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Macroscopic differential equations that accurately account for microscopic phenomena can be systematically generated using rigorous upscaling methods. However, such methods are time-consuming, prone to error, and become quickly intractable for complex systems with tens or hundreds of equations. To ease these complications, we propose a method of automatic upscaling through symbolic computation. By streamlining the upscaling procedure and derivation of applicability conditions to just a few minutes, the potential for democratization and broad utilization of upscaling methods in real-world applications emerges. We demonstrate the ability of our software prototype, Symbolica, by reproducing homogenized advective–diffusive–reactive (ADR) systems from earlier studies and homogenizing a large ADR system deemed impractical for manual homogenization. Novel upscaling scenarios previously restricted by unnecessarily conservative assumptions are discovered, and numerical validation of the models derived by Symbolica is provided.

There are multiscale coupling relationships during the operation of dc/dc converters, where the macroscale is the overall working principle of the circuit and the microscale is the device mechanism model of the circuit components. Modeling only at the macroscale cannot reflect the effect of the device’s internal effects on the circuit, while modeling the device at the microscale cannot show the operating characteristics of the circuit. To obtain the analytical solutions of the state variables for dc/dc converters at circuit- and device-level scales, a method for establishing a multiscale model of a dc/dc converter is proposed. Firstly, the device mechanism at the microscale is appropriately combined with the circuit model at the macroscale. Secondly, the traditional piecewise switching function that represents the switching state is replaced by a continuous switching fitting function. Thereby, a continuous multiscale unified model of the dc/dc converter is reached. Afterward, by adopting the improved equivalent small parameter (ESP) method proposed in this article, the steady-state analytical solutions of the model in the open- and closed-loop states can be obtained, respectively. Finally, the steady-state analytical solutions are compared with the results of simulation and experiment.

A subgridding unconditionally stable finite-element time-domain method based on local eigenvalue solution (SUSL-FETD) is proposed to solve multiscale modeling. In this method, subgridding elements are used to discrete a multiscale computational domain, and the explicit central-difference method is applied for temporal discretization. Compared with traditional elements, the subgridding elements have a more complex distribution of edges and nodes. Therefore, an efficient subgridding scheme is given to form the element matrix for each subgridding element. Such system matrices assembled by all element matrices are symmetric. The subgridding FETD (S-FETD) is then further developed into the subgridding unconditionally stable FETD (SUS-FETD) by filtering spatial unstable modes. It is time-consuming to obtain the unstable modes by global eigenvalue decomposition. In this article, the local eigenvalue decomposition is proposed to get the unstable modes, which further reduces the memory storage and computing time. Numerical examples certify that the proposed SUSL-FETD has high accuracy and efficiency.

In this article, a novel multiscale modeling method is proposed for transient computational fluid dynamics (CFD) simulations of the human airways. The developed method is the first attempt to incorporate spatial coupling and temporal coupling into transient human airway simulations, aiming to improve the flexibility and the efficiency of these simulations. In this method, domain decomposition was used to separate the complex airway model into different scaled domains. Each scaled domain could adopt a suitable mesh and timestep, as necessary: the coarse mesh and large timestep were employed in the macro regions to reduce the computational cost, while the fine mesh and small timestep were used in micro regions to maintain the simulation accuracy. The radial point interpolation method was used to couple data between the coarse mesh and the fine mesh. The continuous micro solution–intermittent temporal coupling method was applied to bridge different timesteps. The developed method was benchmarked using a well-studied four-generation symmetric airway model under realistic normal breath conditions. The accuracy and efficiency of the method were verified separately in the inhalation phase and the exhalation phase. Similar airflow behavior to previous studies was observed from the multiscale airway model. The developed multiscale method has the potential to improve the flexibility and efficiency of transient human airway simulations without sacrificing accuracy.

