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 (UQ) in models of complex systems, structures and components. These methods range from purely interval and fuzzy approaches over advanced probabilistic schemes to imprecise probabilistic concepts. Also, the application of machine learning-inspired techniques such as active learning is becoming ever more popular in this context. This mini-symposium focuses on novel developments of these techniques for the representation of uncertainty and applications of in advanced engineering modelling activities, especially in the context of UQ, reliability analysis and senstivitiy analysis.

Researchers and practitioners focusing on UQ, reliability analysis and senstivitiy analysis in numerical modelling for engineering applications with limited data, ranging from uncertainty propagation methodologies, inverse identification and quantification techniques to optimisation under uncertainty as well as recent implementations and developments of Machine Learning for dealing with uncertainty are invited to submit an abstract to this mini-symposium.

Guiding high-consequence decision making in engineering applications involving complex dynamical systems such as aerostructures, bridges, nuclear power plants and wind turbines to name a few,  requires strategies beyond Machine Learning (ML) because of: (i) limited volume of informative data (poor generalisation performance with respect to unseen conditions), (ii) risk of yielding accurate-but-wrong predictions (physically inconsistent or implausible predictions); (iii) need to explicitly deal with uncertainties; (iv) need of providing Explainable and Interpretable inferences. Physics-Enhanced Machine Learning is an umbrella term used to described strategies for building hybrid physics-data models. PEML strategies integrates physics and ML strategies via the introduction of biases including (but not limited to): observational biases (e.g. data augmentation), inductive biases (e.g. physical constraints), learning biases (e.g. inference/learning algorithm setup), and model form/discrepancy biases (e.g. equation terms describing a partially known physics-based model) – often included in the inductive biases.

This special session invites contributions showcasing:

- Methodological techniques including (but not limited to): Physics-Informed ML, Physics-Encoded ML and Physics-Guided ML strategies.
-Recent advances on:
    i. informing physics (including: identification of models, of unknown constitutive laws, of physics-based model parameters, of governing equations, of reduced order models)
   ii. enabling explainable, interpretable, fast and accurate inferences under uncertainties.
   iii. Learning from both simulations (forward modelling) and monitoring data (inverse modelling)
   iv. Laboratory and real-world applications.

Computational models are commonly used in science and engineering to predict the behavior of complex physical and mechanical systems. These models must constantly trade model complexity with the availability and accuracy of data used as model inputs. This balance is particularly crucial in the development of digital twins, which handle high model complexity and strive for both reliability and precision, all while enabling rapid evaluation. Decision-critical scenarios using these digital twins, such as clinical decision support or autonomous car driving, further stress the need to properly balance model complexity with predictive accuracy.

Global sensitivity analysis is a valuable tool for comprehending how changes in input parameters influence model outputs. This process helps refine and simplify models while ensuring their accuracy is maintained. By recognizing essential parameters and their effects, sensitivity analysis helps reduce uncertainties, enhance model robustness, and support model validation through effective data collection. Several sensitivity analysis methods have been developed to address high computational costs, model complexities, and different output probability distributions. In this mini-symposium, we look for contributions that address either methodological developments or novel applications of global sensitivity analysis in computational models of engineering and scientific systems.

Topics of interest include but are not limited to advanced methods for global sensitivity analysis, applications of global sensitivity analysis to complex computational models, techniques for reducing model complexity while maintaining accuracy, sensitivity analysis in the presence of spatial/temporal dependence of uncertainty, integration of sensitivity analysis with surrogate modeling, green (or given-data) sensitivity analysis, applications in optimal experimental design, and the use of high-performance computing and machine learning to accelerate sensitivity analysis.

Keywords: Global sensitivity analysis, Uncertainty Quantification, Digital Twin, Computational models, Model complexity

Keywords: model reduction, proper orthogonal decomposition (POD), reduced-basis (RB), uncertainty quantification, Bayesian inverse problems, reliability analysis.

Uncertainty quantification (UQ) enhances the reliability and credibility of model-based predictions, which is essential for informed decision-making and effective risk management across science and engineering. Classical UQ methods, including those based on Monte Carlo simulations, require multiple model evaluations to achieve accurate uncertainty estimates. Engineering models often rely on costly numerical solutions of partial differential equations, making the generation of numerous model evaluations highly computationally expensive and resource demanding. Model reduction addresses this problem by identifying dominant subspaces and constructing surrogate models to approximate the behaviour of the full model through projection of the high-dimensional equation system onto a low-dimensional subspace. Unlike purely data-driven surrogate models, projection-based model reduction delivers surrogates that reflect the structure of the governing equations of the underlying physical system, facilitating analysis of the reduced models and often enabling accurate approximation with zero or limited data.

