Multiscale modelling: approaches and challenges

Design of mechanically intelligent structures: Review of modelling stimuli-responsive materials for adaptive structures

Smart materials are upcoming in many industries due to their unique properties and wide range of applicability. These materials have the potential to transform traditional engineering practices by enabling the development of more efficient, adaptive, and responsive systems. However, smart materials are characterized by nonlinear behaviour and complex constitutive models, posing challenges in modelling and simulation. Therefore, understanding their mechanical properties is crucial for model-based design. This review aims for advancements in numerically implementing various smart materials, especially focusing on their nonlinear deformation behaviours. Different mechanisms and functionalities, classification, constitutive models and applications of smart materials were analyzed. In addition, different numerical approaches for modelling across scales were investigated. This review also explored the strategies and implementations for mechanically intelligent structures using smart materials. In conclusion, the potential model-based design methodology for the multiple smart material-based structures is proposed, which provides guidance for the future development of mechanically intelligent structures in industrial applications.

Prediction of Fracture Toughness of Pultruded Composites Based on Supervised Machine Learning

Prediction of mechanical properties is an essential part of material design. State-of-the-art simulation-based prediction requires data on microstructure and inter-component interactions of material. However, due to high costs and time limitations, such parameters, which are especially required for the simulation of advanced properties, are not always available. This paper proposes a data-driven approach to predicting the labor-consuming fracture toughness based on a series of standard, easy-to-measure mechanical characteristics. Three supervised machine-learning (ML) models (artificial neural networks, a random forest algorithm, and gradient boosting) were designed and tested for the prediction of mechanical properties of pultruded composites. A considerable dataset of mechanical properties was acquired as results of standard tensile, compression, flexure, in-plane shear, and Charpy tests and utilized as the input to predict the fracture toughness. Furthermore, this study investigated the correlations between the obtained mechanical characteristics. Analysis of ML performance showed that fracture toughness had the highest correlations with longitudinal bending and transverse tension and a strong correlation with the longitudinal compression modulus and tensile strength. The gradient boosting decision tree-based algorithms demonstrated the best prediction performance for fracture toughness, with an MSE less than 10% of the average value, providing a prediction within the range of experimental error. The ML algorithms showed potential in terms of determining which macro-level parameters can be used to predict micro-level material characteristics and how. The results provide inspiration for future pultruded composite material design and can enhance the numerical simulations of material.

Uncertainty quantification patterns for multiscale models

Uncertainty quantification (UQ) is a key component when using computational models that involve uncertainties, e.g. in decision-making scenarios. In this work, we present uncertainty quantification patterns (UQPs) that are designed to support the analysis of uncertainty in coupled multi-scale and multi-domain applications. UQPs provide the basic building blocks to create tailored UQ for multiscale models. The UQPs are implemented as generic templates, which can then be customized and aggregated to create a dedicated UQ procedure for multiscale applications. We present the implementation of the UQPs with multiscale coupling toolkit Multiscale Coupling Library and Environment 3. Potential speed-up for UQPs has been derived as well. As a proof of concept, two examples of multiscale applications using UQPs are presented. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

When we can trust computers (and when we can't)

With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the domains of science and engineering which are relatively simple and firmly grounded in theory, these methods are indeed powerful. Even so, the availability of code, data and documentation, along with a range of techniques for validation, verification and uncertainty quantification, are essential for building trust in computer-generated findings. When it comes to complex systems in domains of science that are less firmly grounded in theory, notably biology and medicine, to say nothing of the social sciences and humanities, computers can create the illusion of objectivity, not least because the rise of big data and machine-learning pose new challenges to reproducibility, while lacking true explanatory power. We also discuss important aspects of the natural world which cannot be solved by digital means. In the long term, renewed emphasis on analogue methods will be necessary to temper the excessive faith currently placed in digital computation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

An Early Stage Researcher's Primer on Systems Medicine Terminology

Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields. Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references. Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic.

Multiscale modelling, simulation and computing: from the desktop to the exascale

This short contribution introduces a theme issue dedicated to 'Multiscale modelling, simulation and computing: from the desktop to the exascale'. It holds a collection of articles presenting cutting-edge research in generic multiscale modelling and multiscale computing, and applications thereof on high-performance computing systems. The special issue starts with a position paper to discuss the paradigm of multiscale computing in the face of the emerging exascale, followed by a review and critical assessment of existing multiscale computing environments. This theme issue provides a state-of-the-art account of generic multiscale computing, as well as exciting examples of applications of such concepts in domains ranging from astrophysics, via material science and fusion, to biomedical sciences. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

Multiscale computing for science and engineering in the era of exascale performance

In this position paper, we discuss two relevant topics: (i) generic multiscale computing on emerging exascale high-performing computing environments, and (ii) the scaling of such applications towards the exascale. We will introduce the different phases when developing a multiscale model and simulating it on available computing infrastructure, and argue that we could rely on it both on the conceptual modelling level and also when actually executing the multiscale simulation, and maybe should further develop generic frameworks and software tools to facilitate multiscale computing. Next, we focus on simulating multiscale models on high-end computing resources in the face of emerging exascale performance levels. We will argue that although applications could scale to exascale performance relying on weak scaling and maybe even on strong scaling, there are also clear arguments that such scaling may no longer apply for many applications on these emerging exascale machines and that we need to resort to what we would call multi-scaling. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

Multi-scale high-performance computing in astrophysics: simulating clusters with stars, binaries and planets

