Topological representations of crystalline compounds for the machine-learning prediction of materials properties

Jiang, Yi; Chen, Dong; Chen, Xin; Li, Tangyi; Wei, Guowei; Pan, Feng

doi:10.1038/s41524-021-00493-w

Cited by 54 publications

(33 citation statements)

References 47 publications

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“…[15][16][17][18][19][20][21][22][23][24][25][26] for a review). Most of the current ML related innovations in materials science and engineering successfully aim at accelerated material discovery [27][28][29][30] , efficient interatomic potential development [31][32][33][34] or feature identification in complex pattern that have relevance for materials performance [35][36][37][38][39] . However, we show here that ML can also help to fundamentally change the way how we solve (non-linear) partial differential equation systems in conjunction with advanced constitutive laws that describe complex material microstructures, much faster than via classical finite element or spectral solvers 11,40 .…”

Section: A Machine Learning Approach Based On U-netmentioning

confidence: 99%

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

Mianroodi

Siboni²,

Raabe

2021

npj Comput Mater

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We propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers.

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Section: A Machine Learning Approach Based On U-netmentioning

confidence: 99%

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

Mianroodi

Siboni²,

Raabe

2021

npj Comput Mater

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“…(a) Cyclohexane and its persistent barcodes with all elements and the carbon element selected, respectively (reprinted with permission from Reference 137). (b) The construction of element‐specific topological descriptor for BaTiO 3 (reprinted with permission from Reference 138)…”

Section: Topological Descriptormentioning

confidence: 99%

“…A recent study was devoted to the development of element‐specific persistent homology for the investigation of inorganic periodic crystals 138 . Due to the periodicity, a cutoff radius has to be introduced to define the range within which all constituent atoms will participate in the construction of persistent barcodes for the central atom.…”

Section: Topological Descriptormentioning

confidence: 99%

Encoding the atomic structure for machine learning in materials science

Liu

Dong

et al. 2021

WIREs Comput Mol Sci

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In recent years, we have witnessed a widespread application of machine learning techniques in the field of materials science, owing to the increased availability of research data and sophisticated algorithms. At the core of this technology lies the ability to encode material structures into descriptors that are understandable for a computer. Although significant advances have been made in this area, there is a continued need to explore efficient structure‐encoding strategies so as to maximize the predictive power of the machine learning models. Here we present a revision of the exciting progress in four representative structural features that are capable of describing the structures of diverse materials: structure graph, Coulomb matrix, topological descriptor, and diffraction fingerprint. Particular attention is given to the studies of crystalline solids, which appear more challenging to be encoded than molecules. By summarizing previous works and presenting critical appraisals of these descriptors, this review could offer some guideline for the selection of structural features and stimulate inspiration for the design of powerful descriptors suited towards different tasks. This article is categorized under: Structure and Mechanism > Computational Materials Science Data Science > Artificial Intelligence/Machine Learning

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“…[54][55][56][57][58][59][60][61][62][63][64][65] for a review). These applications include accelerated material discovery [66][67][68][69], efficient interatomic potential development [70][71][72][73], feature identification from complex patterns that have relevance for materials performance [74][75][76][77][78], or facilitating predictive simulations which solve macroscopic (non-linear) partial differential equation systems [24,39,79]. This has the potential to revolutionize continuumbased simulations of materials, allowing a substantial enhancement in the modeling of systems and topologies with high complexity.…”

Section: Network Architecture and Trainingmentioning

confidence: 99%

Lossless Multi-Scale Constitutive Elastic Relations with Artificial Intelligence

Mianroodi¹,

Rezaei²,

Siboni³

et al. 2021

Preprint

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The elastic properties of materials derive from their electronic and atomic nature.However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless and lossless transition of the constitutive description of the elastic response of materials between these two scales has been so far elusive. Here we show how this problem can be overcome by using Artificial Intelligence (AI). A Convolutional Neural Network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corresponding elasticity tensor, calculated from Molecular Statics (MS), as output. Trained with the atomistic data, the CNN model captures the size-and poredependency of the material's elastic properties which, on the physics side, can stem from surfaces and non-local effects. Such effects are often ignored in upscaling from atomistic to classical continuum theory. To demonstrate the accuracy and the efficiency of the trained CNN model, a Finite Element Method (FEM) based result of an elastically deformed nanoporous beam equipped with the CNN as constitutive law is compared with that by a full atomistic simulation. The good agreement between the atomistic simulations and the FEM-AI combination for a system with size and surface effects establishes a new lossless scale bridging approach to such problems. The trained CNN model deviates from the atomistic result by 9.6% for porosity scenarios of up to 90% but it is about 230 times faster than the MS calculation and does not require to change simulation methods between different scales. The efficiency of the CNN evaluation together with the preservation of important atomistic effects makes the trained model an effective atomistically-informed constitutive model for macroscopic simulations of nanoporous materials, optimization of nano-structures, and solving of inverse problems.

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Topological representations of crystalline compounds for the machine-learning prediction of materials properties

Cited by 54 publications

References 47 publications

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

Encoding the atomic structure for machine learning in materials science

Lossless Multi-Scale Constitutive Elastic Relations with Artificial Intelligence

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