This MS is intended to foster development and interaction in the area of computational multiscale modelling with uncertainties (aleatoric and/or epistemic). Thus novel computational contributions to different non-deterministic simulation techniques with wide application to multiscale and multiphysics problems are invited. These problem classes may e.g. cover stochastic and heterogeneous elasticity, plasticity, generic rheology, heat conduction, magneto- and electro-statics, etc., and their various couplings. Thereby possible multiscale simulation techniques may typically build on (but are certainly not restricted to) e.g.:

• Stochastic Galerkin Method
• Monte-Carlo Simulation
• Stochastic Collocation Method
• Perturbation Methods
• Imprecise Probability Modeling
• Fuzzy, Fuzzy-Stochastic, and Interval-Stochastic Modeling
• Constitutive Modelling under Uncertainty
• Direct Numerical Simulations of Non-ergodic Media
• Others

In computational science and engineering, numerical models of physical systems are constructed with aim at reproducing experimental observations. The parameters of the numerical models are determined by combining information from different sources such as direct measurements of the parameters or the system behavior, expert knowledge, categorical data and information from literature. In probability theory, the process of combining information to learn model parameters is formalized in the concept of Bayesian updating. Thereby, the prior probability distribution of the model parameters is updated with new data to a posterior distribution. The derived distribution can be further used for forward uncertainty propagation and reliability assessment of the system performance.

This mini-symposium aims to attract papers that address either methodological developments or novel applications on Bayesian analysis of numerical models. Individual relevant topics include: Markov chain Monte Carlo methods; sequential Montel Carlo methods; Taylor series approximations to the posterior; Kriging/Gaussian process models; conjugate priors and Gibbs sampling; approximate Bayesian computation; Bayesian updating with surrogate models; multilevel/multifidelity methods; structural identification; reliability updating; updating in the presence of spatial/time variability; applications that investigate the influence of prior considerations on the analysis results; definition of the likelihood function; representation of model errors; optimal experimental design.

Due to factors related to manufacturing or construction processes, ageing, loading, environmental & boundary conditions, measurement errors, modeling assumptions / inefficiencies and numerous others, almost every engineering system is characterized by uncertainty. The propagation of uncertainty through the system gives rise to corresponding complexities during simulation of its structural response, yet also during its characterization based on experimental data. Consequently, only a limited degree of confidence can be attributed in the behavior, reliability and safety of structural systems in particular throughout their life cycle. For this purpose, it is imperative to develop models and processes able to encompass the aforementioned uncertainties. 

This mini-symposium deals with uncertainty quantification and propagation methods applicable to the simulation and identification of complex engineering systems. It covers theoretical and computational issues, applications in structural dynamics, earthquake engineering, mechanical and aerospace engineering, as well as other related engineering disciplines. Topics relevant to the session include: dynamics of structural systems, structural health monitoring methods for damage and reliability prognosis, theoretical and experimental system identification for systems with uncertainty, uncertainty quantification in model selection and parameter estimation, stochastic simulation techniques for state estimation and model class selection, structural prognosis techniques, updating response and reliability predictions using data. Papers dealing with experimental investigation and verification of theories are especially welcomed.

Recent developments in non-deterministic modelling approaches introduced a very broad spectrum of highly advanced numerical methods for reliability analysis and uncertainty quanti cation, including probabilistic, interval, fuzzy or imprecise methods. The application of these techniques however requires the analyst to accurately specify the relevant uncertain model parameters. Since direct measurement of such model quantities is often not feasible, or in practice too expensive, inverse techniques are commonly applied.

This mini-symposium aims to gather experts researchers, academics and practising engineers concerned with inverse methods for uncertainty quantification to present their recent ndings, methodological developments and innovative applications. Papers discussing advances in techniques from both frequentist and Bayesian interpretations of probability theory, as well as interval and possibilistic methods and concepts based on imprecise probabilities are invited.

The use of high-dimensional physics-based computational models (high-fidelity models) is critical to assessing the behavior of complex physical systems. Given uncertainties in the model input and/or parameters, the problem is set in a probabilistic framework in order to quantify the uncertainty in the behavior/response of the physical system. However, this comes at great computational cost as it requires many repeated simulations at sample points spanning the, often high dimensional, uncertain parameter space.  Computational constraints motivate the need to carefully select the sample points at which the solution is evaluated and then use these points to build a surrogate and/or reduced order model. A surrogate model is a simpler mathematical model describing the physical system that is inexpensive to evaluate and accurately approximates/ interpolates the solution between the sample points where the exact solution is known. A reduced-order model (ROM), on the other hand, aims to preserve the governing equations while drastically reducing the number of degrees of freedom. This mini-symposium aims to attract papers that address either methodological developments or novel applications on reduced-order and surrogate models used in the framework of uncertainty quantification. Individual relevant topics include:

• Stochastic collocation methods
• Generalized polynomial chaos expansions
• Gaussian process regression / kriging
• Machine learning and artificial neural networks
• Reduced basis and nonlinear projection-based ROMs
• Adaptive sampling methods for efficient surrogate generation 
• High dimensional sampling and interpolation
• Novel applications in mechanics, materials, and other relevant fields.

