Table of Contents
Overview
Definition and Importance
Multiscale modeling is defined as a modeling approach that employs multiple models operating at different scales to describe a system, with each model focusing on varying levels of resolution. This methodology often integrates models derived from distinct physical laws, such as continuum mechanics and molecular dynamics, leading to what is referred to as multi-physics modeling.[1.1] The significance of multiscale modeling is particularly evident in the field of materials science, where it addresses a wide array of length and time scales relevant to material behavior, thereby highlighting the necessity of connecting these scales to effectively tackle multiscale problems.[3.1] The development of multiscale modeling has been significantly influenced by advancements in parallel computing, which facilitated the creation of concurrent multiscale models. A notable example is the integration of molecular dynamics codes into finite element codes, pioneered by Michael Ortiz and his collaborators.[2.1] Furthermore, the recognition of multiscale modeling's importance is underscored by the awarding of the Nobel Prize in Chemistry in 2013 to Martin Karplus, Michael Levitt, and Arieh Warshel for their contributions to multiscale modeling methods that combine classical and quantum mechanical theories to analyze complex chemical systems.[2.1] In the physical sciences, multiscale modeling serves as a crucial tool for solving problems that span multiple spatial and temporal scales. It is particularly valuable in biological contexts, where it helps to connect various biological processes across different scales, thereby enabling the prediction of spatial-dependent pharmacokinetics in complex systems such as solid tumors.[4.1] The challenge of linking microscale understanding to macroscale functional behavior is a defining aspect of mesoscale science, emphasizing the need for careful calibration and consideration of intermediate scales to avoid errors in modeling.[37.1] Thus, multiscale modeling not only enhances our understanding of complex systems but also plays a vital role in the accurate prediction and manipulation of material and biological behaviors across different scales.[38.1]Applications in Various Fields
Multiscale modeling has found significant applications across various fields, particularly in addressing complex challenges such as climate change, urban design, and healthcare technologies. In the realm of agriculture, an advanced multiscale crop modeling framework is being developed to facilitate a gene-to-farm design of resilient and sustainable crop production systems, which is crucial for adapting to changing climate conditions at regional and global scales.[9.1] In urban studies, multiscale climate models are employed to analyze the intricate physical processes that shape urban climates. These models help quantify the impacts of climate change and urbanization on local climates, thereby providing essential insights for urban planning and environmental management.[10.1] Furthermore, the integration of multiscale modeling with artificial intelligence (AI) is enhancing climate models and projections, enabling more effective strategies for climate change mitigation and adaptation.[11.1] The healthcare sector also benefits from multiscale modeling, particularly in advancing AI applications and improving healthcare technologies. Research in multiscale brain modeling demonstrates the potential for interdisciplinary collaboration to address public health challenges.[13.1] Moreover, the integration of multiscale modeling techniques in engineering design is transforming sustainable practices. By connecting models from process to planet, these frameworks facilitate sustainable engineering applications that consider various scales, from micro to macro.[18.1] This integration is vital for optimizing energy generation, water regeneration, and waste processing in building designs, thereby promoting robust sustainability and climate action.[21.1]History
Key Milestones in Multiscale Modeling
The development of multiscale modeling (MSM) has been marked by several key milestones that have significantly influenced the field of materials science and engineering. One of the earliest breakthroughs occurred in 1998 when researchers linked quantum and classical molecular methods with continuum methods to study crack propagation in silicon. This innovative approach utilized tight-binding molecular dynamics (MD) near the crack tip while employing classical MD further away, thereby effectively integrating different scales of modeling to address complex material behaviors.[56.1] The historical evolution of multiscale modeling has also been shaped by the contributions of notable figures in the field. For instance, the first concurrent multiscale model was developed by Michael Ortiz at Caltech, who embedded the molecular dynamics code Dynamo into a finite element code. This integration marked a significant advancement in the application of multiscale modeling techniques.[43.1] Furthermore, the Nobel Prize in Chemistry awarded in 2013 to Martin Karplus, Michael Levitt, and Arieh Warshel recognized their development of a multiscale modeling method that combined classical and quantum mechanical theories to model large and complex chemical systems.[43.1] As computational power advanced, the capabilities of multiscale modeling expanded significantly. The rise of high-performance computing (HPC) has enabled researchers to tackle increasingly complex problems, facilitating a paradigm shift in MSM implementations.[45.1] The integration of machine learning (ML) with MSM has further enhanced the precision and efficiency of simulations, allowing for the rapid exploration of vast material databases and the prediction of new materials.[55.1]Recent Advancements
Theoretical Frameworks