We invite talks that discuss methodological developments and novel applications of model reduction in all areas of uncertainty quantification, including but not limited to uncertainty propagation, uncertainty-based sensitivity analysis, Bayesian inversion, reliability analysis and optimization under uncertainty.

The evaluation of engineering structures under various disastrous dynamic actions involves significant uncertainties inherent in both external excitations and structural parameters. Assessing the safety of these structures subjected to multiple hazards and developing appropriate response analysis methods are of paramount importance. In recent years, the field has encountered substantial challenges in refining and efficiently conducting uncertainty propagation and probabilistic performance assessments for complex real-world engineering structures. These challenges underscore the need for advanced methodologies and collaborative efforts to improve our understanding and management of these uncertainties. This mini-symposium (MS) invites contributions that address the following topics:

• Methods for uncertainty propagation in complex nonlinear dynamic systems.
• Reliability analysis of engineering structures and systems under stochastic loadings.
• Data-driven and artificial intelligence-aided techniques for uncertainty propagation and reliability assessment.
• Probabilistic performance assessment and performance-based design of structures.
• Lifecycle assessment, resilience recovery, and performance enhancement measures for structures and infrastructure systems under multi-hazard scenarios.
• Impact of climate change on the performance and decision-making of civil engineering structures facing multiple hazards.

We encourage researchers, engineers, and practitioners to share their insights and advancements in these areas. By fostering a collaborative environment, this MS aims to propel the development of innovative solutions and methodologies to effectively manage and mitigate the uncertainties in engineering structures, thereby enhancing their safety and reliability in the face of diverse challenges.

The integration of uncertainty quantification with modern tools from data science and scientific machine learning can accelerate (and optimize) simulation and analysis for scientific discovery and engineering.  In mathematical modeling of complex systems, one typically progresses from observations of the world first to equations for a model, and then to the analysis of the model to make predictions. However, several major challenges arise in this process since the complex high-dimensional physical systems of interest often involve multiple physics, multiple length- and time-scales, as well as nonlinear and history dependent behaviors. To further complicate matters, physics-based models must contend with a myriad of uncertainties such as inherent stochasticity in the physics (aleatory uncertainty) and uncertainties in model-form (epistemic uncertainties).   To this end, manifold learning, a widely-used machine learning task can be utilized to develop useful reduced-order/surrogate models that can accelerate uncertainty quantification, sensitivity analysis, and reliability analysis. Yet, for very large, complex multiscale, high-dimensional, nonlinear, and expensive to evaluate systems, direct application of these techniques alone is not enough: their effectiveness relies heavily on access to training data which, in the context of high-dimensional complex systems, is often limited due to the high costs associated with simulation and experimentation.

This MS aims to bring together leading experts in the fields of uncertainty quantification and data-driven mathematical modeling and highlight recent advances in manifold and scientific machine learning for UQ, that will enhance our ability to develop reliable reduced-order models for complex physical systems. 

Over the past few decades, computer simulation has become a cornerstone in all engineering and applied science disciplines. High-fidelity simulators, such as finite element models, are extensively utilized throughout the design process of complex systems. However, directly employing these models for design optimization, uncertainty impact on reliability and robustness, model calibration from experimental data, or global sensitivity analysis is often impractical due to their significant computational cost, even when relying on high-performance computing resources. Consequently, surrogate modelling has garnered substantial interest in recent years. Surrogate models are fastevaluating analytical functions that approximate the input/output relationships of the original simulators. They are constructed using limited data generated from the complex high-fidelity models.

This mini-symposium aims to spotlight emerging research trends in surrogate modelling. We invite contributions on established techniques such as (sparse) polynomial chaos expansions, Kriging, support vector regression, and sparse grid interpolation, as well as data-driven approaches derived from machine learning, including (deep) neural networks, random forests, etc. Topics of interest encompass, but are not limited to, active learning, ensemble modelling, and dimensionality reduction. We also welcome significant applications in new or emerging fields.