A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be effectively treated by a conventional method, such as woven fabrics. The framework is a generalization of the "finite element squared" (or FE2) method in which a localized portion of the periodic subscale structure is modeled using finite elements. The numerical solution of displacement driven problems involving this model can be adapted to the context of membranes by a variant of the Klinkel-Govindjee method[1] originally proposed for using finite strain, three-dimensional material models in beam and shell elements. This approach relies on numerical enforcement of the plane stress constraint and is enabled by the principle of frame invariance. Computational tractability is achieved by introducing a regression-based surrogate model informed by a physics-inspired training regimen in which FE$^2$ is utilized to simulate a variety of numerical experiments including uniaxial, biaxial and shear straining of a material coupon. Several alternative surrogate models are evaluated including an artificial neural network. The framework is demonstrated and validated for a realistic Mars landing application involving supersonic inflation of a parachute canopy made of woven fabric., Comment: 29 pages, 12 figures

The generation of large amounts of omics data is increasingly enabling not only the processing and analysis of large data sets but also the development of computational models in the field of stem cell research. Although computational models have been proposed in recent decades, we believe that the stem cell community is not fully aware of the potentiality of computational modeling in guiding their experimental research. In this regard, we discuss how single-cell technologies provide the right framework for computational modeling at different scales of biological organization in order to address challenges in the stem cell field and to guide experimentalists in the design of new strategies for stem cell therapies and treatment of congenital disorders.

Guidance is an efficient crowd management measure used to save lives in emergencies because it can reduce the disorientation of pedestrians. This study investigates an optimal guidance strategy for large-scale crowd evacuations. To increase computational efficiency, a pedestrian cell transmission model is extended to create a rapid simulation of guided crowd dynamics. To solve the conflicts between the limited guidance capacity and the desire to improve evacuation efficiency, a strategic guidance model is proposed, which generates a leader location and exit selection plan. A simulation algorithm is proposed to integrate a pedestrian following model and strategic guidance model based on the follower-leader interaction. Finally, a hybrid multiscale approach for modeling guided crowd evacuations is established to evaluate the performance of the guidance strategy. The experimental results show that the required CPU time of the proposed model is much less than that of the microscopic models. Because the number of leaders is minimized and the exit is selected by taking both risk and congestion into account, the obtained guidance strategy can realize the full use of guidance capacity, information confusion reduction and uniform exit usage, all of which contribute to a reduction in evacuation time.

Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.

Adsorption of CO2 with porous solid materials is gaining attention as a promising CO2 capture technology due to the potential improvement in energy efficiency and cost reductions. This study investigates for the first time the potential performance of the MOFs Cu-BTC, Mg-MOF-74, and UTSA-16 for CO2 capture at a commercial large-scale using multiscale modeling; in addition, a selected activated carbon was included for comparative purposes, and zeolite 13X was used as the benchmark. We have developed a multiscale model that integrates molecular simulation results with a process model of a pressure/vacuum swing adsorption (P/VSA) process. The model was first validated at the pilot scale and then used to assess the performance of the above-mentioned adsorbents and processes attached to a 550 MW coal plant, in order to achieve the 90% recovery and 95% purity targets of the US Department of Energy. The optimal design, scheduling and operating conditions of these adsorbents were obtained while minimizing total cost and improving the non-monetized key performance indicators (KPIs) such as productivity, selectivity, working capacity, energy consumption and the modified adsorption figure of merit (AFM) obtained in global sensitivity analyses. A key finding from this study is that the recently proposed UTSA-16 MOF can be as good as the traditional zeolite 13X for industrial-scale post-combustion capture and compression, at a cost of

Computational methodologies have been critical to our understanding of defects at nanometer scales. These methodologies have been dominated by two classes: quantum mechanics (QM)-based methods and semiempirical/classical methods. The former, while accurate and versatile, are time consuming, while the latter are efficient but limited in versatility and transferability. Recently, machine learning (ML) methods have shown initial promise in bridging these two limitations due to their accuracy and flexibility. In this work, the true capability of ML methods is explored by simulating defects in platinum over several length/time scales. We compare our results with density functional theory (DFT) for atomic-level defect behavior and with experiments for nanolevel behavior. We also compare our predictions with several classical potentials. This work aims to showcase the length/time scales attainable using ML, as well as the complexity they are capable of capturing, demonstrating that these methodologies may be effectively used, in the future, to bridge experiments and QM methods.

This article establishes a multiscale modeling framework for the parametrically homogenized crystal plasticity model (PHCPM) for single crystal Ni-based superalloys. The PHCPMs explicitly incorporate morphological statistics of the $$\gamma -\gamma '$$ intragranular microstructure in their crystal plasticity constitutive coefficients. They enable highly efficient and accurate calculations for image-based polycrystalline microstructural simulations. The single crystal PHCPM development process involves: (1) construction of statistically equivalent RVEs or SERVEs, (2) image-based modeling with a dislocation-density crystal plasticity model, (3) identification of representative aggregated microstructural parameters, (4) selection of a PHCPM framework and (5) self-consistent homogenization. Novel machine learning tools are explored at every development phase. Supervised and unsupervised learning methods, such as support vector regression, artificial neural networks, k-means, and symbolic regression, enhanced optimization, model emulation and sensitivity analysis methods are all critical components of the multiscale modeling pipeline. The integration of machine learning tools with physics-based models enables the creation of powerful single crystal constitutive models for polycrystalline simulations.

