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Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

Optimization and Control · Mathematics 2024-03-01 Alfredo Vitorino , Francisco A. M. Gomes

The mechanical properties of periodic microstructures are pivotal in various engineering applications. Homogenization theory is a powerful tool for predicting these properties by averaging the behavior of complex microstructures over a…

Computational Physics · Physics 2025-10-06 Yu Xing , Yang Liu , Lipeng Chen , Huiping Tang , Lin Lu

Multiscale topology optimization is crucial for designing porous infill structures with high stiffness-to-weight ratios and excellent energy absorption. Although gradient-based methods provide a rigorous framework, they are computationally…

Optimization and Control · Mathematics 2025-10-13 Shuzhi Xu , Yifan Guo , Hiroki Kawabe , Kentaro Yaji

This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…

Optimization and Control · Mathematics 2019-07-16 Marc Dambrine , Helmut Harbrecht

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

Neurons and Cognition · Quantitative Biology 2023-01-30 Tananun Songdechakraiwut , Moo K. Chung

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Machine Learning · Computer Science 2025-10-31 Di Zhang

Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…

Computational Engineering, Finance, and Science · Computer Science 2024-04-17 Yaqi Guo , Saurav Sharma , Siddhant Kumar

We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…

Computational Engineering, Finance, and Science · Computer Science 2025-05-27 Jonathan Stollberg , Tarun Gangwar , Oliver Weeger , Dominik Schillinger

Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…

Machine Learning · Computer Science 2026-02-24 Michael Trimboli , Mohammed Alsubaie , Sirani M. Perera , Ke-Gang Wang , Xianqi Li

Heterogeneity and uncertainty in a composite microstructure lead to either computational bottlenecks if modeled rigorously or to solution inaccuracies in the stress field and failure predictions if approximated. Although methods suitable…

Machine Learning · Computer Science 2024-05-31 Emil Pitz , Kishore Pochiraju

Magnetic soft robots embedded with hard magnetic particles enable untethered actuation via external magnetic fields, offering remote, rapid, and precise control, which is highly promising for biomedical applications. However, designing such…

Robotics · Computer Science 2025-07-15 Liwei Wang

Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…

Numerical Analysis · Mathematics 2021-10-22 Felipe Rocha , Simone Deparis , Pablo Antolin , Annalisa Buffa

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…

Analysis of PDEs · Mathematics 2023-07-10 Stefano Almi , Ulisse Stefanelli

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies…

Materials Science · Physics 2021-11-29 Dominik K. Klein , Mauricio Fernández , Robert J. Martin , Patrizio Neff , Oliver Weeger

Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in…

Materials Science · Physics 2026-04-29 Sarvesh Joshi , Jingye Tan , Craig M. Hamel , Stavros Gaitanaros , Nikolaos Bouklas

This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumor-associated microvesicles (TMVs) are randomly distributed with heterogeneous patterns. This imposes a…

Machine Learning · Statistics 2019-03-22 Xiwei Tang , Xuan Bi , Annie Qu

Stochastic microstructure reconstruction has become an indispensable part of computational materials science, but ongoing developments are specific to particular material systems. In this paper, we address this generality problem by…

Materials Science · Physics 2018-05-09 Xiaolin Li , Yichi Zhang , He Zhao , Craig Burkhart , L Catherine Brinson , Wei Chen

Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature…

Materials Science · Physics 2017-05-01 Ruijin Cang , Yaopengxiao Xu , Shaohua Chen , Yongming Liu , Yang Jiao , Max Yi Ren

The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…

Computational Engineering, Finance, and Science · Computer Science 2017-08-25 Dengyang Zhao , Ming Li , Yusheng Liu

The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…

Numerical Analysis · Mathematics 2024-10-18 N. Kovács , M. A. Maia , I. B. C. M. Rocha , C. Furtado , P. P. Camanho , F. P. van der Meer
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