Recent advancements in multiscale modeling have been significantly influenced by the integration of various theoretical frameworks that span multiple disciplines, including mathematics, physics, and materials science. A historical review highlights the evolution of these frameworks, particularly noting the role of parallel computing in enhancing multiscale modeling capabilities. The first concurrent multiscale model was developed by Michael Ortiz, who integrated molecular dynamics with finite element methods, marking a pivotal moment in the field.[85.1] One prominent approach within multiscale modeling is the "bottom-up" method, which utilizes detailed, fine-scale information to inform broader, coarser-scale models. This technique is particularly effective in predicting the mechanical, thermal, and electronic properties of materials based on their molecular composition and structure.[88.1] Additionally, the multi-scale finite element method (MsFEM) combines the advantages of finite element analysis with sub-scale models, allowing for accurate simulations of complex systems across various length scales.[87.1] The integration of classical and quantum mechanical theories has also seen notable advancements. Quantum Mechanics/Molecular Mechanics (QM/MM) approaches have emerged as a preferred methodology for studying chemical reactions in biomolecular systems, balancing accuracy and computational efficiency by treating specific regions of interest at the quantum level while applying molecular mechanics to the remainder of the system.[98.1] Furthermore, the recent incorporation of machine learning and modern optimization algorithms has accelerated material property predictions and facilitated the development of hybrid models that leverage both classical and quantum mechanics.[97.1] In the context of two-dimensional (2D) materials, recent literature has systematically reviewed the integration of techniques such as density functional theory (DFT), molecular dynamics (MD), phase field (PF) modeling, and continuum mechanics, underscoring the importance of computational modeling in understanding the structures and properties of these materials.[96.1] Moreover, the exploration of fractional-order models has introduced new dimensions to multiscale dynamics. Unlike traditional integer-order models, fractional-order systems incorporate memory effects, allowing for a more nuanced representation of real-world physical behaviors.[105.1] This capability has proven advantageous in various applications, as fractional-order models can provide better fits to data compared to their integer-order counterparts, particularly in complex systems where memory plays a critical role.[106.1]Integration of Machine Learning Techniques
Recent advancements in multiscale modeling have increasingly integrated machine learning (ML) techniques, significantly enhancing predictive capabilities in materials science. The synergy between ML and multiscale modeling has facilitated the design of energy materials by establishing complex relationships between atomic structures and their resulting properties, thereby accelerating the identification of candidates with desirable characteristics.[100.1] This integration allows for the development of robust predictive models that can manage ill-posed problems and explore extensive design spaces, particularly in the context of complex materials.[111.1] Machine learning has also been employed to improve the efficiency of multiscale modeling approaches, particularly in predicting material behavior under varying conditions. For instance, innovative methods such as Physics-Informed Neural Networks (PINNs) have been integrated with traditional modeling techniques to predict the behavior of crystalline materials, including their plasticity and constitutive behaviors.[110.1] Additionally, ML algorithms have been utilized to screen materials databases, which has proven essential in identifying optimal materials for specific applications.[100.1] Moreover, the application of ML in multiscale modeling has extended to the integration of multimodal and multifidelity data, revealing correlations between intertwined phenomena. This capability is particularly valuable in advancing human health and understanding complex biological systems.[112.1] The incorporation of ML techniques into multiscale modeling not only enhances the accuracy and efficiency of predictions but also opens new avenues for research in various fields, including biomedical and behavioral sciences.[112.1]In this section:
Methodologies
Concurrent and Adaptive Resolution Methods
Concurrent multiscale modeling represents a sophisticated approach that integrates fully coupled simulation models across multiple scales, facilitating both bottom-up predictions of collective responses based on microstructure and top-down assessments of microstructure-scale responses influenced by higher length and time scale behaviors. This methodology is characterized by the coupling of models that operate at different scales, which is essential for comprehensive multiscale/multilevel simulation-based design.[124.1] The multi-scale finite element method (MsFEM) exemplifies a computational technique that merges the finite element method (FEM) with sub-scale models, enabling accurate simulations and analyses of complex systems across various length scales. Additionally, the lattice element method (LEM) extends the FEM by incorporating the lattice structure of materials, thereby enhancing the modeling of mechanical behavior in composite materials with diverse constituent phases.[125.1] The historical development of concurrent multiscale modeling has been significantly influenced by advancements in parallel computing, which have enabled the integration of molecular dynamics with finite element codes. Notably, the pioneering work of Michael Ortiz and his team at Caltech marked the first instance of embedding molecular dynamics into finite element analysis, setting a precedent for future developments in the field.[126.1] Moreover, the integration of machine learning (ML) with multiscale modeling is emerging as a transformative force, particularly in addressing the complexities associated with modern problems. Machine learning techniques can enhance traditional multiscale modeling approaches by managing ill-posed problems and improving predictive capabilities through the integration of physics-based knowledge and data-driven solutions.[113.1] This synergy not only facilitates the analysis of high-dimensional partial differential equations but also opens new avenues for uncertainty quantification in material properties, thereby enriching the understanding of multiscale phenomena.[112.1]Coarse-Graining Techniques
