life engineering applications. Considering these two sources of uncertainty in isolation limits our knowledge regarding the sources of uncertainty, their relative magnitudes, their interaction and the accuracy of uncertainty estimates. For the reasons given, a methodology is necessary to amalgamate uncertainties of different nature. In this paper is outlined a framework to carry out uncertainty quantification for such mixed uncertainty cases. The results are compared to those from aleatoric only and epistemic only studies to analyze the manner in which aleatoric and epistemic uncertainties interact and affect final results in complex turbulent flows and heat transfer. We compare and contrast the relative contributions of these sources to the overall uncertainty. The results obtained for our test cases exhibit that only considering aleatoric or epistemic uncertainty sources in isolation tends to severely under-predict the uncertainty in simulations. Utilizing the framework, we show that considering both sources together leads to a satisfactory prediction of the uncertainty in simulation results because of the underlying relations between these sources uncertainty in their propagation.

Data envelopment analysis based procedure for selection and ranking of ground motion prediction equations

One of the influential components in the probabilistic seismic-hazard analysis (PSHA) is selecting appropriate ground motion prediction equations (GMPEs). To handle the source of epistemic uncertainty, the most common approach is considering several GMPEs in a logic tree framework. In such an approach, the selected GMPEs and the weights assigned for each one are usually determined by experts, mostly according to gut feeling. In order to reduce the role of subjectivity in selecting GMPEs, some statistical criteria based on goodness-of-fit measures were developed in recent years. In this study, in order to incorporate different criteria in the ranking procedure, we present to use data envelopment analysis (DEA) as a multi-criteria efficiency evaluation framework. One of the advantages of the DEA procedure is that it is able to determine the efficiency or inefficiency of each GMPE. Also, the DEA methodology is able to handle the situation in which several target intensity measures such as spectral amplitude in different structural periods are interested to be considered in the ranking procedure. In this study, the DEA procedure is applied to the Central Iran seismotectonic province. The results show that the DEA can well evaluate the efficiency of GMPEs, and can be used as supplements to existing ranking procedures.

A high-resolution, long-term wave resource assessment of Japan with wave–current effects

The largest source of uncertainty in estimating annual energy production from a wave energy converter is natural variability. Standards recommend the collection of long-term on-site records, but with a concurrent requirement of dense data coverage, it becomes intractable to assess resources even at the feasibility development stage. Here, we provide uncertainty estimates of wave energy resources along the coast of Japan at 1 km resolution based on 21-year long numerical simulation, assuring a mean absolute percentage error of 4%. The uncertainties of the annual, seasonal and monthly climatologies are provided, and the epistemic uncertainty due to the effects of ocean current and finite depth on wave power estimation are quantified. Additionally, a significant wave height threshold is applied to exclude severe storm periods when devices are not in operation. The estimated total available wave power in Japan is 115.1 GW, whereas with a 3 m significant wave height threshold, it reduces to about 70 GW. Wave modeling under strong influence of ocean current is yet another source of epistemic uncertainty and the local and remote effects of strong current field are discussed. Results from the wave resource assessment are accessible to the public via a user-friendly web-based Geographical Information System, which was developed to help foster the use of marine renewable energy.