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 adoption of Uncertainty Quantification (UQ) as a tool for quantitative and performance-based engineering has been rapidly growing in the past decades. This is not last thanks to the increase in availability of powerful software solutions, that consistently lower both the computational costs, and the technical floor required to perform complex analysis on realistic case studies.

Software for UQ can target widely different groups, from highly specialized methodological researchers, to more focused technical users in production environments. Portability, repeatability and accessibility of state-of-the art algorithms and test cases have also proven highly valuable for the dissemination of proper uncertainty-quantification tools across disciplines.

With this minisymposium, we aim at fostering dialogue between well-established and innovative players in the international UQ software scene, as well as current and perspective users from different research and development fields. Software developers are encouraged to give insights into the current developments in their software, as well as to open the discussion into how to best support the UQ community. We invite presentations on topics including: non-intrusive UQ techniques, surrogate modelling, HPC in UQ, general-purpose UQ software, dimensionality reduction techniques and case studies and applications of UQ software to real-scale industrial problems.

The significance of high-fidelity physical models that incorporate model and parameter uncertainties, and operate across a wide range of design parameters and length scales, is widely recognized, often resulting in large or even prohibitive computational costs. This MiniSymposium focuses on applications in structural dynamics involving high-fidelity computational models, high stochastic dimension, linear and nonlinear computational models, and for which general methods are developed, pertaining but not limited to:

• Uncertainty quantification and propagation
• Statistical inverse problems, robust model updating, and non-convex optimization
• Data-driven surrogate modeling, generative models, and model reduction
• Probabilistic and machine-learning techniques for efficient high-fidelity simulations
• Stochastic fracture and damage in random heterogeneous media
• Wave propagation and stochastic finite elements in multiscale mechanics

Uncertainty Quantification (UQ) in the context of computationally expensive models poses significant challenges, requiring advanced methodologies for statistical, sensitivity, and reliability analyses, and also for effective dimensional reduction and finding latent variables. Integral to these analyses is the design of experiments (DoE), which strategically selects input points to maximize information about the Quantity of Interest (QoI) while minimizing computational burden. This minisymposium aims to bring together researchers and practitioners working on novel methodologies for designing experiments in UQ for computationally expensive models. The discussions will explore advancements in one-shot and adaptive designs, integration with surrogate models, and the application of active learning techniques to enhance the efficiency and effectiveness of UQ analyses.

Topics to be Addressed:

One-Shot Designs:

- Classical methods like Monte Carlo sampling (including Latin Hypercube Sampling and variance reduction techniques such as importance sampling), Quasi-Monte Carlo (QMC) methods, and low-discrepancy designs.
- Space-filling designs utilizing distance-based criteria to ensure comprehensive coverage of the input domain.

Sequential and Adaptive Designs:

- Transitioning from one-shot designs to sequential and adaptive approaches once initial information from the model is available.
- Effective strategies for updating the design iteratively to enhance the accuracy and efficiency of UQ analyses.

Surrogate Models and Active Learning:

- Construction of surrogate models (e.g., kriging, polynomial chaos expansions) facilitated by DoE.
- Active learning strategies tailored to specific applications and integrated with surrogate models to optimize experimental designs.

We invite contributions that address but are not limited to the following topics:

• Comparison and evaluation of one-shot versus sequential/adaptive DoE methods,
• Development of novel space-filling criteria for DoE in UQ,
• Applications of surrogate modeling techniques enabled by advanced DoE strategies, and
• Case studies demonstrating the effectiveness of active learning approaches in specific UQ applications.

In the last decades, 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 modelling and enhanced methods to study random heterogeneous media and metamaterials. In this respect, topics of interest include but are not limited to:

• Random field modelling of heterogeneous media
• Efficient simulation of random microstructure/morphology
• Design / Optimization of composite materials and structures considering uncertainty
• Stochastic modelling of fracture and damage
• Scale-dependent homogenization of random composites
• Homogenization of materials with random microstructure
• Finite element solution of multiscale stochastic partial differential equations
• Stochastic finite element (SFE) analysis of composite materials and structures
• Efficient algorithms to accelerate the SFE solution of multiscale problems
• Methods for improving the efficiency of Monte Carlo simulation
• Large-scale applications considering uncertainty
• Machine learning techniques for efficient material modelling
• Advanced computational methods for material modelling
• Data-driven material modelling

Stochastic simulation techniques, which involve computing expectations as sample averages, are employed in many fields of science and engineering. Such techniques are used due to either inherently stochastic model dynamics or a lack of suitable deterministic solvers for a given problem. Examples include simulating chemical processes, kinetic equations, and financial models. The result of such a simulation is characterized by an error containing a noise term whose variance decreases with an increasing number of solver samples and hence computational cost. In this minisymposium, we consider uncertainty quantification through the application of Monte Carlo sampling on top of such a solver. In this setting, one must carefully balance the number of inner solver samples and outer uncertainty quantification samples, to avoid unnecessary computational effort. We aim to bring together researchers producing fundamental algorithmic developments and tackling such problems in practical applications, to discuss the state of the art.

