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Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Machine Learning · Computer Science 2025-07-03 Yaohua Zang , Phaedon-Stelios Koutsourelakis

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Machine Learning · Computer Science 2025-11-06 Gang Bao , Yaohua Zang

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically…

Computational Engineering, Finance, and Science · Computer Science 2026-01-13 Weipeng Xu , Ziyuan Xie , Haoju Lin , Xinyu Wang , Guangjin Mou , Tianju Xue

Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable…

Machine Learning · Statistics 2026-02-17 Matthaios Chatzopoulos , Phaedon-Stelios Koutsourelakis

Designing composite materials as per the application requirements is fundamentally a challenging and time consuming task. Here we report the development of a deep neural network based computational framework capable of solving the forward…

Materials Science · Physics 2022-09-14 Ashank , Soumen Chakravarty , Pranshu Garg , Ankit Kumar , Manish Agrawal , Prabhat K. Agnihotri

Inverse design of heterogeneous material microstructures is a fundamentally ill-posed and famously computationally expensive problem. This is exacerbated by the high-dimensional design spaces associated with finely resolved images,…

Machine Learning · Computer Science 2026-03-17 Reza T. Batley , Sourav Saha

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of…

Materials Science · Physics 2023-07-18 Kang-Hyun Lee , Hyoung Jun Lim , Gun Jin Yun

Understanding how nano- or micro-scale structures and material properties can be optimally configured to attain specific functionalities remains a fundamental challenge. Photonic metasurfaces, for instance, can be spectrally tuned through…

Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand…

Computational Engineering, Finance, and Science · Computer Science 2024-03-28 Doksoo Lee , Lu Zhang , Yue Yu , Wei Chen

In this work, we present Multimodal Equivariant Inverse Design Network (MEIDNet), a framework that jointly learns structural information and materials properties through contrastive learning, while encoding structures via an equivariant…

Materials Science · Physics 2026-01-30 Anand Babu , Rogério Almeida Gouvêa , Pierre Vandergheynst , Gian-Marco Rignanese

The inverse design of microstructures plays a pivotal role in optimizing metamaterials with specific, targeted physical properties. While traditional forward design methods are constrained by their inability to explore the vast…

Computer Vision and Pattern Recognition · Computer Science 2025-02-06 Tianyang Xue , Haochen Li , Longdu Liu , Paul Henderson , Pengbin Tang , Lin Lu , Jikai Liu , Haisen Zhao , Hao Peng , Bernd Bickel

Deep generative models like GAN and VAE have shown impressive results in generating unconstrained objects like images. However, many design settings arising in industrial design, material science, computer graphics and more require that the…

Machine Learning · Computer Science 2024-06-07 Aaron Ferber , Arman Zharmagambetov , Taoan Huang , Bistra Dilkina , Yuandong Tian

The research of metamaterials has achieved enormous success in the manipulation of light in an artificially prescribed manner using delicately designed sub-wavelength structures, so-called meta-atoms. Even though modern numerical methods…

Optics · Physics 2019-01-31 Wei Ma , Feng Cheng , Yihao Xu , Qinlong Wen , Yongmin Liu

Inverse design is a common yet challenging engineering problem, particularly for nonlinear functional responses such as mechanical behavior or spectral analysis. Deep generative models are motivated by intractability, non-existence or…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Haoxuan Dylan Mu , Mingjian Tang , Wei Gao , Wei "Wayne" Chen

Materials discovery is fundamental to advance next-generation technologies as well as for sustainable and circular economy. Beyond computational screening, generative models are efficient at finding materials with desired properties, via…

The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials--truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of…

Computational Engineering, Finance, and Science · Computer Science 2024-04-17 Li Zheng , Konstantinos Karapiperis , Siddhant Kumar , Dennis M. Kochmann

High Q-factor narrow-band absorption exhibits high spectral selectivity enabling high-sensitive photodetectors, sensors and thermal emitters. All-dielectric metasurfaces are widely regarded as excellent candidates for giving rise to such…

Optics · Physics 2025-07-25 Sreeraj Rajan Warrier , Jayasri Dontabhaktuni

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…

Machine Learning · Computer Science 2024-11-14 Weiheng Zhong , Hadi Meidani

Disordered metamaterials are promising for programming physical properties across diverse applications, yet their inverse design remains challenging due to the non-intuitive structure-property relationships and large design spaces. Recent…

Computational Engineering, Finance, and Science · Computer Science 2026-03-18 Ziyuan Xie , Weipeng Xu , Dazhi Zhao , Wenchang Zhang , Daoyang Dong , Bingbing Xu , Ning Liu , Sheng Mao , Tianju Xue

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Machine Learning · Computer Science 2025-10-29 Sharmila Karumuri , Lori Graham-Brady , Somdatta Goswami
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