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Nature-inspired architected materials using unsupervised deep learning

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Communications engineering 2022年第1期1卷 1-15页

作者： Shen, Sabrina Chin-yun Buehler, Markus J. Laboratory for Atomistic and Molecular Mechanics (LAMM) Massachusetts Institute of Technology 77 Massachusetts Ave. Cambridge 02139 MA United States Department of Materials Science and Engineering Massachusetts Institute of Technology 77 Massachusetts Ave. Cambridge 02139 MA United States Center for Computational Science and Engineering Schwarzman College of Computing Massachusetts Institute of Technology 77 Massachusetts Ave. Cambridge 02139 MA United States

Nature-inspired material design is driven by superior properties found in natural architected materials and enabled by recent developments in additive manufacturing and machine learning. Existing approaches to push design beyond biomimicry typically use supervised deep learning algorithms to predict and optimize properties based on experimental or simulation data. However, these methods constrain generated material designs to abstracted labels and to “black box” outputs that are only indirectly manipulable. Here we report an alternative approach using an unsupervised generative adversarial network (GAN) model. Training the model on unlabeled data constructs a latent space free of human intervention, which can then be explored through seeding, image encoding, and vector arithmetic to control specific parameters of de novo generated material designs and to push them beyond training data distributions for broad applicability. We illustrate this end-to-end with new materials inspired by leaf microstructures, showing how biological 2D structures can be used to develop novel architected materials in 2 and 3 dimensions. We further utilize a genetic algorithm to optimize generated microstructures for mechanical properties, operating directly on the latent space. This approach allows for transfer of information across manifestations using the latent space as mediator, opening new avenues for exploration of nature-inspired materials. © The Author(s) 2022.

关键词： Mechanical engineering Materials science engineering

Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise

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arXiv 2021年

作者： Hong, Jialin Hou, Baohui Sun, Liying Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the interior penalty discontinuous Galerkin finite element method to discretize space variable and present two semi-discrete schemes, respectively. Then we make use of the discrete gradient method and the Pad'e approximation to propose efficient fully-discrete schemes. These semi-discrete and fully-discrete schemes are proved to preserve the discrete averaged energy evolution law. In particular, we also prove that the proposed fully-discrete schemes exactly inherit the averaged energy evolution law almost surely if the considered model is driven by additive noise. Numerical experiments are given to confirm theoretical findings. © 2021, CC BY.

关键词： Finite difference method

On the convergence of stochastic gradient descent with bandwidth-based step size

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arXiv 2021年

作者： Wang, Xiaoyu Yuan, Ya-Xiang Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences No.19A Yuquan Road Beijing100049 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate under mild conditions and large initial step size is proved. Our analysis provides comparable theoretical error bounds for SGD associated with a variety of step sizes. In addition, the convergence rates for some existing step size strategies, e.g., triangular policy and cosine-wave, can be revealed by our analytical framework under the boundary constraints. The bandwidth-based step size provides efficient and flexible step size selection in optimization. We also propose a 1/t up-down policy and give several non-monotonic step sizes. Numerical experiments demonstrate the efficiency and significant potential of the bandwidth-based step-size in many *** Codes 65K05, 65K10, 90C15 Copyright © 2021, The Authors. All rights reserved.

关键词： Bandwidth

Space-time hp finite elements for heat evolution in laser-based additive manufacturing

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arXiv 2021年

作者： Kopp, Philipp Calo, Victor Rank, Ernst Kollmannsberger, Stefan Computational Modeling and Simulation Technische Universität München Munich Germany Computational Geoscience & Applied Mathematics School of Electrical Engineering Computing & Mathematical Science Curtin University Perth Australia Institute for Advanced Study Technische Universität München Munich Germany