Analysis and management of engineering systems require decision-making under uncertainty. Such uncertainty stems from the intrinsic variabilities in the system and manufacturing processes, ambiguity in the computational model due to lack of precise knowledge of the governing physics as well as noisy measurements/data. Optimization methods have widespread application in engineering decision-making. Accounting for the uncertainty in engineering models during optimization often involves dealing with high-dimensional uncertain inputs, which poses additional computational challenges. Recent advances in the fields of uncertainty quantification and machine learning provide effective tools for optimization under uncertainty. This mini-symposium aims at bringing together researchers, academics and practicing engineers concerned with the various forms of optimization in the presence of uncertainties. We seek contributions discussing novel optimization algorithms and methods, as well as applications to practical problems. Areas of interest include, but are not limited to, (multiobjective) design optimization of engineering systems under uncertainty, robust optimization, performance-based optimization, reliability-based optimization, stochastic optimization, risk management and optimization, optimal decision-making in presence of uncertainty, development and application of (machine learning) surrogate models for optimization under uncertainty, reduced order modeling, multi-level and multi-fidelity formulations and datadriven optimization.

Key words: Optimization, design, computational models, uncertainty quantification, machine learning

This minisymposium focuses on cutting-edge research at the intersection of AI, multiphysics, multiscale modeling, and UQ. We aim to bridge the gap between mathematical modeling and practical applications in engineering and scientific domains by integrating AI-driven techniques with traditional physics-based simulations to enhance the predictability, robustness, and sensitivity analysis of computational models.

Topics include AI-aided methods for linking microscale phenomena to macroscale behaviors, improving understanding of underlying scientific phenomena and enhancing computational efficiency and accuracy. These methods will be demonstrated on applications across different fields. This includes developing methods for identifying and quantifying the key driving variables through sensitivity analysis, correlation studies, and importance measures, as well as techniques for discovering governing equations and addressing challenges such as hidden variables and the need for effective coordinate transformations.

Key words: AI, machine learning, data-driven methods, multi-physics, multiscale modeling, robustness, UQ.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Institutional release number LLNL-PROP-867645. This research was funded by the National Nuclear Security Administration, Defense Nuclear Nonproliferation Research and Development (NNSA DNN R&D). The authors acknowledge important interdisciplinary collaboration with scientists and engineers from LANL, LLNL, MSTS, PNNL, and SNL.

The significant computational cost associated with computing discrete solutions of PDEs for single- or multi-physics problems, poses severe limitations to the ability of characterizing predictive uncertainty, and therefore to generate reliable and robust designs for applications in science and engineering. A possible solution to this problem is to combine small datasets from high-fidelity simulation outputs or costly experiments with large amounts of solutions that can be cheaply obtained from possibly biased low-fidelity information sources. This combination mechanism may depend on the specific focus of the analysis, for example when solving a direct or inverse problem, or when constructing emulators using tools from functional approximation or neural network-based predictors.

This minisymposium brings together researchers working on the broad theme of multi-fidelity information management. This includes leveraging the solution of multiple problems based on their correlation, the smoothness of their discrepancy, data augmentation or information transfer where the memory of the low-fidelity model needs to be conveniently preserved, avoiding catastrophic forgetting.

We encourage the submission of contributions in (but not limited to) theory, algorithms, and the comparison of approaches for (1) the solution of direct and inverse problems using multi-fidelity estimators and emulators, (2) traditional, Gaussian process-based and data-driven emulators, (3) multi-level, multi-index, multi-fidelity estimators and their combination, (4) dimensionality reduction and approaches to fuse information between model with dissimilar parameterization, (5) sequential multi-fidelity estimation, filtering and smoothing, (6) data augmentation and transfer learning in data-driven predictors. This minisymposium aims to advance the field of multi-fidelity information management, fostering collaborations and innovations in computational science and engineering.