Coarse-graining techniques in multiscale modeling involve the simplification of complex systems by reducing the number of degrees of freedom while retaining essential features of the original model. These techniques are crucial for bridging the gap between atomic-level details and macroscopic behavior. Most hierarchical models incorporate a continuum approximation based on the properties of a subscale model, such as a molecular dynamics (MD) model, where intrinsic material properties are determined at the atomic level and embedded in the continuum model through a homogenization procedure.[145.1] The formulation of a multiscale model typically involves a collection of coupled single-scale submodels. This approach allows for the definition of a multiscale modeling language that serves as a bridge between application design and computer implementation. The process of 'scale splitting' illustrates how a multiscale model can be decomposed into several coupled single-scale submodels, facilitating the analysis of their mutual coupling.[146.1] When selecting appropriate sub-scale models for different materials or systems, it is essential to achieve a fair degree of accuracy and efficiency. The effectiveness of a model is evaluated based on its ability to provide rational results and precise estimations while maintaining a low computational cost and requiring a short or moderate execution time.[147.1] The linking of scales can be achieved through hierarchical, concurrent, or synergistic approaches, where micromechanics or subscale simulations are performed a priori, and the results are utilized in subsequent macroscale models.[148.1] Data-driven approaches, particularly machine learning (ML), play a significant role in refining the parameters of sub-scale models. ML techniques can enhance model performance by recognizing patterns and generating predictions based on datasets and past experiences. For instance, ML has been successfully applied in various domains, including email management automation and stock market trend forecasting, demonstrating its potential to improve the accuracy and efficiency of multiscale modeling.[151.1] Additionally, real-world applications of ML, such as enhancing public sector transparency, highlight its capability to impact various sectors positively.[150.1]In this section:
Multiple ScalesMicrostructureMechanical BehaviorComposite MaterialsPartial Differential Equations
Challenges And Limitations
Computational Complexity
Multiscale modeling in mechanical engineering faces significant computational complexities, primarily due to the high dimensionality of the solution space associated with complex multiscale systems. This complexity renders traditional modeling approaches computationally onerous, necessitating the exploration of more efficient methodologies.[172.1] Recent advancements suggest that machine learning (ML) can effectively address these challenges by serving as a surrogate for traditional models, thereby accelerating computations and enhancing predictive capabilities.[172.1] For instance, ML techniques can facilitate representation learning, which involves creating low-fidelity, cost-effective models that approximate the behavior of more complex systems.[169.1] This approach not only reduces memory and storage requirements but also allows for the integration of multimodal and multifidelity data, revealing correlations among intertwined phenomena.[170.1] Moreover, a systematic framework has been proposed that bridges large-scale simulations with reduced-order models, significantly decreasing computational effort while maintaining prediction accuracy.[173.1] This framework exemplifies how learning effective dynamics can streamline the simulation process across various applications, from chemistry to fluid mechanics.[173.1] In addition to ML, concurrent multiscale modeling approaches have been developed, which involve fully coupled simulation models across multiple scales. This method allows for both bottom-up predictions based on microstructural behavior and top-down assessments of microstructure-scale responses, thereby enhancing the overall modeling efficiency.[162.1]Coupling Techniques Across Scales
The integration of data across various biological scales is essential for enhancing the accuracy and predictive power of multiscale models in life sciences. Machine learning (ML) has emerged as a powerful technique that can facilitate this integration by managing ill-posed problems and handling sparse and noisy data, thereby improving the robustness of predictive models.[165.1] Multiscale modeling, in turn, can leverage machine learning to create surrogate models, identify system dynamics, and analyze sensitivities, which are crucial for understanding the emergence of function across different scales.[166.1] Despite the growing number of publications combining experiments and computer simulations, challenges remain in achieving systematic integration, particularly in the context of multiscale modeling of biological events.[167.1] The complexity of biological systems necessitates the consideration of multiple influences at different physiological scales, which often requires the integration of overlapping models, such as those spanning genes to molecules and molecules to cells.[168.1] Moreover, the limitations of current algorithms in multiscale modeling can significantly affect the accuracy and reliability of predictions. Traditional methods often struggle with the high nonlinearity and complexity of mechanical systems, leading to inadequate performance in medium- and long-term prediction tasks.[178.1] Recent advancements suggest that machine learning can address these challenges by providing representation learning techniques that reduce memory and storage requirements, thus enhancing the predictive capabilities of multiscale models.[181.1] In mechanical engineering, multiscale modeling has been successfully applied to various challenges, such as understanding the behavior of materials and processes in metal forming, bending, welding, and casting.[186.1] These applications demonstrate the potential of multiscale modeling to provide valuable insights and improve the design and performance of engineering systems. However, the integration of machine learning with multiscale modeling is crucial for overcoming existing limitations and achieving more accurate predictions in complex systems.[182.1]In this section:
Mechanical EngineeringComputational ComplexitiesSystematicLarge-scale SimulationsFluid Mechanics
Future Directions
Emerging Trends in Multiscale Modeling