The direct numerical simulation of metal additive manufacturing processes such as laser powder bed fusion is challenging due to the vast differences in spatial and temporal scales. Classical approaches based on locally refined finite elements combined with time-stepping schemes can only address the spatial multi-scale nature and provide only limited scaling potential for massively parallel computations. We address these shortcomings in a space-time Galerkin framework where the finite element interpolation also includes the temporal dimension. In this setting, we construct four-dimensional meshes that are locally refined towards the laser spot and allow for varying temporal accuracy depending on the position in space. By splitting the mesh into conforming time-slabs, we recover a stepwise solution to solve the space-time problem locally in time at this slab;additionally, we can choose time-slab sizes significantly larger than classical time-stepping schemes. As a result, we believe this setting to be well suited for large-scale parallelization. In our work, we use a continuous Galerkin-Petrov formulation of the nonlinear heat equation with an apparent heat capacity model to account for the phase change. We validate our approach by computing the AMB2018-02 benchmark, where we obtain an excellent agreement with the measured melt pool shape. Using the same setup, we demonstrate the performance potential of our approach by hatching a square area with a laser path length of about one meter. © 2021, CC BY.

关键词： 3D printers

Survey of physics reasoning on uncertainty concepts in experiments: an assessment of measurement uncertainty for introductory physics labs

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arXiv 2023年

作者： Vignal, Michael Geschwind, Gayle Pollard, Benjamin Henderson, Rachel Caballero, Marcos D. Lewandowski, H.J. JILA National Institute of Standards and Technology The University of Colorado BoulderCO80309 United States Department of Physics University of Colorado 390 UCB BoulderCO80309 United States Department of Physics Worcester Polytechnic Institute 100 Institute Road WorcesterMA01609 United States Department of Physics & Astronomy CREATE for STEM Institute Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science & Engineering Michigan State University East LansingMI48824 United States Department of Physics Center for Computing in Science Education University of Oslo Oslo0315 Norway

Measurement uncertainty is a critical feature of experimental research in the physical sciences, and the concepts and practices surrounding measurement uncertainty are important components of physics lab courses. However, there has not been a broadly applicable, research-based assessment tool that allows physics instructors to easily measure students’ knowledge of measurement uncertainty concepts and practices. To address this need, we employed Evidence-Centered Design to create the Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE). SPRUCE is a pre-post assessment instrument intended for use in introductory (first- and second-year) physics lab courses to help instructors and researchers identify student strengths and challenges with measurement uncertainty. In this paper, we discuss the development of SPRUCE’s assessment items guided by Evidence-Centered Design, focusing on how instructors’ and researchers’ assessment priorities were incorporated into the assessment items and how students’ reasoning from pilot testing informed decisions around item answer options. We also present an example of some of the feedback an instructor would receive after implementing SPRUCE in a pre-post fashion, along with a brief discussion of how that feedback could be interpreted and acted upon. © 2023, CC BY.

关键词： Uncertainty analysis

Stochastic Higher-Order Three-Scale Strength Prediction Model for Composite Structures with Micromechanical Analysis

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SSRN

SSRN 2022年

作者： Dong, Hao Yang, Zihao Guan, Xiaofei Cui, Junzhi School of Mathematics and Statistics Xidian University Xi’an710071 China School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710129 China School of Mathematical Sciences Tongji University Shanghai China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Stochastic multiscale modeling and analysis for the strength prediction of composite structures with complex multiscale random configurations remains a challenging problem. This is mainly due to the facts of high-dimensional physical properties, non-linear and non-Gaussian features, which many repeated evaluations of the corresponding stochastic multiscale model are often required. In this paper, we develop a stochastic higher-order three-scale strength prediction (SHTSP) model for composite structures, which is designed to overcome limitations of prohibitive computation involving the microscale, the mesoscale and the macroscale. By virtue of asymptotic homogenization theory and micromechanical analysis, the SHTSP model is derived from the detailed stochastic higher-order three-scale homogenization analysis implemented with analytic solutions of composite structures subjected to tension, bending and twist loads. The SHTSP model represents strength anisotropy through different strength criterions for evaluating the yield state of the different component materials of composite structures, which are induced by aggregate-matrix interface deboning or matrix cracking in multiple scales. Moreover, these are constructed and calibrated from the high-accuracy mechanical analysis with help of two classes of mesoscopic and microscopic auxiliary cell functions, respectively. The corresponding numerical algorithm of SHTSP model and a preprocessing multilevel strategy is designed to improve the computational efficiency. Finally, the numerical experiments in 3D cases illustrate the outstanding performance of the proposed SHTSP model, and the proposed method can significantly reduce the computational time. © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

