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.

The ability to make decisions under limited data is becoming increasingly important in the context of modelling for engineering applications. Several approaches are currently emerging to perform Uncertainty Quantification in complex models, ranging from purely interval and fuzzy approaches over polymorphic concepts to advanced probabilistic schemes. Also, the application of AI-inspired techniques is becoming ever more popular in this context. This mini-symposium focuses on the application of these techniques for the representation of uncertainty in advanced engineering modelling activities. Researchers focusing on UQ in numerical modelling for engineering applications with limited data, ranging from uncertainty propagation methodologies, inverse identification and quantification techniques to optimisation under uncertainty are invited to submit an abstract to this mini-symposium.

Computational homogenization of heterogeneous materials often requires the solution of non-deterministic problems including different types of uncertainties. These uncertainties result from different sources: lack of knowledge on the microstructure (epistemic uncertainties), a natural variability of the microstructure (aleatoric uncertainties), or both simultaneously (polymorphic uncertainties).

Depending on quantities affected by uncertainties we can distinguish between physical uncertainties (perturbation of material properties), geometrical uncertainties (random interfaces), topological uncertainties (changing number of voids or inclusions), and uncertainties in loading and boundary conditions. Often randomness is considered on the microscale, however, the last type occurs also on the meso- and macroscale (random loading on the macroscale induces random boundary conditions on the meso- and microscale).

The various types of uncertainties can be modeled using a variety of probabilistic and non-probabilistic methods.

Further important aspects to counteract the high costs of non-deterministic simulations and non-deterministic computational homogenization are reduced order modeling and parallel computing.

Extension of existing techniques to more sophisticated multi-physic and inelastic problems (plasticity, rheology, electro-magnetism, thermo-elasticity, etc.) is also of high priority.

Contributions to all these topics are kindly welcomed in this Minisymposium.

The exponentially growing availability of data and computational power during the last decades has drew attention to methods which allow models and physical laws to be inferred from data. Nowadays, data-driven modelling opens new paths to scientific discovery in the engineering, physical and biological sciences.

This mini symposium will explore recent advances in data driven modelling, error quantification and guarantees. For these topics we will focus on spatio-temporal statistical models, multivariate models, as well as machine learning and statistical inference techniques. We are particularly interested in models that can efficiently capture data variability in big datasets, characterize space-time data dependencies and cross-correlations among variables, and overcome simplifying--and often unsuitable---assumptions such as the Gaussian distribution, the temporal and spatial separability of covariance functions, and the Markovian property. Applications of interest include but are not limited to materials design, multi-scale modeling of molecular systems, clean energy forecasting, and environmental monitoring and risk assessment. 

Biology, biomedicine, and behavioral sciences are currently witnessing a shift from solving forward problems based on sparse data towards data assimilation and solving inverse problems to explain large datasets. Very often, multiscale simulations in biomedicine and bioengineering seek to infer the behavior of a system, assuming access to massive amounts of data, while the governing equations and their parameters may be uncertain. This is where machine learning may become critical: machine learning allows us to systematically preprocess massive amounts of data, integrate and analyze it from different input modalities and different levels of fidelity, identify correlations, discover hidden physics and infer the dynamics of the overall system, as well as build reduced order models for forward and inverse uncertainty quantification tasks. Similarly, we can use machine learning to tackle high-dimensional forward-predictive tasks, as well as inverse problems that aim to calibrate large-scale computational models to reproduce experimentally measured features across multiple scales. This mini-symposium aims to showcase current advances in machine learning and uncertainty quantification methods for biological systems, including (but not limited to) topics in data fusion, experimental design, Bayesian inference, systems identification, multi-fidelity modeling, hybrid model- and data-driven approaches, parameter estimation, data assimilation, and model personalization in computational medicine.

The confluence of physical and data sciences has always been fertile with opportunities to redefine both the instruments and the impact of scientific exploration. This MS explores the impact of recent growth in and synergies between experimental techniques, data analytics, and computational science on the interpretability of the world around us and our ability to engineer it. The MS provides a forum for fundamental mathematical and scientific questions as well as for related computational and operational challenges that continue to emerge at this interface. The focus will be on perspectives that explore uncertainty quantification and machine learning with a view to accelerate both scientific discovery and design optimization. Applications and demonstration problems that highlight various aspects of related challenges or opportunities are also welcome.