Recent advancements in multiscale modeling techniques have significantly enhanced the study and design of two-dimensional (2D) materials. These techniques encompass a range of computational methods, from quantum chemistry to molecular dynamics and continuum modeling, which are essential for accurately capturing the intricate structures and properties of 2D materials.[198.1] The integration of machine learning (ML) and modern optimization algorithms has emerged as a pivotal trend, accelerating material property predictions and fostering the development of hybrid ML models that can effectively manage complex data.[201.1] One of the most promising areas of development is the application of machine learning to improve the accuracy and efficiency of simulations across different scales. ML techniques can integrate physics-based knowledge, such as governing equations and boundary conditions, to address ill-posed problems and handle sparse or noisy data effectively.[202.1] Active learning, a subset of ML, further enhances this process by intelligently selecting the most informative data points for model training, resulting in faster simulations without compromising accuracy.[203.1] However, challenges remain, particularly regarding the quality and availability of data, which can undermine the effectiveness of ML models in predicting properties like bandgap in 2D materials.[211.1] Quantum computing is another emerging trend that holds the potential to address limitations in current multiscale modeling techniques. The direct application of quantum-based calculators promises higher accuracy and reliability in quantum calculations, particularly when combined with classical computing methods.[207.1] Recent developments have proposed multiscale quantum computing frameworks that integrate various computational methods to efficiently simulate complex chemical systems, such as enzymatic reactions.[206.1] This integration is crucial for advancing the capabilities of multiscale modeling in addressing complex quantum systems and enhancing the overall predictive power of simulations.[207.1] As the field progresses, the interplay between machine learning and multiscale modeling is expected to evolve, particularly in the context of 2D materials. The unique properties of these materials, combined with the ability to tailor heterostructures, present an unprecedented platform for materials design.[210.1] However, the challenges associated with data dependence, interpretability, and collaborative platform development must be addressed to fully realize the potential of this interdisciplinary approach.[212.1] Overall, the future of multiscale modeling is poised to be shaped by these emerging trends, which promise to enhance our understanding and manipulation of complex materials systems.In this section:
References
[1] Multiscale modeling - Scholarpedia — Multiscale modeling refers to a style of modeling in which multiple models at different scales are used simultaneously to describe a system. The different models usually focus on different scales of resolution. They sometimes originate from physical laws of different nature, for example, one from continuum mechanics and one from molecular dynamics.In this case, one speaks of multi-physics
[2] Multiscale modeling - Wikipedia — Multiscale modeling - Wikipedia Multiscale modeling Horstemeyer 2009, 2012 presented a historical review of the different disciplines (mathematics, physics, and materials science) for solid materials related to multiscale materials modeling. The advent of parallel computing also contributed to the development of multiscale modeling. The first concurrent multiscale model occurred when Michael Ortiz (Caltech) took the molecular dynamics code Dynamo, developed by Mike Baskes at Sandia National Labs, and with his students embedded it into a finite element code for the first time. Martin Karplus, Michael Levitt, and Arieh Warshel received the Nobel Prize in Chemistry in 2013 for the development of a multiscale model method using both classical and quantum mechanical theory which were used to model large complex chemical systems and reactions. Multiscale modeling
[3] 10 - What is multiscale modeling? - Cambridge University Press & Assessment — In Chapter 1, we looked at a wide range of length and time scales relevant to materials modeling, motivating the case that materials science is filled with multiscale problems. Indeed, the message we have tried to carry throughout this book is that there is a need to model materials at many scales, and to make connections between them.
[4] Multiscale Modeling - an overview | ScienceDirect Topics — Multiscale modeling is often used in physical sciences to solve problems on multiple scales (e.g., spatial, temporal). We advocate using multiscale modeling as a means to connect different biological processes at different scales to account for the time- and spatial-dependent kinetic processes, and thereby enable the description or prediction of spatial-dependent PK in solid tumors caused by
[9] Towards a multiscale crop modelling framework for climate change ... — An advanced multiscale crop modelling framework will enable a gene-to-farm design of resilient and sustainable crop production systems under a changing climate at regional-to-global scales.
[10] Multiscale modeling techniques to document urban climate change — Urban climate models—focused on various scales and perspectives—provide important means to analyze complex physical processes forming urban climates and further quantify the ways climate change and urbanization have resulted, and will result, in local-scale modification of climate in the built environment. This chapter aims to provide an overview of the state-of-the-art in modeling urban
[11] AI-empowered next-generation multiscale climate modelling for ... - Nature — AI-empowered next-generation multiscale climate modelling for mitigation and adaptation | Nature Geoscience Climate and Earth system modelling Causally-informed deep learning to improve climate models and projections. and M.R.’s research for this study was funded by the European Research Council (ERC) Synergy Grant ‘Understanding and Modeling the Earth System with Machine Learning’ (USMILE) under the Horizon 2020 Research and Innovation programme (grant agreement no. Additional funding for P.G. and D.M.L. by the National Science Foundation Science and Technology Center, Learning the Earth with Artificial Intelligence and Physics, LEAP (grant no. V.E. led the writing and developed the multiscale climate modelling approach with AI for urgent mitigation and adaptation needs jointly with P.G. and all co-authors.
[13] Frontiers | Multiscale brain modeling: bridging microscopic and ... — It also highlights the clinical potential of multiscale models, including their role in advancing artificial intelligence (AI) applications and improving healthcare technologies. By examining current research and proposing future directions for interdisciplinary collaboration, this work demonstrates how multiscale brain modeling can
[18] Process to planet: A multiscale modeling framework toward sustainable ... — However, existing methods for sustainable engineering design ignore the economy scale, while existing methods for life cycle assessment do not consider the equipment scale. This work proposes an integrated, multiscale modeling framework for connecting models from process to planet and using them for sustainable engineering applications.