The demand on simulation software in astrophysics has dramatically increased over the last decades. This increase is driven by improvements in observational data and computer hardware. At the same time, computers have become more complicated to program due to the introduction of more parallelism and hybrid hardware. To keep up with these developments, much of the software has to be redesigned. In order to prevent the future need to rewrite again when new developments present themselves, the main effort should go into making the software maintainable, flexible and scalable. In this paper, we explain our strategy for coupling elementary solvers and how to combine them into a high-performance multi-scale environment in which complex simulations can be performed. The elementary parts can remain succinct while supporting the aggregation to more satisfactory functionality by coupling them on a higher level. The advanced code-coupling strategies we present here allow such a hierarchy and support the development of complex codes. A library of simple elementary solvers subsequently stimulates the rapid development of more complex code that can co-evolve with the latest advances in computer hardware. We demonstrate how to combine several of these elementary solvers in a hierarchical and generic system, and how the resulting complex codes can be applied to multi-scale problems in astrophysics. Our aim is to achieve the best of several worlds with respect to performance, flexibility and maintainability while reducing development time. We succeeded in the development of the hierarchical coupling strategy and the general framework, but a comprehensive library of minimal fundamental-physics solvers is still unavailable. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

A generalised Landau-Lifshitz fluctuating hydrodynamics model for concurrent simulations of liquids at atomistic and continuum resolution

A new hybrid molecular dynamics-hydrodynamics method based on the analogy with two-phase flows is implemented that takes into account the feedback of molecular dynamics on hydrodynamics consistently. The consistency is achieved by deriving a discrete system of fluctuating hydrodynamic equations whose solution converges to the locally averaged molecular dynamics field exactly in terms of the locally averaged fields. The new equations can be viewed as a generalisation of the classical continuum Landau-Lifshitz fluctuating hydrodynamics model in statistical mechanics to include a smooth transition from large-scale continuum hydrodynamics that obeys a Gaussian statistics to all-atom molecular dynamics. Similar to the classical Landau-Lifshitz fluctuating hydrodynamics model, the suggested generalised Landau-Lifshitz fluctuating hydrodynamics equations are too complex for analytical solution; hence, a computational scheme for solving these equations is suggested. The scheme is implemented in a popular open-source molecular dynamics code GROMACS (GROningen MAchine for Chemical Simulations), and numerical examples are provided for liquid argon simulations under equilibrium conditions and under macroscopic flow effects.

Strategies for calibrating models of biology

Computational and mathematical modelling has become a valuable tool for investigating biological systems. Modelling enables prediction of how biological components interact to deliver system-level properties and extrapolation of biological system performance to contexts and experimental conditions where this is unknown. A model's value hinges on knowing that it faithfully represents the biology under the contexts of use, or clearly ascertaining otherwise and thus motivating further model refinement. These qualities are evaluated through calibration, typically formulated as identifying model parameter values that align model and biological behaviours as measured through a metric applied to both. Calibration is critical to modelling but is often underappreciated. A failure to appropriately calibrate risks unrepresentative models that generate erroneous insights. Here, we review a suite of strategies to more rigorously challenge a model's representation of a biological system. All are motivated by features of biological systems, and illustrative examples are drawn from the modelling literature. We examine the calibration of a model against distributions of biological behaviours or outcomes, not only average values. We argue for calibration even where model parameter values are experimentally ascertained. We explore how single metrics can be non-distinguishing for complex systems, with multiple-component dynamic and interaction configurations giving rise to the same metric output. Under these conditions, calibration is insufficiently constraining and the model non-identifiable: multiple solutions to the calibration problem exist. We draw an analogy to curve fitting and argue that calibrating a biological model against a single experiment or context is akin to curve fitting against a single data point. Though useful for communicating model results, we explore how metrics that quantify heavily emergent properties may not be suitable for use in calibration. Lastly, we consider the role of sensitivity and uncertainty analysis in calibration and the interpretation of model results. Our goal in this manuscript is to encourage a deeper consideration of calibration, and how to increase its capacity to either deliver faithful models or demonstrate them otherwise.

Mechanism of Exfoliation and Prediction of Materials Properties of Clay-Polymer Nanocomposites from Multiscale Modeling

We describe the mechanism that leads to full exfoliation and dispersion of organophilic clays when mixed with molten hydrophilic polymers. This process is of fundamental importance for the production of clay-polymer nanocomposites with enhanced materials properties. The chemically specific nature of our multiscale approach allows us to probe how chemistry, in combination with processing conditions, produces such materials properties at the mesoscale and beyond. In general agreement with experimental observations, we find that a higher grafting density of charged quaternary ammonium surfactant ions promotes exfoliation, by a mechanism whereby the clay sheets slide transversally over one another. We can determine the elastic properties of these nanocomposites; exfoliated and partially exfoliated morphologies lead to substantial enhancement of the Young's modulus, as found experimentally.

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

Chemically specific multiscale modeling of clay-polymer nanocomposites reveals intercalation dynamics, tactoid self-assembly and emergent materials properties

A quantitative description is presented of the dynamical process of polymer intercalation into clay tactoids and the ensuing aggregation of polymer-entangled tactoids into larger structures, obtaining various characteristics of these nanocomposites, including clay-layer spacings, out-of-plane clay-sheet bending energies, X-ray diffractograms, and materials properties. This model of clay-polymer interactions is based on a three-level approach, which uses quantum mechanical and atomistic descriptions to derive a coarse-grained yet chemically specific representation that can resolve processes on hitherto inaccessible length and time scales. The approach is applied to study collections of clay mineral tactoids interacting with two synthetic polymers, poly(ethylene glycol) and poly(vinyl alcohol). The controlled behavior of layered materials in a polymer matrix is centrally important for many engineering and manufacturing applications. This approach opens up a route to computing the properties of complex soft materials based on knowledge of their chemical composition, molecular structure, and processing conditions.