Keywords: surrogate modelling, statistical learning, deep learning, model reduction, low-rank approximations, computational mechanics, fluid-structure coupling

This symposium is held in honor of Prof. Hermann G. Matthies, Institute of Scientific Computing, Technische Universität Braunschweig, Germany, on the occasion of his retirement. Prof. Matthies research is of very wide scope ranging from computational mechanics to the propagation of uncertainty in nonlinear models. Prof. Matthies’s motivation, 24 years of academic and 16 years of industrial expertise, and engagement with and influence on scientific computing research worldwide place him among the great contributors to thefield. His major contributions are in
- Uncertainty quantification
- Low-rank approximation algorithms,
- Inverse problems,
- Model reduction,
- Elastoplasticity theory,
- Multiscale algorithms,
- and fluid-structure coupling

fields, among others.

Prof. Matthies collaborators, colleagues and friends will present theoretical and computational contributions in topics as stated above.

The use of surrogate models has become quite popular in uncertainty propagation (UP) of costly-to-evaluate physical models. Several types of surrogate models are available, with their own advantages and limits. These models are applied to a large variety of UP problems, such as reliability analysis, sensitivity analysis and optimal design under uncertainty among others. Efforts are made to take the best of such techniques, in order to improve the efficiency of the devised algorithms: adaptive enrichment strategies, dimension reduction, multi-fidelity models, ensemble of surrogates, surrogate-based sampling, … The objective of this Mini-Symposium is to discuss the requirements of surrogate-based approaches (in terms of code implementation, computer resources needed, parameter tuning), their applicability to challenging problems (e.g. high dimensional input spaces, complex physical models, systems) and their efficiency/robustness with respect to other reference techniques. The proposal of benchmark physical models challenging for surrogate-based approaches is expected from the contributed papers, with a clear model description and reference solutions.

In this mini symposium we will discuss recent advances in uncertainty characterization, order reduction as well as optimization and design under uncertainty. For these topics we will focus on new models (e.g. physically motivated covariance Kernels) or frameworks that overcome simplifying and often unnecessary assumptions such as the Gaussian assumption, the temporal and spatial separability, as well as models defined over rich parameter spaces that can efficiently capture space-time data dependencies and cross-correlations. We will explore the connection of the above with machine learning approaches, multivariate formulations (e.g., co-kriging, multivariate covariance functions), sensitivity analysis, as well as optimization and design under uncertainty (e.g., wave propagation in random media).

In many engineering problems from the field of uncertainty quantification the interest is in the effect of uncertainty on a specific Quantity of Interest (QoI), that is only known implicitly as the solution of some equations (e.g. a system of partial differential equations). As a result, it holds that determining a numerical value of the QoI for a specific realization of the uncertain parameters is computationally expensive. This limits the applicability of straightforward uncertainty propagation and quantification methods, as the number of evaluations of the underlying model must remain small to keep the approach tractable.

An example of such a problem is predicting the effect of uncertain boundary conditions on the characteristics of fluid flow, also known as a forward problem. Another, but not less important example, is calibrating the boundary conditions from noisy (i.e. "uncertain") measurements, which is referred to as an inverse problem.

In this minisymposium, recent developments and practical techniques are discussed to numerically approximate solutions for both the forward and the inverse problem. The focus is on non-intrusive approaches, i.e. on efficient collocation techniques, bringing together researchers working on: efficient sampling, surrogate models, machine learning techniques, etc. A common theme in all approaches is the limited number of possible model evaluations.

Uncertainty quantification (UQ) has become a central topic in virtually all fields of applied sciences over the past decade. Including uncertainty quantification in predictive models is a technical challenge that fostered the development of techniques such as (non-)probabilistic modelling of the sources of uncertainty, surrogate modelling, sensitivity analysis, model calibration, robust optimization, etc. The deployment and further diffusion of such techniques to a larger audience, however, depends critically on the availability of proper software that be incorporated by researchers and practioners into their own workflows.

This minisymposium aims at bringing together leading and innovative players in the international UQ software scene to foster discussions and exchange of ideas between developers and prospective users. Contributions are welcome on the following topics: non-intrusive UQ techniques, surrogate modelling, HPC in UQ, general-purpose UQ software, dimensionality reduction techniques and case studies and applications to real-csale industrial problems.

Key words: Data Uncertainty and Modelling, Computational Mechanics, Numerical Design

The numerical analysis and design of structures is currently characterised by deterministic thinking and methods. Deterministic modelling of the reality indicates preciseness and safety, while, on contrary all available data and information are characterized by uncertainty (variability, imprecision, incompleteness), which cannot be neglected.