[21] Multiscale Design and Integration of Sustainable Building Functions - AAAS — robust sustainability and climate change action ( 1- 5). To date, the design of sustain-able buildings has optimized the genera-tion of energy separately from the regenera-tion of water and the processing of waste. However, the integration of macro-, micro-, and nanoscale engineering principles has enabled examples of synergistic optimiza-
[37] Multiscale materials modelling at the mesoscale - Nature — The challenge to link understanding and manipulation at the microscale to functional behaviour at the macroscale defines the frontiers of mesoscale science.
[38] Computational Homogenization and Multiscale Modeling — −Calibration from macroscale experiments or subscale modeling →"upscaling" •Multiscale constitutive modeling: P¯{H¯ } −Subscale modeling within RVE →homogenization −Calibration from macroscale experiments or further lower subscale modeling →"upscaling" −Always boils down to modeling on (lowest) scale, ab initio does not exist!
[43] Multiscale modeling - Wikipedia — Multiscale modeling - Wikipedia Multiscale modeling Horstemeyer 2009, 2012 presented a historical review of the different disciplines (mathematics, physics, and materials science) for solid materials related to multiscale materials modeling. The advent of parallel computing also contributed to the development of multiscale modeling. The first concurrent multiscale model occurred when Michael Ortiz (Caltech) took the molecular dynamics code Dynamo, developed by Mike Baskes at Sandia National Labs, and with his students embedded it into a finite element code for the first time. Martin Karplus, Michael Levitt, and Arieh Warshel received the Nobel Prize in Chemistry in 2013 for the development of a multiscale model method using both classical and quantum mechanical theory which were used to model large complex chemical systems and reactions. Multiscale modeling
[45] A survey of multiscale modeling: foundations, historical milestones ... — Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A para-digm shift in MSM implementations is being fueled by the rapid advances and emerging
[55] Accelerating Computational Materials Discovery with Machine Learning ... — Accelerating Computational Materials Discovery with Machine Learning and Cloud High-Performance Computing: from Large-Scale Screening to Experimental Validation | Journal of the American Chemical Society Accelerating Computational Materials Discovery with Machine Learning and Cloud High-Performance Computing: from Large-Scale Screening to Experimental Validation Accelerating Computational Materials Discovery with Machine Learning and Cloud High-Performance Computing: from Large-Scale Screening to Experimental Validation https://pubs.acs.org/doi/10.1021/jacs.4c03849 Here, we demonstrate how this vision became reality by combining state-of-the-art machine learning (ML) models and traditional physics-based models on cloud high-performance computing (HPC) resources to quickly navigate through more than 32 million candidates and predict around half a million potentially stable materials. You may have access to this article through your institution. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c03849.
[56] Multiscale molecular modeling in nanostructured material design and ... — One of the first breakthrough examples of multiscale modeling of materials is the linking of quantum and classical molecular methods with continuum methods to study crack propagation in silicon (Abraham, Broughton, Bernstein, & Kaxiras, 1998). Here tight-binding MD was carried out near the crack tip, classical MD was employed farther away, and
[85] Multiscale modeling - Wikipedia — Multiscale modeling - Wikipedia Multiscale modeling Horstemeyer 2009, 2012 presented a historical review of the different disciplines (mathematics, physics, and materials science) for solid materials related to multiscale materials modeling. The advent of parallel computing also contributed to the development of multiscale modeling. The first concurrent multiscale model occurred when Michael Ortiz (Caltech) took the molecular dynamics code Dynamo, developed by Mike Baskes at Sandia National Labs, and with his students embedded it into a finite element code for the first time. Martin Karplus, Michael Levitt, and Arieh Warshel received the Nobel Prize in Chemistry in 2013 for the development of a multiscale model method using both classical and quantum mechanical theory which were used to model large complex chemical systems and reactions. Multiscale modeling
[87] Multi-Scale Modeling - an overview | ScienceDirect Topics — The multi-scale finite element method (MsFEM) is a computational technique that combines the advantages of the finite element method (FEM) with sub-scale models to accurately simulate and analyse complex systems across multiple length scales. The lattice element method (LEM) is a continuum-based multi-scale modelling approach that extends the FEM by considering the lattice structure of materials. For example, in materials science, hybrid multi-scale modelling can simulate the mechanical behaviour of composite materials with different constituent phases . Through the integration of different length scales, hierarchical structures and coupled processes, multi-scale modelling provides a powerful tool for studying and simulating concrete deterioration in a detailed and accurate manner.
[88] Multiscale Modeling | Precision, Complexity & Efficiency — One common approach in multiscale modeling is the "bottom-up" method, where detailed, fine-scale information feeds into the broader, coarser-scale models. This method is particularly useful in predicting the mechanical, thermal, and electronic properties of materials based on their molecular composition and structure.