Computational models are widely used in science and engineering to predict the response of complex physical and mechanical systems. The parameters of these models often cannot be determined uniquely as they are affected by uncertainties. Bayesian inference provides a powerful tool for making statistical inference of the uncertain model parameters by use of data and other available information. The methods for Bayesian inference most commonly rely on sampling algorithms to explore the outcome space of the uncertain parameters. For problems in which evaluation of the computational model is costly, such exploration can require enormous computational efforts. Hence, recent research focuses on the development of efficient Bayesian inference methods based on novel mathematical formulations or advanced sampling techniques. In this mini-symposium, we look for contributions that address either methodological developments or novel applications on Bayesian inference of computational models of engineering systems. In this respect, topics of interest include, but are not limited to, the following: advanced sampling methods for Bayesian analysis, inference in the presence of spatial/temporal dependence of uncertainty, structural identification, recursive Bayesian inference, virtual sensing, hierarchical Bayesian models, optimal experimental design, Bayesian reliability updating, Bayesian inference with surrogate models, accelerated Bayesian inference using machine leaning and high performance computing.

Key words: Bayesian inference, computational models, reliability updating, sampling-based inference, machine learning

Self-supervised learning (SSL) enables the training of large neural nets using raw data without requiring labels. Those foundation models are effective as few shot learners meaning that they are adapted to downstream tasks via fine tuning using a small number of annotated data. Self-supervision promises the creation more robust predictions attached with more reliable uncertainty estimates. The research performed especially in the field of Scientific Machine Learning (SciML) is focused on operator learning, in-context learning, physics-informed neural networks, Kolmogorov-Arnold networks, Gaussian Process operator learning, etc.  This minisymposium will invite experts and practitioners from the fields of Uncertainty Quantification (UQ) and SciML who will discuss the advantages, challenges, utility and next steps of quantifying and mitigating uncertainty in the era of SSL, showcasing:

• Training, validating and fine-tuning of PDE foundation models.
• Algorithmic and methodological approaches to perform transfer learning with lowest uncertainty estimates.
• Comparisons between stand-alone and fine-tuned models in terms of uncertainty.
• New types of uncertainty in SSL (e.g., uncertainty in learned representations).
• Adaptation of SSL arsenal to PDEs, randomness and measurement errors and more broadly to SciML.

Uncertainty quantification (UQ) and Machine Learning (ML) are two up to date and cutting -edge theory and technology in Sciences and Engineering. UQ provides a numerical relation of the uncertainty of the output response of a physical system when the respective variability of the input is defined. ML is the tool to interconnect the data driven approach to real problem solutions. Namely, the dataset obtained that govern a physical problem is processed and functions-models are formulated that provide the solution and response to the aforementioned problem. UQ and ML can be combined in order to obtain a broader solution to the physical problem considering its stochastic nature.

In this minisymposium, all applications for all possible aspects in Sciences and Engineering, of all Engineering disciplines, that implement UQ and ML are welcomed. Some representative but not restrictive occasions are provided.

1. UQ studies that implement Stochastic Random Field sums (Karhunen-Loeve, Spectral Representation), importance or fair probability sampling (Latin Hypercube sampling, Markov Chain Monte Carlo simulations)
2. ML studies that use all possible aspects of the theory (Neural Networks, optimization methods and Neural Networks formulation, convolutional autoencoders, methods of modelling with small dataset size)
3. All possible theoretical works that at least have a small application are also welcomed

Any inquiries about the suitability of a work to this minisymposium, can be sent to the email provided.  

The rapidly evolving field of Scientific Machine Learning (SciML) stands at the intersection of machine learning, computational science, and engineering, offering powerful new tools for advancing our understanding of complex systems. This mini-symposium aims to explore recent advancements in SciML, focusing on topics such as neural operators and their role in approximating complex systems, generative modeling techniques for data-driven discovery, and methods for uncertainty quantification in SciML.

Additionally, we will delve into cutting-edge developments in physics-informed machine learning approaches, which seamlessly integrate foundational scientific principles with data-driven models to enhance predictive accuracy and interpretability. The application areas for these techniques are broad, spanning fluid dynamics, climate modeling, materials science, and beyond. By bringing together experts from diverse disciplines, this mini-symposium aims at providing a platform for discussing the latest research, identifying challenges, and exploring the potential for SciML to drive innovation across scientific domains.