The main focus is the presentation of methods for the numerical simulation of structures under consideration of data uncertainty. With the help of the mini-symposium, the opportunities of inter- and transdisciplinary shall be used for the generation of synergies between mathematics and engineering sciences.

Engineering solutions are characterized by inherent robustness and flexibility as essential features for a faultless life of structures and systems under uncertain and changing conditions. An implementation of these features in a structure or system requires a comprehensive consideration of uncertainty in the model parameters and environmental and man imposed loads as well as other types of intrinsic and epistemic uncertainties. Numerical design of structures should be robust with respect to (spatial and time dependent) uncertainties inherently present in resistance of materials, boundary conditions etc.

This requires in turn the availability of a reliable numerical analysis, assessment and prediction of the lifecycle of a structure taking explicitly into account the effect of the unavoidable uncertainties.
Challenges in this context involve, for example, limited information, human factors, subjectivity and experience, linguistic assessments, imprecise measurements, dubious information, unclear physics etc. Due to the polymorphic nature and characteristic of the available information both probabilistic and set-theoretical approaches are relevant for solutions.

This mini-symposium aims at bringing together researchers, academics and practicing engineers concerned with the various forms of advanced engineering designs. Recent deve-lopments of numerical methods in the field of engineering design which include a comprehensive consideration of uncertainty and associated efficient analysis techniques, such as advanced Monte Carlo simulation, meta-model approximations, and High Performance Computing strategies are explicitly invited. These may involve imprecise probabilities, interval methods, Fuzzy methods, and further concepts. The contributions may address specific technical or mathematical details, conceptual developments and solution strategies, individual solutions, and may also provide overviews and comparative studies.

Particular attention should be paid to practical applicability in engineering. Besides the applications of the involved engineering sciences, “real world” scenarios should be presented. The distinction between early stage of design and final design is significant.

The theoretical and numerical aspects of uncertainty quantification (UQ) in engineering and science have been well developed in past decades, however, they suffer the lack of accurate experimental data for validation.

This minisymposium focusses on the practical UQ when experimental data on uncertain parameters and structural responses are available. The challenges in this context involve, for instance, robust stochastic inverse methods for UQ identification when limited data are available; probability estimation from experimental data; spectral representation of spatially random fields using measured data; etc.

The goals aim to bring together researchers, academics and industry experts in various areas of engineering and science to discuss the latest and recent methods and techniques combining experimental UQ with theoretical and numerical methods. Contributions addressing UQ in experimental structural dynamics, vibration analysis, modal analysis, acoustic problems, earthquake engineering and risk analysis are particularly welcome.

Over the last few years, the development of multiscale methods in a stochastic setting for uncertainty quantification and reliability analysis of composite materials and structures, as well as the integration of stochastic methods into a multiscale framework are becoming an emerging research frontier. This Mini-Symposium aims at presenting recent advances in the field of multiscale analysis and design of random heterogeneous media. In this respect, topics of interest include but are not limited to:

• Random field modeling of heterogeneous media
• Efficient simulation of random microstructure/morphology
• Finite element solution of multiscale stochastic partial differential equations
• Stochastic finite element (SFE) analysis of composite materials and structures
• Methods for improving the efficiency of Monte Carlo simulation
• Efficient algorithms to accelerate the SFE solution of multiscale problems
• Large-scale applications

This MS is devoted to the presentation of advances in engineering software for uncertainty quantification. It addresses both academic as well as commercial software advances covering applied science and engineering problems with emphasis in UQ as well as optimization under uncertainties including multiscale analysis and design as well model validation and verification. 

This MS invites contributions showcasing the potential of machine learning tools in tackling uncertainty quantification and uncertainty propagation problems in physical, engineering, and biological systems. Particular areas of focus include scalability to high-dimensional parameter spaces, the robustness and interpretability of data-driven algorithms, and their ability to enable  downstream tasks such as adaptive data acquisition, experimental design, transfer/multi-fidelity learning and optimization under uncertainty.

Developing timely and efficient maintenance strategies of structures and systems in operating conditions is one of the current main industrial challenges. This is of particular importance for complex and critical systems such as aerostructures, bridges, nuclear power plant or disposal for radioactive waste to name some.

Inspection activities are very effective to improve the reliability and safety of such systems but on the other hand they are extremely expensive. For this reason, there is the need of developing robust predictive maintenance tools where mathematical algorithms are used to solve difficult modelling, decision making and classification problems. This will involve optimizing the number of inputs to the models, finding the minimum data requirement for accurate prediction of possible untoward events, and designing experiments to maximize the information content of the data.

This MS invites contributions on advanced techniques and industrial applications showcasing recent advances in the failure prevention of complex systems.