[96] Multiscale computational modeling techniques in study and design of 2D ... — This article provides an overview of recent advances, challenges, and opportunities in multiscale computational modeling techniques for study and design of two-dimensional (2D) materials. We discuss the role of computational modeling in understanding the structures and properties of 2D materials, followed by a review of various length-scale
[97] Recent advances in machine learning towards multiscale soft materials ... — The multiscale design of soft materials requires an ensemble of computational techniques spanning quantum-chemistry to molecular dynamics to continuum modeling. The recent emergence of machine-learning (ML) and modern optimization algorithms has accelerated material property prediction, as well as stimulated the development of hybrid ML
[98] Quantum mechanics/molecular mechanics multiscale modeling of ... — Quantum Mechanics/Molecular Mechanics (QM/MM) approaches have become the methodology of choice for studying chemical reactions in biomolecular systems due to their versatility and the fact that they provide an attractive compromise between accuracy and computational efficiency, which are two of the main challenges of biomolecular modeling. Thus, by defining a region of interest to be calculated at the QM level and treating the rest of the system at the MM level, Quantum Mechanics/Molecular Mechanics (QM/MM) approaches combine the best of both worlds to allow for an accurate and efficient treatment of large biomolecular systems, among other applications. One key step to simulate a biomolecular system at the QM/MM level is to define which part of the system will be treated quantum mechanically and which region will be handled using molecular mechanics force fields.
[100] Recent Advances in Machine Learning‐Assisted Multiscale Design of ... — This review highlights recent advances in machine learning (ML)-assisted design of energy materials. Initially, ML algorithms were successfully applied to screen materials databases by establishing complex relationships between atomic structures and their resulting properties, thus accelerating the identification of candidates with desirable properties.
[105] What are the advantages of using fractional systems ... - ResearchGate — Fractional-order models have been utilized for modelling certain behaviors of real-world physical systems. Most importantly, memory is what a fractional-order model can describe.
[106] PDF — important is that the misspecification of physical models using integer order derivatives leads to a variable coefficient fit (struggling to fit the data at each location, for example) whereas it was shown in the literature that the "correct" fractional order model can fit all the data with a constant coefficient model.
[110] Advancing material simulations: Physics-Informed Neural Networks and ... — An innovative method for predicting the behavior of crystalline materials is presented by integrating Physics-Informed Neural Networks (PINNs) with an object-oriented Crystal Plasticity Finite Element (CPFE) code within a large deformation framework. Techniques such as machine learning and deep learning are being employed for a range of applications, including predicting material plasticity (Mozaffar et al., 2019, Mao et al., 2023), acquiring Young’s modulus from elastic imaging (Haghighat et al., 2021, Hoerig et al., 2020), and modeling constitutive behaviors of hyperelastic materials (Li and Chen, 2022). Studies have demonstrated neural network models for rate and temperature-dependent hardening with dynamic strain aging (Li et al., 2022), the use of neural networks to represent von Mises plasticity with isotropic hardening (Zhang and Mohr, 2020), and a machine learning framework to predict local strain distribution and the evolution of plastic anisotropy in additively manufactured alloys (Muhammad et al., 2021).
[111] Integrating machine learning and multiscale modeling ... - Nature — There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces.
[112] Integrating machine learning and multiscale modeling—perspectives ... — Over the past decade, modeling multiscale phenomena has been a major point of attention, which has advanced detailed deterministic models and their coupling across scales.13 Recently, machine learning has permeated into the multiscale modeling of hierarchical engineering materials3,44,47,48 and into the solution of high-dimensional partial differential equations with deep learning methods.34,43,49–53 Uncertainty quantification in material properties is also gaining relevance,54 with examples of Bayesian model selection to calibrate strain energy functions55,56 and uncertainty propagation with Gaussian processes of nonlinear mechanical systems.57–59 These trends for non-biological systems point towards immediate opportunities for integrating machine learning and multiscale modeling in the biological, biomedical, and behavioral sciences and opens new perspectives that are unique to the living nature of biological systems.
[113] Multiscale modeling meets machine learning: What can we learn? — In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. 94.Raissi M, Perdikaris P, Karniadakis GE Physics informed deep learning (Part I): Data-driven solutions of nonlinear partial differential equations. 96.Raissi M, Karniadakis GE Hidden physics models: Machine learning of nonlinear partial differential equations.
[124] Multiscale Modeling - an overview | ScienceDirect Topics — Concurrent multiscale modeling is a specific class of multiscale modeling approaches that involves fully coupled simulation models at multiple scales; this enables both bottom-up prediction of collective responses as a function of microstructure, and top-down assessment of microstructure-scale responses given higher length and time scale behavior. This may be viewed as a coupling of models written at different length (and time) scales, and will be discussed in Chapter 9 in terms of an interaction matrix for multiscale/multilevel simulation-based design. The remainder is organized as follows: In Section 13.2, we review the formulation and implementation of a unified multiscale modeling framework for composite materials that encompasses multiple time and length scales for response and life prediction.
[125] Multi-Scale Modeling - an overview | ScienceDirect Topics — The multi-scale finite element method (MsFEM) is a computational technique that combines the advantages of the finite element method (FEM) with sub-scale models to accurately simulate and analyse complex systems across multiple length scales. The lattice element method (LEM) is a continuum-based multi-scale modelling approach that extends the FEM by considering the lattice structure of materials. For example, in materials science, hybrid multi-scale modelling can simulate the mechanical behaviour of composite materials with different constituent phases . Through the integration of different length scales, hierarchical structures and coupled processes, multi-scale modelling provides a powerful tool for studying and simulating concrete deterioration in a detailed and accurate manner.
