Methods for data-driven multiscale model discovery for materials

Brunton, Steven L.; Kutz, J. Nathan

doi:10.1088/2515-7639/ab291e

Cited by 50 publications

(22 citation statements)

References 93 publications

(131 reference statements)

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“…Materials design strategies requires complex data analysis that either follow data driven discovery 20 or functionally driven discovery 21 , 22 . In the latter desired target properties are used as an input to predict the require components that give rise to these properties.…”

Section: Introductionmentioning

confidence: 99%

Magnetic properties of the complex concentrated alloy system CoFeNi0.5Cr0.5Alx

Morley

Quintana-Nedelcos

et al. 2020

Sci Rep

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We study the change in magnetisation with paramagnetic Al addition in the CoFeNi 0.5 cr 0.5-Al x (x: 0, 0.5, 1, and 1.5) complex concentrated alloy. The compositions were developed utilising the Mulliken electronegativity and d-electron/atom ratio. Spherical FeCr rich nanoprecipitates are observed for X: 1.0 and 1.5 in an AlCoNi-rich matrix. A ~ 5 × increase in magnetisation (from 22 to 96 Am 2 /kg) coincides with this nanoprecipitate formation-the main magnetic contribution is determined to be from FeCr nanoprecipitates. The magnetisation increase is strange as paramagnetic Al addition dilutes the ferromagnetic Fe/Co/Ni additions. In this paper we discuss the magnetic and structural characterisation of the cofeni 0.5 cr 0.5-Al x composition and attempt to relate it to the interfacial energy. The innovation of new materials has been deemed to be the key topic for development of new technologies in our modern world. For alloys, the traditional approach has been to consider the effect of multiple dilute additions to a larger alloy matrix. New complex concentrated alloys (CCAs), which are near-equimolar multiple element alloys (> 3) challenge this view and have pushed alloy research towards the centre of phase diagrams 1,2. Multiple alloying components mean that they can possess large property permutations owing to the vast compositional space that they cover. Considerable work has been done on understanding how compositionalstructure affects mechanical properties. However, their functional properties are rarely the primary focus. As the base elements of CCAs are often CoFeNi (which is a known soft magnetic alloy), this can provide a basis for alloy design 1-5. Our motivation in this work is to therefore investigate the potential of CCAs as soft magnetic materials.

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Section: Introductionmentioning

confidence: 99%

Magnetic properties of the complex concentrated alloy system CoFeNi0.5Cr0.5Alx

Morley

Quintana-Nedelcos

et al. 2020

Sci Rep

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“…In particular, for a given spatial distribution of oxidizing agents on the sample, an optimal value of the annealing temperature could be found, yielding a minimal distortion of the plane and a sizeable recovery of the sp 2 carbon domains. Finally, we mention that our simulation data could actually be further integrated into materials databases [44,45], for further use of machine learning algorithms [46][47][48][49] to extrapolate on morphologies and physical properties (electronic and thermal) of a large spectrum of reduced GOs morphologies. This could enable faster access to important information for designing composites with improved performances.…”

Section: Discussionmentioning

confidence: 99%

Impact of oxidation morphology on reduced graphene oxides upon thermal annealing

2019

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Thermal reduction of graphene oxide (GO) is an essential technique to produce low-cost and higher quality graphene-based materials and composites used today in a plethora of applications. However, despite a demonstrated efficiency of high-temperature annealing in reducing the oxygen content of GO, the impact of the morphology of the initially oxidized samples on the restored sp 2 graphene plane versus remaining sp 3 imperfections remains unclear and out-of-control. Here using classical molecular dynamics, we simulate the process of thermal reduction on several GO samples for a variety of initial conditions and elucidate how both the concentration of oxygen functional groups and their spatial distribution jeopardize the reduction process efficiency. Our simulations suggest thermal annealing strategies to further optimize the crystallinity of reduced GO, enhancing their transport properties and hence making the resulting composites even more performant for electronic applications.

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“…15 The candidate functions are chosen either by expert knowledge 15 or through sparse approximation techniques. 16,17 An application of these model discovery techniques in material science can be found in Reference [18]. However, the success of the method heavily depends on the built library, and we generally need to perform computations in the full-order system dimension, thus making the method very challenging in large-scale settings.…”

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confidence: 99%

Learning reduced‐order dynamics for parametrized shallow water equations from data

Yıldız

Goyal

Benner

et al. 2021

Numerical Methods in Fluids

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This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation. We consider the shallow water equation in non-traditional form (NTSWE). We focus on learning low-dimensional models in a non-intrusive way. That means, we assume not to have access to a discretized form of the NTSWE in any form. Instead, we have snapshots that can be obtained using a black-box solver. Consequently, we aim at learning reduced-order models only from the snapshots. Precisely, a reduced-order model is learnt by solving an appropriate least-squares optimization problem in a low-dimensional subspace. Furthermore, we discuss computational challenges that particularly arise from the optimization problem being ill-conditioned. Moreover, we extend the non-intrusive model order reduction framework to a parametric case, where we make use of the parameter dependency at the level of the partial differential equation. We illustrate the efficiency of the proposed non-intrusive method to construct reduced-order models for NTSWE and compare it with an intrusive method (proper orthogonal decomposition). We furthermore discuss the predictive capabilities of both models outside the range of the training data. K E Y W O R D Sdata-driven modeling, model order reduction, operator inference, scientific machine learning, shallow water equation INTRODUCTIONShallow water equations (SWE) are a popular set of hyperbolic partial differential equations (PDEs) with the capability of describing geophysical wave phenomena, for example, the Kelvin and Rossby waves in the atmosphere and the oceans. They are frequently used in geophysical flow prediction, 1 investigation of baroclinic instability, 2,3 and planetary flows. 4 In this paper, we study a model order reduction (MOR) technique for SWE. MOR techniques allow us to construct low-dimensional models or reduced-order models (ROMs) for a large-scale dynamical system. We refer to the books 5,6 for an overview of the available techniques. These ROMs are computationally efficient and accurate, and are worthy when a full order model (FOM) needs to be simulated multiple-times for different parameter settings. Additionally, ROMs are even more valuable in the case of SWE, when the interest lies in simulating the model for a very long time horizon. MOR problems for SWE have been intensively studied in the literature, see, for example, References [7-12].

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Methods for data-driven multiscale model discovery for materials

Cited by 50 publications

References 93 publications

Magnetic properties of the complex concentrated alloy system CoFeNi0.5Cr0.5Alx

Magnetic properties of the complex concentrated alloy system CoFeNi0.5Cr0.5Alx

Impact of oxidation morphology on reduced graphene oxides upon thermal annealing

Learning reduced‐order dynamics for parametrized shallow water equations from data

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