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, [Formula: see text] , and large-scale fluctuations, [Formula: see text] , of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

Immunotherapy has shown great potential in the treatment of cancer; however, only a fraction of patients respond to treatment, and many experience autoimmune‐related side effects. The pharmaceutical industry has relied on mathematical models to study the behavior of candidate drugs and more recently, complex, whole‐body, quantitative systems pharmacology (QSP) models have become increasingly popular for discovery and development. QSP modeling has the potential to discover novel predictive biomarkers as well as test the efficacy of treatment plans and combination therapies through virtual clinical trials. In this work, we present a QSP modeling platform for immuno‐oncology (IO) that incorporates detailed mechanisms for important immune interactions. This modular platform allows for the construction of QSP models of IO with varying degrees of complexity based on the research questions. Finally, we demonstrate the use of the platform through two example applications of immune checkpoint therapy.

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

Mathematical homogenization theory as a multiscale modeling strategy for deriving macroscopic models is gaining relevance in modeling electrochemical energy storage systems (ESSs) for its ability to capture the detailed microstructural properties of a material. Stochastic modeling, on the other hand, captures molecular fluctuations and uncertainties associated with ESSs. In this short review, modeling ESSs using both tools is presented. Integrating mathematical homogenization theory and stochastic modeling provides an effective tool for deriving macroscopic models that accurately predict various macroscopic behavior and electrochemical properties of ESSs to enable optimization and manufacturing of high performance ESSs.

Precision medicine (PM) refers to the use of available genomic information from an individual patient to select the most appropriate therapy for a disease. In this paper, we have developed a mechan...

Drug research, therapy development, and other areas of pharmacology and medicine can benefit from simula- tions and optimization of mathematical models that contain a mathematical description of interactions between systems elements at the cellular, tissue, organ, body, and population level. This approach is the foundation of systems medicine and precision medicine. Here, simulated experiments are performed with computers (in silico) first, and they are then replicated through lab experiments (in vivo or in vitro) or clinical studies. In turn, these experiments and studies can be used to validate or improve the models. This iterative loop of dry and wet lab work is successful when biomedical researchers tightly collaborate with data scientists and modelers. From an educational point of view, the interdisciplinary research in systems biology can be sustained most ef- fectively when specialists have been trained to have both a strong background in the disciplines of biology or modeling and strong communication skills, which make them able to communicate with other specialists. This overview addresses possible interdisciplinary communication gaps. Focusing our attention on biomedical re- searchers, we describe the reasons for using modeling and ways to collaborate with modelers, including their needs for specific biological expertise and data. This review includes an introduction to the principles of several widely used mechanistic modeling methods, focusing on their areas of applicability as well as their limitations. A potential complementary role of machine-learning methods in the development of mechanistic models is also discussed. The descriptions of the methods also include links to corresponding modeling software tools as well as practical examples of their application. Finally, we also explicitly address different aspects of multiscale mod- eling approaches that allow a more complete and holistic perspective of the human body.

Significance Here we present an unprecedented multiscale simulation platform that enables modeling, hypothesis generation, and discovery across biologically relevant length and time scales to predict mechanisms that can be tested experimentally. We demonstrate that our predictive simulation-experimental validation loop generates accurate insights into RAS-membrane biology. Evaluating over 100,000 correlated simulations, we show that RAS–lipid interactions are dynamic and evolving, resulting in: 1) a reordering and selection of lipid domains in realistic eight-lipid bilayers, 2) clustering of RAS into multimers correlating with specific lipid fingerprints, 3) changes in the orientation of the RAS G-domain impacting its ability to interact with effectors, and 4) demonstration that RAS–RAS G-domain interfaces are nonspecific in these putative signaling domains., RAS is a signaling protein associated with the cell membrane that is mutated in up to 30% of human cancers. RAS signaling has been proposed to be regulated by dynamic heterogeneity of the cell membrane. Investigating such a mechanism requires near-atomistic detail at macroscopic temporal and spatial scales, which is not possible with conventional computational or experimental techniques. We demonstrate here a multiscale simulation infrastructure that uses machine learning to create a scale-bridging ensemble of over 100,000 simulations of active wild-type KRAS on a complex, asymmetric membrane. Initialized and validated with experimental data (including a new structure of active wild-type KRAS), these simulations represent a substantial advance in the ability to characterize RAS-membrane biology. We report distinctive patterns of local lipid composition that correlate with interfacially promiscuous RAS multimerization. These lipid fingerprints are coupled to RAS dynamics, predicted to influence effector binding, and therefore may be a mechanism for regulating cell signaling cascades.