[126] Multiscale modeling - Wikipedia — Multiscale modeling - Wikipedia Multiscale modeling Horstemeyer 2009, 2012 presented a historical review of the different disciplines (mathematics, physics, and materials science) for solid materials related to multiscale materials modeling. The advent of parallel computing also contributed to the development of multiscale modeling. The first concurrent multiscale model occurred when Michael Ortiz (Caltech) took the molecular dynamics code Dynamo, developed by Mike Baskes at Sandia National Labs, and with his students embedded it into a finite element code for the first time. Martin Karplus, Michael Levitt, and Arieh Warshel received the Nobel Prize in Chemistry in 2013 for the development of a multiscale model method using both classical and quantum mechanical theory which were used to model large complex chemical systems and reactions. Multiscale modeling
[145] PDF — multiscale methods. Most hierarchical models contain a continuum approximation based on the properties of a subscale model, such as a MD model. The intrinsic properties of the material are determined at the atomic level and embedded in the continuum model according to a homogenization procedure. Concurrent multiscale methods employ an
[146] A framework for multi-scale modelling - PMC — Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation. Illustration of the process of ‘scale splitting’: a multi-scale model (a) is decomposed into several ‘single-scale’ coupled submodels (b). From analysing several multi-scale systems and the way their submodels are mutually coupled, we reach the conclusion that the relations shown in table 1 hold between any two coupled submodels X and Y with a single-domain relation.
[147] A comparative review of multiscale models for effective properties of ... — A fair degree of accuracy and efficiency needs to be achieved when conducting multiscale modelling of any composite type. The selection of a competent model depends on its ability to provide rational results and precise estimations while requiring a short or moderate console execution time at a low computational cost.
[148] PDF — The linking of scales can be achieved in a hierarchical, concurrent, or synergistic sense.11 With hierarchical multiscale ap-proaches, micromechanics or subscale simulations are preformed a priori, and the results obtained from those simulations are utilized in subsequent macroscale, or structural level, models.
[150] 10 Top Machine Learning Examples & Applications in Real Life - Omdena — 10 Top Machine Learning Examples & Applications in Real Life Top 10 Machine Learning Examples in Real Life (Which Make the World a Better Place) In particular, we will look into the machine learning examples in real life that impact and aim to make the world a better place. Use of the appropriate emoticons, suggestions about friend tags on Facebook, filtered on Instagram, content recommendations and suggested followers on social media platforms, etc., are examples of how machine learning helps us in social networking. Top 10 examples of machine learning in real life (which make the world a better place) Another example is where a team of data scientists and ML engineers at, Omdena successfully applied machine learning to enhance public sector transparency by enabling increased access to government contract opportunities.
[151] Machine Learning Examples - GeeksforGeeks — Machine Learning & Data Science Tutorials Sorting Algorithms Tutorial Algorithms Tutorial Python Data Visualization Tutorial By harnessing algorithms that enable computers to learn from and make decisions based on data, ML is not just reshaping industries but also redefining our everyday interactions with technology. Machine Learning has become a integral part of our daily lives, often operating behind the scenes to enhance user experience, improve efficiency and solve problems across various domains. Machine Learning Examples In the modern era, Machine Learning (ML) has emerged as a cornerstone technology driving innovation and efficiency across various sectors. By harnessing algorithms that enable computers to learn from and make decisions based on data, ML is not just reshaping industries but also redefining our everyd 9 min read
[162] Multiscale Modeling - an overview | ScienceDirect Topics — Concurrent multiscale modeling is a specific class of multiscale modeling approaches that involves fully coupled simulation models at multiple scales; this enables both bottom-up prediction of collective responses as a function of microstructure, and top-down assessment of microstructure-scale responses given higher length and time scale behavior. This may be viewed as a coupling of models written at different length (and time) scales, and will be discussed in Chapter 9 in terms of an interaction matrix for multiscale/multilevel simulation-based design. The remainder is organized as follows: In Section 13.2, we review the formulation and implementation of a unified multiscale modeling framework for composite materials that encompasses multiple time and length scales for response and life prediction.
[165] Multiscale modeling meets machine learning: What can we learn? — In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. 94.Raissi M, Perdikaris P, Karniadakis GE Physics informed deep learning (Part I): Data-driven solutions of nonlinear partial differential equations. 96.Raissi M, Karniadakis GE Hidden physics models: Machine learning of nonlinear partial differential equations.
[166] Integrating machine learning and multiscale modeling ... - Nature — There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces.
[167] Editorial: Combining Simulations, Theory, and Experiments into ... — The number of publications that combine experiments and computer simulations has been growing steadily in the last 10 years. However, several challenges still need to be addressed in order to achieve a systematic integration, especially in the context of multiscale modeling of biological events. Computationally connecting the different scales—or more precisely the different system
[168] Multiscale Modeling and Data Integration in the Virtual Physiological ... — It has become increasingly evident that the descriptions of many complex diseases are only possible by taking into account multiple influences at different physiological scales. To do this with computational models often requires the integration of several models that have overlapping scales (genes to molecules, molecules to cells, cells to tissues). The Virtual Physiological Rat (VPR) Project
[169] Challenges and Opportunities for Machine Learning in Multiscale ... — Recent works suggest that machine learning (ML) has the potential to overcome the limitations of traditional multiscale modeling methods (Fig. 1).For instance, to address the issue of memory and storage requirements in hierarchical modeling, ML techniques can be applied to learn a coarse, low fidelity, and low-cost representation, referred to as representation learning, of pre-computed QoIs [].