Scaling Laws of Graph Neural Networks for Atomistic Materials Modeling

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arXiv 2025年

作者： Li, Chaojian Ye, Zhifan Pasini, Massimiliano Lupo Choi, Jong Youl Wan, Cheng Lin, Yingyan Balaprakash, Prasanna Computational Sciences and Engineering Division Oak Ridge National Laboratory United States Computer Science and Mathematics Division Oak Ridge National Laboratory United States Computing and Computational Sciences Directorate Oak Ridge National Laboratory United States Georgia Institute of Technology United States

Atomistic materials modeling is a critical task with wide-ranging applications, from drug discovery to materials science, where accurate predictions of the target material property can lead to significant advancements in scientific discovery. Graph Neural Networks (GNNs) represent the state-of-the-art approach for modeling atomistic material data thanks to their capacity to capture complex relational structures. While machine learning performance has historically improved with larger models and datasets, GNNs for atomistic materials modeling remain relatively small compared to large language models (LLMs), which leverage billions of parameters and terabyte-scale datasets to achieve remarkable performance in their respective domains. To address this gap, we explore the scaling limits of GNNs for atomistic materials modeling by developing a foundational model with billions of parameters, trained on extensive datasets in terabyte-scale. Our approach incorporates techniques from LLM libraries to efficiently manage large-scale data and models, enabling both effective training and deployment of these large-scale GNN models. This work addresses three fundamental questions in scaling GNNs: the potential for scaling GNN model architectures, the effect of dataset size on model accuracy, and the applicability of LLM-inspired techniques to GNN architectures. Specifically, the outcomes of this study include (1) insights into the scaling laws for GNNs, highlighting the relationship between model size, dataset volume, and accuracy, (2) a foundational GNN model optimized for atomistic materials modeling, and (3) a GNN codebase enhanced with advanced LLM-based training techniques. Our findings lay the groundwork for large-scale GNNs with billions of parameters and terabyte-scale datasets, establishing a scalable pathway for future advancements in atomistic materials modeling. Copyright © 2025, The Authors. All rights reserved.

关键词： Materials properties

The Basics of Quantum computing for Chemists

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arXiv 2022年

作者： Claudino, Daniel Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

The rapid and successful strides in quantum chemistry in the past decades can be largely credited to a conspicuous synergy between theoretical and computational advancements. However, the architectural computer archetype that enabled such a progress is approaching a state of more stagnant development. One of the most promising technological avenues for the continuing progress of quantum chemistry is the emerging quantum computing paradigm. This revolutionary proposal comes with several challenges, which span a wide array of disciplines. In chemistry, it implies, among other things, a need to reformulate some of its long established cornerstones in order to adjust to the operational demands and constraints of quantum computers. Due to its relatively recent emergence, much of quantum computing may still seem fairly nebulous and largely unknown to most chemists. It is in this context that here we review and illustrate the basic aspects of quantum information and their relation to quantum computing insofar as enabling simulations of quantum chemistry. We consider some of the most relevant developments in light of these aspects and discuss the current landscape when of relevance to quantum chemical simulations in quantum computers. © 2022, CC BY.

关键词： Quantum optics

Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

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arXiv 2024年

作者： Shin, Myeongjin Lee, Seungwoo Lee, Junseo Lee, Mingyu Ji, Donghwa Yeo, Hyeonjun Jeong, Kabgyun School of Computing KAIST Daejeon34141 Korea Republic of Quantum AI Team Norma Inc. Seoul04799 Korea Republic of Department of Computer Science and Engineering Seoul National University Seoul08826 Korea Republic of College of Liberal Studies Seoul National University Seoul08826 Korea Republic of Department of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of Research Institute of Mathematics Seoul National University Seoul08826 Korea Republic of School of Computational Sciences Korea Institute for Advanced Study Seoul02455 Korea Republic of

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network. Copyright © 2024, The Authors. All rights reserved.

关键词： Hilbert spaces