In this chapter we start with a discussion of a fundamental assumption on the nature of matter, namely the idea of particles as basic constituents and the consequences thereof. In Sects. 2.1–2.3 we focus on clarifying some terminology in computational multiscale modeling and learn about the concepts of “models” in science. Section 2.4 focuses on hierarchical modeling concepts in classical and quantum physics which is followed by discussing the standard model of elementary particle physics and the attempts of reducing all understanding of material behavior to the interactions of some basic constituents (particles). In Sect. 2.6 we introduce the basics of computer science such as recursive programming, the concepts of formal (computer) languages, finite automata, complexity theory and the Turing machine. The chapter ends with some reading suggestions and several problems as an offer for the ambitious reader.

Viscoelastic (VE) dampers are one of the most promising techniques for reducing vibration in engineering structures caused by earthquakes and wind. This work aims to develop a kind of high-...

Neuroscience incorporates knowledge from a range of scales, from molecular dynamics to neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB®scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.Information Sharing StatementBoth the source code and documentation of the Subcellular Workflow are available athttps://github.com/jpgsantos/Subcellular_Workflowand licensed under GNU General Public License v3.0. The model is stored in the SBtab format (Lubitz et al. 2016). Model reduction, parameter estimation and global sensitivity analysis tools are written in MATLAB®(RRID:SCR_001622) and require the SimBiology®toolbox. Conversion script to VFGEN (Weckesser 2008), MOD and SBML (RRID:SCR_007422) is written in R (RRID:SCR_001905). Conversion to SBML requires the use of libSBML (RRID:SCR_014134). Validations are run in COPASI (RRID:SCR_014260; Hoops et al. 2006), NEURON (RRID:SCR_005393; Hines and Carnevale 1997) and with the subcellular simulation setup application (RRID:SCR_018790; available athttps://subcellular.humanbrainproject.eu/model/simulations) that uses a spatial solver provided by STEPS (RRID:SCR_008742; Hepburn et al. 2012) and network-free solver NFsim (available athttp://michaelsneddon.net/nfsim/). The medium spiny neuron model (Lindroos et al. 2018) used in NEURON simulations is available in ModelDB database (RRID:SCR_007271) with access code 237653. The FindSim use case model is available inhttps://github.com/BhallaLab/FindSim(Viswan et al. 2018).

In the modern world, knowledge and advanced technologies determine the effectiveness of the economy, and they can radically improve the quality of life of people, modernize infrastructure and public administration, and ensure law and order, as well as security. The creation of a research infrastructure based on a high-performance hybrid cluster, allows detailed calculations of complex phenomena and processes without full-scale experiments. It has become possible to apply modern methods of multiscale computer modeling most efficiently by developing prototypes of the new materials with the desired properties for their further synthesis. Such approaches can significantly reduce the cost and speed up the development of modern technologies for producing new semiconductor materials for nanoelectronics, composite materials for the aerospace industry, and others. Thus, the use of multiscale modeling methods in combination with the use of high-performance software tools have made it possible to create a computer model of a nanoscale heterostructure, to develop the means for predictive computer modeling of the physical structure of nanoelectronic devices and the neuromorphic architecture of multilevel memory devices, as well as studying the processes of defect formation in composite materials.

In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas from the different research fronts. We illustrate how homogenization may help characterizing the nature and the form of nonlocal interactions hypothesized in nonlocal models. We also offer some perspective on how studies of nonlocality may help the development of more effective numerical methods for homogenization.