Keywords: Uncertainty quantification, manifold learning, surrogate modeling, Bayesian statistics, inverse analysis, statistical learning, deep learning, model reduction, low-rank approximations

The discretization of parametric or stochastic PDEs and ODEs describing complex physical and/or structural systems considering uncertainties leads to high-dimensional problems, the solution of which requires a massive computational effort. In order to address the challenge of quantitative predictive  modeling considering uncertainties, developments of low-cost approximates (surrogates) of high-dimensional functions, reduced-order models (ROMs), active manifold learning and multi-fidelity methods have been in the forefront of data-driven UQ. 

For example, developing lower-dimension (manifold) representations of the high-fidelity models in order to inform iterative/adaptive UQ efforts (active learning) can lead to the development of nonlinear, projection-based surrogates used for the predictive modeling.

Important is also to identify which class of problems allows sparse/low-rank/ROM approximations, and how the approximation error propagates into the statistical quantities of interest such as the mean, variance, and quantiles.

This MS aims to bring together leading experts in the fields of uncertainty quantification and data science and highlight recent advances in surrogate modeling using manifold learning for UQ, reduced-order modeling, low-rank and sparse techniques for UQ, data assimilation and Bayesian Inference.

• Areas of interest include, but are not limited to
• Uncertainty quantification for large-scale, high-dimensional problems.
• Reduced order modeling and multi-fidelity approximations
• Inverse problems in high dimensions
• Machine/deep learning approaches for predictive modeling in materials science.

There is the need for developing robust Structural Health Monitoring (SHM) tools for timely decision making and maintenance scheduling. This is of particular importance for complex and critical engineering structures and infrastructures such as bridges, wind turbines, nuclear power plant and aerostructures to name a few. One of the current main research challenges in SHM is integrating information obtained with physics-based models with those obtained with data-based models (based on data obtained in operating condition or during laboratory experiments) in order to detect anomalies in the behaviour of structures and infrastructures, estimating safe remaining life and suggest preventive actions to restore normal conditions.

This special session invites contributions on techniques and industrial applications showcasing recent advances on the use of integrated approaches for SHM combining physics-based models of structures (including surrogated models) and machine learning techniques applied to recorded data (sensors measurements and/or reports) and laboratory experiments.

Uncertainty quantification (UQ) methods that aim at taking into account model- and parameters uncertainty have received much attention in the mechanical, civil, and aerospace engineering communities over the past two decades. Some well-known approaches such as polynomial chaos expansions, global sensitivity analysis (Sobol’ indices) or active learning methods for reliability are nowadays commonly applied in an industrial context.

However, accurate computational models (e.g., using finite element analysis) of complex structures or systems are usually costly. A single run of these models may last minutes to hours, even on powerful computers. In order to use them for uncertainty quantification or optimization, which require repeated calls to the computational code, it is necessary to develop a substitute that may be evaluated thousands to millions of times at low cost: these substitutes are referred to as meta-models or surrogate models.

The aim of this mini-symposium is to confront various kinds of meta-modelling techniques in the context of uncertainty propagation including classical response surfaces, polynomial chaos expansions, Kriging, support vector regression, deep neural networks, sparse grid interpolation, etc. Multi-fidelity surrogate models will also be considered. Papers that present new methodology developments or large scale industrial applications that make use of surrogate models are welcome.

Structural Health Monitoring (SHM) approaches rely on accurate and informative recorded data to detect anomalies and make safe estimations as to remaining operating life. To extract such data, monitoring systems should be optimized in terms of sensor types, numbers, and locations. One of the key challenges in SHM is the placement of sensors on structures and infrastructures for which little or no previous data is available. 

This minisymposium invites contributions on techniques and industrial applications showcasing recent advances on sensor placement under uncertain information. Techniques combining physics-based models and uncertainty quantification techniques (both forward and inverse) are particularly welcome.