[170] Integrating machine learning and multiscale modeling ... - Nature — There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces.
[172] Challenges and Opportunities for Machine Learning in Multiscale ... — Abstract. Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional
[173] Multiscale simulations of complex systems by learning their effective ... — Multiscale simulations of complex systems by learning their effective dynamics | Nature Machine Intelligence Multiscale simulations of complex systems by learning their effective dynamics Here we present a novel systematic framework that bridges large-scale simulations and reduced-order models to learn the effective dynamics of diverse, complex systems. Learning the effective dynamics is applicable to systems ranging from chemistry to fluid mechanics and reduces the computational effort by up to two orders of magnitude while maintaining the prediction accuracy of the full system dynamics. P.K. conceived the project; P.R.V., G.A., C.U. and P.K. designed and performed research; P.R.V. and G.A. contributed new analytic tools; P.R.V., G.A. and P.K. analysed data and P.R.V., G.A. and P.K. wrote the paper. Vlachas, P.R., Arampatzis, G., Uhler, C. Multiscale simulations of complex systems by learning their effective dynamics.
[178] Bearing Lifespan Reliability Prediction Method Based on Multiscale ... — Accurate prediction of the remaining useful life (RUL) of rolling bearings was crucial for ensuring the safe operation of machinery and reducing maintenance losses. However, due to the high nonlinearity and complexity of mechanical systems, traditional methods failed to meet the requirements of medium- and long-term prediction tasks. To address this issue, this paper proposed a recurrent
[181] Challenges and Opportunities for Machine Learning in Multiscale ... — Recent works suggest that machine learning (ML) has the potential to overcome the limitations of traditional multiscale modeling methods (Fig. 1).For instance, to address the issue of memory and storage requirements in hierarchical modeling, ML techniques can be applied to learn a coarse, low fidelity, and low-cost representation, referred to as representation learning, of pre-computed QoIs [].
[182] Integrating machine learning and multiscale modeling ... - Nature — There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces.
[186] PDF — quality cast components. Multiscale modeling and simulation play a crucial role in understanding and predicting the behavior of materials and processes at different length scales. In the context of metal forming, bending, welding, and casting processes, multiscale modeling and simulation techniques offer valuable insights and advantages.
[198] Recent advances in machine learning towards multiscale soft materials ... — The multiscale design of soft materials requires an ensemble of computational techniques spanning quantum-chemistry to molecular dynamics to continuum modeling. The recent emergence of machine-learning (ML) and modern optimization algorithms has accelerated material property prediction, as well as stimulated the development of hybrid ML
[201] Integrating machine learning and multiscale modeling ... - Nature — There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces.
[202] Multiscale Modeling Meets Machine Learning: What Can We Learn? - Springer — In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data
[203] How AI is Improving Simulations with Smarter Sampling Techniques - AI ... — The result is faster simulations without compromising accuracy. Active Learning Active learning, a subset of machine learning, further enhances sampling by iteratively selecting the most informative data points for training models. In simulations, this means the algorithm can intelligently choose the next best sample point based on prior knowledge.
[206] Calculating the energy profile of an enzymatic reaction on a quantum ... — We have developed a fully automatic multi-scale quantum computational framework and applied it for the CO 2 subscript CO 2 ext{CO}_{2} CO start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT hydration catalysed by Carbonic Anhydrase running on actual quantum hardware. To our knowledge, this is the first quantum computing application in modeling enzymatic
[207] Simulating quantum circuits using the multi-scale entanglement ... — Understanding the limiting capabilities of classical methods in simulating complex quantum systems is of paramount importance for quantum technologies. Although many advanced approaches have been proposed and recently used to challenge quantum advantage experiments, novel efficient methods for the approximate simulation of complex quantum systems are still in high demand. Here, we propose a
[210] When Machine Learning Meets 2D Materials: A Review — The availability of an ever-expanding portfolio of 2D materials with rich internal degrees of freedom (spin, excitonic, valley, sublattice, and layer pseudospin) together with the unique ability to tailor heterostructures made layer by layer in a precisely chosen stacking sequence and relative crystallographic alignments, offers an unprecedented platform for realizing materials by design.
[211] From prediction to design: Recent advances in machine learning for the ... — Notably, these challenges are distinctly different from those in scenarios used for predicting electronic band gaps, magnetism, or catalytic performance, as machine learning applied to the discovery and design of two-dimensional materials must address more complex and variable problems.
[212] Challenges and Opportunities for Machine Learning in Multiscale ... — Next, we discuss current challenges for ML in multiscale computational modeling, such as the data/discretization dependence, interpretability, data sharing and collaborative platform development.