A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to illustrate the main steps and issues involved. To this end, a set of generalized moments are constructed first to optimally represent the underlying velocity distribution. The well-known closure problem is then solved with the aim of best capturing the associated dynamics of the kinetic equation. The issue of physical constraints such as Galilean invariance is addressed and an active learning procedure is introduced to help ensure that the dataset used is representative enough. The reduced system takes the form of a conventional moment system and works regardless of the numerical discretization used. Numerical results are presented for the BGK (Bhatnagar--Gross--Krook) model and binary collision of Maxwell molecules. We demonstrate that the reduced model achieves a uniform accuracy in a wide range of Knudsen numbers spanning from the hydrodynamic limit to free molecular flow., Comment: Proceedings of the National Academy of Sciences (2019)

In the community of computational materials science, one of the challenges in hierarchical multiscale modeling is information-passing from one scale to another, especially from the molecular model to the continuum model. A machine-learning-enhanced approach, proposed in this paper, provides an alternative solution. In the developed hierarchical multiscale method, molecular dynamics simulations in the molecular model are conducted first to generate a dataset, which represents physical phenomena at the nanoscale. The dataset is then used to train a material failure/defect classification model and stress regression models. Finally, the well-trained models are implemented in the continuum model to study the mechanical behaviors of materials at the macroscale. Multiscale modeling and simulation of a molecule chain and an aluminum crystalline solid are presented as the applications of the proposed method. In addition to support vector machines, extreme learning machines with single-layer neural networks are employed due to their computational efficiency.

As a computationally attractive alternative for global large eddy simulations (LESs), we investigate the possibility of using comprehensive three‐dimensional LESs as a superparameterization that can replace all traditional parameterizations of atmospheric processes that are currently used in global models. We present the technical design for a replacement of the parameterization for clouds, convection, and turbulence of the global atmospheric model of the European Centre for Medium‐Range Weather Forecasts by the Dutch Atmospheric Large Eddy Simulation model. The model coupling consists of bidirectional data exchange between the global model and the high‐resolution LES models embedded within the columns of the global model. Our setup allows for selective superparameterization, that is, for applying superparameterization in local regions selected by the user, while keeping the standard parameterization of the global model intact outside this region. Computationally, this setup can result in major geographic load imbalance, because of the large difference in computational load between superparameterized and nonsuperparameterized model columns. To resolve this issue, we use a modular design where the local and global models are kept as distinct model codes and organize the model coupling such that all the local models run in parallel, separate from the global model. First simulation results, employing this design, demonstrate the potential of our approach.

Across spatial scales, biological systems exhibit exquisite hierarchy in architecture and function, leading to complex, observable phenomena. In the articular cartilage of our joints, the organization of molecule- to tissue-level structures governs the interplay of macromolecules and determines the biological activity of embedded cells (chondrocytes), motivating the development of new computational models to provide insight and understanding. We review recent work on multiscale modeling of cartilage, with an emphasis on finite element based methods, and emerging experimental approaches that enable calibration and validation. Through new nested modeling approaches, we are now able to dissect interactions of constituent macromolecules, and we envision the ability to soon define the mechanical microenvironment experienced by and within single cells that guide biological activity.

Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation period of the fastest atomic motion, rendering long-time simulations very expensive. To resolve this bottleneck, we propose a supervised parallel-in-time algorithm for stochastic dynamics (SPASD) to accelerate long-time Lagrangian particle simulations. Our method is inspired by bottom-up coarse-graining projections that yield mean-field hydrodynamic behavior in the continuum limit. Here as an example, we use the dissipative particle dynamics (DPD) as the Lagrangian particle simulator that is supervised by its macroscopic counterpart, i.e., the Navier-Stokes simulator. The low-dimensional macroscopic system (here, the Navier-Stokes solver) serves as a predictor to supervise the high-dimensional Lagrangian simulator, in a predictor-corrector type algorithm. The results of the Lagrangian simulation then correct the mean-field prediction and provide the proper microscopic details (e.g., consistent fluctuations, correlations, etc.). The unique feature that sets SPASD apart from other multiscale methods is the use of a low-fidelity macroscopic model as a predictor. The macro-model can be approximate and even inconsistent with the microscale description, but SPASD anticipates the deviation and corrects it internally to recover the true dynamics., Comment: 17 pages, 19 figures

Free-radical emulsion polymerization is a heterogeneous process where simultaneous and competitive physicochemical events occur over a wide range of time/length scales. Although a highly accurate representation of the process is possible by multiscale modeling, common approaches face several issues, including the stochastic nature of finer scales, the timely exchange of information between scales, and the high computational load for the model solution. In this work, a reduced-order computationally-tractable multiscale model is proposed while preserving a good predictive capability. The model integrates microscopic-scale calculations based on kinetic Monte Carlo simulations (stochastic), a mesoscopic-scale representation of the particle size distribution through a novel statistical approach and a deterministic description of the macroscopic-scale. The proposed model resulted in faster satisfactory predictions (compared to the model based on the Fokker Planck Equation) of traditional macro and mesoscopic variables, along with the average number of free radicals and secondary nucleation on a microscopic scale.