Uncertainty quantification (UQ) is a staple of engineering design, predictive modeling and more in general scientific and technological applications. Including uncertainty quantification in modeling workflows can be a technical challenge on many fronts, including (non-)probabilistic modeling of the sources of uncertainty, surrogate models and machine learning, sensitivity analysis, model calibration, robust optimization, etc. As a consequence of this large range of applications, the deployment and further diffusion of modern UQ techniques relies on the availability of proper software that can be incorporated by researchers and practitioners into their own workflows.

This mini-symposium 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, big-data and dimensionality reduction techniques and case studies and applications to real-scale industrial problems. 

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
• Design / Optimization of composite structures considering uncertainty
• Methods for improving the efficiency of Monte Carlo simulation
• Efficient algorithms to accelerate the SFE solution of multiscale problems
• Large-scale applications

The numerical analysis and design of structures is usually 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, inaccuracy), which cannot be neglected. The consideration of aleatoric as well as epistemic uncertainties yields polymorphic uncertainty features, which are currently in the focus of multiple research projects associated with Priority Programme “SPP1886 – Polymorphic Uncertainty Modelling for the Numerical Design of Structures” funded by the German Research Foundation (DFG).

Engineering solutions are characterized by inherent robustness and flexibility as essential features for a faultless life of structures and systems at uncertain and changing conditions. In order to ensure these structural properties, a comprehensive consideration of material and geometric parameters as well as imposed loads as being polymorphically uncertain is required.

The main focus of the mini-symposium is the presentation of methods for the numerical simulation of structures under consideration of data uncertainty. This includes data based uncertainty quantification with suitable uncertainty models as well as multivariate uncertain structural responses and related inverse uncertainty quantification methods. Considering structural design in engineering as optimization task involves advanced single- and multiobjective optimization schemes incorporating uncertainties and feasible surrogate models for either fundamental solutions or uncertainty propagation.

By the mini-symposium, the opportunities of inter- and transdisciplinary shall be used for the stimulation of synergies between mathematics and engineering sciences. Therefore, this minisymposium aims at recent developments of numerical methods in the field of engineering modelling and design which include a comprehensive consideration of uncertainty and associated efficient analysis techniques. In this respect, topics of interest include the following areas but are not limited to:

• polymorphic uncertainty modelling,
• fuzzy-Set theory, imprecise probability,
• constitutive modelling with uncertainties,
• surrogate Models in uncertainty quantification,
• uncertainties with spatial and temporal dependencies,
• solutions for invers uncertainty quantification,
• structural single- and multi-objective optimization considering uncertainties.

One of the main drivers of today’s computer-based innovations in industry and research is evidence-based modelling of complex physical systems. Computational models validated through experimental observations allow for robust predictions of the response of complex physical and mechanical systems. Areas like personalized medical treatment and innovative synthesis of materials and pharmaceuticals rely ever-increasingly on evidence-validated computer-based simulations and analysis. To this purpose, Bayesian inference is, perhaps, the most powerful tool. This method relies almost exclusively on sampling algorithms that explore the parameters’ distribution space based on the repeated evaluation of thousands of independent computational simulations. Such extensive exploration demands enormous computational power, rendering the use of traditional computational solvers inadequate. This is especially the case for problems that require a rigorous account of the intricacies of coupled dynamical processes characterized by uncertainty at various length and time scales. In this regard, the development of efficient Bayesian methods based on novel mathematical formulations or accelerated by machine-learning techniques and HPC programming is an emerging research direction with significant impact on science and the industry. 

The topics of the Minisymposium include, but are not limited to, the following:

Bayesian methods

- Hierarchical Bayesian models
- Advanced Markov Chain Monte Carlo methods
- Multi-fidelity information assimilation

Machine learning surrogates for multiscale-multiphysics models

- Deep Neural Network models
- Autoencoders
- Diffusion Maps, POD/PCA, Kernel PCA, Local Polynomial approximations

Efficient Solvers for large-scale problems

- Advanced iterative solvers
- Domain Decomposition Solvers
- Multigrid Solvers

High Performance Computing
Bayesian inference in challenging engineering applications

- Computational biology
- Stochastic multiscale material design
- Structural analysis
- Coupled multiphysics/multiscale problems