Declarative modeling uses symbolic expressions to represent models. With such expressions, one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. The potential advantages are particularly relevant in the case of developmental modeling, wherein complex spatial structures exhibit dynamics at molecular, cellular, and organogenic levels to relate genotype to multicellular phenotype. Multiscale modeling can benefit from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects; we define semantics-preserving implementation and semantics-approximating model reduction transformations; and we outline a “meta-hierarchy” for organizing declarative models and the mathematical methods that can fruitfully manipulate them. Electronic supplementary material The online version of this article (10.1007/s11538-019-00628-7) contains supplementary material, which is available to authorized users.

In this article, a computationally efficient multi-split MsXFEM is proposed to evaluate the elastic properties of heterogeneous materials. The multi-split MsXFEM is the combination of multi-split XFEM with multiscale finite element methods (MsFEM). The multi-split XFEM is capable to model multiple discontinuities in a single element which leads to reduction in the number of mesh elements, whereas MsFEM helps in reducing the computational time. Strain energy based homogenization has been implemented on an RVE (having volume fraction of heterogeneities up to 50%) for evaluating the elastic properties. From macro-element size analysis, we estimate that the RVE edge length must be 5 times the edge length of the macro-element. The directional analysis has been performed to verify the isotropic behavior of the material, whereas contrast analysis has been done to check the numerical accuracy of the proposed scheme. A level set correction (LSC) based on higher order shape functions has been proposed to reduce mapping errors of level set values. It is also observed that multi-split MsXFEM is about 16 times computationally more efficient than MsXFEM for 50% volume of heterogeneities.

Understanding protein interactions with inorganic nanoparticle is central to the rational design of new tools in biomaterial sciences, nanobiotechnology, and nanomedicine. Theoretical modeling and simulations provide complementary approaches for experimental studies and are applied for exploring protein–particle surface-binding mechanisms, the determinants of binding specificity toward different surfaces, and the thermodynamics and kinetics of adsorption. The use of multiscale approaches is inevitable because the adsorption events extend over a wide range of time and length scales, which require the system to be addressed at different resolution levels. Here, we review the latest advances in coarse-grained treatment of these systems, usually addressed using residue-level resolution for proteins and mesoscale for the nanoparticle. We illustrate the parameterization strategies, focusing on those combining experimental and atomistic simulation data, within the theoretical framework of multiscale approaches.

Inspired by the complex diversity of collagenous materials in mammalian tissue, collagen-based biomaterials are increasingly utilized for developing drug delivery vehicles and regenerative tissue engineering. Collagen’s broad utility poses important engineering challenges for the rational and predictive design of the resultant biomaterial’s physical and chemical properties. We review the most recent developments in multiscale computational modeling of collagen-based biomaterials to determine their structural, mechanical, and physicochemical properties. Through the materials-by-design paradigm, these developments may eventually lead to rational algorithmic recipes for bottom–up multiscale design of these biomaterials, thereby minimizing the experimental costs of iterative material synthesis and testing. We also highlight the future perspectives and opportunities for expanding multiscale modeling capabilities to incorporate physicochemical and biological functions of collagen-based biomaterials.

Accurate and efficient modeling of microstructural interaction and evolution for prediction of the macroscopic behavior of materials is important for material design and manufacturing process control . This paper approaches this challenge with a reduced-order method called self-consistent clustering analysis (SCA). It is reformulated for general elasto-viscoplastic materials under large deformation . The accuracy and efficiency for predicting overall mechanical response of polycrystalline materials is demonstrated with a comparison to traditional full-field solution methods such as finite element analysis and the fast Fourier transform . It is shown that the reduced-order method enables fast prediction of microstructure–property relationships with quantified variation. The utility of the method is demonstrated by conducting a concurrent multiscale simulation of a large-deformation manufacturing process with sub-grain spatial resolution while maintaining reasonable computational expense. This method could be used for microstructure-sensitive properties design as well as process parameters optimization.

The thrust of this paper is that micromechanics goes beyond homogenization when it is regarded as a multiscale modeling approach. Using metal plasticity as an example, the paper illustrates how macroscopic irreversibility is a natural consequence of emergent behaviour in space and in time. Special attention is given to the currently weak link between discrete dislocation plasticity and continuum crystal plasticity, and how dislocation interactions give rise to powerlaw viscoplasticity. As an outlook it is suggested that, by enlarging its missionto coarse graining in space and time, micromechanics can play an importantrole in the understanding and description of new supramolecular materials.

In recent years, uncertainty appears in different aspects of physical simulations including probabilistic boundary, stochastic loading, and multiscale modeling. Stretching across engineering domains and applied mathematics, uncertainty quantification is a multi-disciplinary field which is an inseparable part of risk analysis. However, many real-world problems deal with large number of simulations or experiments. Considering the limited budget and time to perform all these efforts (specially for practitioners), an essential task is to reduce the computational cost in an uncertain environment. This paper proposes to use a matrix completion technique for reducing the overall computational cost of engineering systems when they are subjected to the simultaneous effects of aleatory and epistemic uncertainties with high dimensions. The proposed method is further improved using hidden information in the uncertain variables based on clustering techniques. Several parametric and Monte Carlo simulations were performed to demonstrate the accuracy of our method with different compression ratios. Experimental results show a decent overall performance of our technique for high-dimensional hybrid uncertain systems.

Modern materials design requires reliable and consistent structure–property relationships. The paper addresses the need through transfer learning of deep material network (DMN). In the proposed learning strategy, we store the knowledge of a pre-trained network and reuse it to generate the initial structure for a new material via a naive approach. Significant improvements in the training accuracy and learning convergence are attained. Since all the databases share the same base network structure, their fitting parameters can be interpolated to seamlessly create intermediate databases. The new transferred models are shown to outperform the analytical micromechanics methods in predicting the volume fraction effects. We then apply the unified DMN databases to the design of failure properties, where the failure criteria are defined upon the distribution of microscale plastic strains. The Pareto frontier of toughness and ultimate tensile strength is extracted from a large-scale design space enabled by the efficiency of DMN extrapolation.

A methodology to model and generate spatially dependent material uncertainties in stochastic multiscale analysis is proposed. The approach consists in defining non-Gaussian random fields through transport maps acting on Gaussian fields, defined by appropriately filtering a Gaussian white noise. In contrast to standard covariance-based representations, the proposed strategy can efficiently accommodate the case of fields with anisotropic correlation structures on nonconvex domains. This case is especially relevant to computational homogenization involving random microstructures with connected phases. The theoretical stochastic framework is first laid down. A numerical application associated with a polydisperse random microstructure is then presented to illustrate various aspects of the method.

The multi-field two-fluid modeling concept has been successfully used in the past to perform Computational Multiphase Fluid Dynamics (CMFD) simulations of forced-convection boiling. Since such simulations are normally performed at the RANS-level, they do not allow for resolving local phenomena at the bubble-scale level. Instead, closure laws making use of empirical correlations deduced from selected experimental data are adopted. As different data sets of reference frequently correspond to different, and not always overlapping, experimental conditions, their application introduces considerable uncertainties into the predictions of the overall CMFD models. It has been shown before (Podowski et al., 1997) that one way to improve the accuracy of computational models is to apply a multiscale modeling approach, in which single-bubble-nucleation-level models, validated against separate-effect experiments, are used to formulate mechanistic RANS-level closure laws. This paper presents a mathematically rigorous and physically consistent model of the bubble ebullition cycle, which takes into account the coupling of transient heat transfer between solid walls and the surrounding coolant during wall quenching period. The proposed modeling approach covers a large spectrum of the geometries pertaining to both experimental boiling test sections and nuclear reactor fuel assemblies. The new model has been parametrically tested and validated against experimental data. A good agreement between the model predictions and experimental data has been obtained. The overall objective of the current work is to establish a first-principle theoretical framework for the formulation of mechanistic ensemble-averaged closure laws compatible with existing CMFD solvers.

In the design and development of novel materials that have excellent mechanical properties, classification and regression methods have been diversely used across mechanical deformation simulations or experiments. The use of materials informatics methods on large data that originate in experiments or/and multiscale modeling simulations may accelerate materials discovery or develop new understanding of materials’ behavior. In this fast-growing field, we focus on reviewing advances at the intersection of data science with mechanical deformation simulations and experiments, with a particular focus on studies of metals and alloys. We discuss examples of applications, as well as identify challenges and prospects.

Comprehensive modeling of a whole cell requires an integration of vast amounts of information on various aspects of the cell and its parts. To divide and conquer this task, we introduce Bayesian metamodeling, a general approach to modeling complex systems by integrating a collection of heterogeneous input models. Each input model can in principle be based on any type of data and can describe a different aspect of the modeled system using any mathematical representation, scale, and level of granularity. These input models are 1) converted to a standardized statistical representation relying on probabilistic graphical models, 2) coupled by modeling their mutual relations with the physical world, and 3) finally harmonized with respect to each other. To illustrate Bayesian metamodeling, we provide a proof-of-principle metamodel of glucose-stimulated insulin secretion by human pancreatic β-cells. The input models include a coarse-grained spatiotemporal simulation of insulin vesicle trafficking, docking, and exocytosis; a molecular network model of glucose-stimulated insulin secretion signaling; a network model of insulin metabolism; a structural model of glucagon-like peptide-1 receptor activation; a linear model of a pancreatic cell population; and ordinary differential equations for systemic postprandial insulin response. Metamodeling benefits from decentralized computing, while often producing a more accurate, precise, and complete model that contextualizes input models as well as resolves conflicting information. We anticipate Bayesian metamodeling will facilitate collaborative science by providing a framework for sharing expertise, resources, data, and models, as exemplified by the Pancreatic β-Cell Consortium.

Computational modeling methods combined with non-invasive imaging technologies have exhibited great potential and unique opportunities to model new bone formation in scaffold tissue engineering, offering an effective alternate and viable complement to laborious and time-consuming in vivo studies. However, existing numerical approaches are still highly demanding computationally in such multiscale problems. To tackle this challenge, we propose a machine learning (ML)-based approach to predict bone ingrowth outcomes in bulk tissue scaffolds. The proposed in silico procedure is developed by correlating with a dedicated longitudinal (12-month) animal study on scaffold treatment of a major segmental defect in sheep tibia. Comparison of the ML-based time-dependent prediction of bone ingrowth with the conventional multilevel finite element (FE2) model demonstrates satisfactory accuracy and efficiency. The ML-based modeling approach provides an effective means for predicting in vivo bone tissue regeneration in a subject-specific scaffolding system. The study develops a machine learning approach for predicting bone regeneration in an additively manufactured bioceramic scaffold, which is correlated with an in vivo sheep model, exhibiting effectiveness for solving such a multiscale modeling problem.

Multiscale Modeling of Electrochemical Reactions and Processes is a practical guide to multiscale computational methodologies. It offers a holistic understanding of the impact of reaction conditions on the overall performance of electrolyzers, fuel cells, and energy storage devices. This book covers reaction conditions such as electrolyte and applied bias potential and support type, as well as how these factors determine the overall performance of devices. These topics, for the first time, are covered in one book. This book presents:A comprehensive examination of the experiment-theory gap of electrochemical reactionsState-of-the-art multiscale methods for modeling the influence of reaction environment, including electrolyte, bias potential, and support type, on the energy conversion efficiency in electrochemical cells.A discussion of how to apply these multiscale modeling techniques to various applications in clean energy technology Multiscale Modeling of Electrochemical Reactions and Processes serves as a valuable resource for scientists, engineers, and students interested in electrochemistry, multiscale modeling, and clean energy applications. It is also a resource for the increasing number of available courses on materials modeling.

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response at the macroscopic level. Such techniques allow the use of fully detailed models to be avoided, thus resulting in a notable decrease in the overall computational cost at fixed numerical accuracy compared to the so-called direct numerical simulations. In the present work, two different multiscale modeling approaches are presented for the analysis of microstructural instability-induced failure in locally periodic fiber-reinforced composite materials subjected to general loading conditions involving large deformations. The first approach, which is of a semi-concurrent kind, consists in the “on-the-fly” derivation of the macroscopic constitutive response of the composite structure together with its microscopic stability properties through a two-way computational homogenization scheme. The latter one is a novel hybrid hierarchical/concurrent multiscale approach relying on a two-level domain decomposition scheme used in conjunction with a nonlinear homogenization scheme performed at the preprocessing stage. Both multiscale approaches have been suitably validated through comparisons with reference direct numerical simulations, by which the ability of the latter approach in capturing boundary layer effects has been demonstrated.