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Deep learning is a promising, ultra-fast approach for inverse design in nano-optics, but despite fast advancement of the field, the computational cost of dataset generation, as well as of the training procedure itself remains a major…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Dynamical Systems · Mathematics 2018-08-24 Francisco J. Gonzalez , Maciej Balajewicz

Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…

Numerical Analysis · Mathematics 2025-04-30 Chang-Ock Lee , Youngkyu Lee , Byungeun Ryoo

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…

Mesoscale and Nanoscale Physics · Physics 2021-06-16 Vittorio Peano , Florian Sapper , Florian Marquardt

The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and…

Machine Learning · Computer Science 2022-05-05 Diab W. Abueidda , Seid Koric , Rashid Abu Al-Rub , Corey M. Parrott , Kai A. James , Nahil A. Sobh

Extreme Learning Machine (ELM) is an efficient and effective least-square-based learning algorithm for classification, regression problems based on single hidden layer feed-forward neural network (SLFN). It has been shown in the literature…

Machine Learning · Computer Science 2020-11-05 Ramesh Ragala , Bharadwaja kumar

Over recent years, there has been a rapid development of deep learning (DL) in both industry and academia fields. However, finding the optimal hyperparameters of a DL model often needs high computational cost and human expertise. To…

Neural and Evolutionary Computing · Computer Science 2022-08-24 Nan Li , Lianbo Ma , Guo Yu , Bing Xue , Mengjie Zhang , Yaochu Jin

Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging…

Information Retrieval · Computer Science 2019-05-01 Lianlin Li , Long Gang Wang , Fernando L. Teixeira , Che Liu , Arye Nehora , Tie Jun Cui

The emergence of deep learning (DL) has provided great opportunities for the high-throughput analysis of atomic-resolution micrographs. However, the DL models trained by image patches in fixed size generally lack efficiency and flexibility…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

Numerical Analysis · Mathematics 2022-09-12 Xiaolong He , Qizhi He , Jiun-Shyan Chen

The accuracy of the information that can be extracted from electron diffraction patterns is often limited by the presence of optical distortions. Existing distortion characterization techniques typically require knowledge of the reciprocal…

Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…

Systems and Control · Electrical Eng. & Systems 2024-09-12 Priyabrata Saha , Saibal Mukhopadhyay

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might…

Machine Learning · Computer Science 2023-10-19 Nicola Rares Franco , Daniel Fraulin , Andrea Manzoni , Paolo Zunino

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…

Computational Physics · Physics 2021-01-27 Stefania Fresca , Andrea Manzoni , Luca Dedè , Alfio Quarteroni

This letter studies deep learning (DL) approaches to optimize beamforming vectors in downlink multi-user multi-antenna systems that can be universally applied to arbitrarily given transmit power limitation at a base station. We exploit the…

Information Theory · Computer Science 2020-07-10 Junbeom Kim , Hoon Lee , Seung-Eun Hong , Seok-Hwan Park

Practical applications of mechanical metamaterials often involve solving inverse problems where the objective is to find the (multiple) microarchitectures that give rise to a given set of properties. The limited resolution of additive…

Deep learning (DL) based unrolled reconstructions have shown state-of-the-art performance for under-sampled magnetic resonance imaging (MRI). Similar to compressed sensing, DL can leverage high-dimensional data (e.g. 3D, 2D+time, 3D+time)…

Image and Video Processing · Electrical Eng. & Systems 2021-03-09 Ke Wang , Michael Kellman , Christopher M. Sandino , Kevin Zhang , Shreyas S. Vasanawala , Jonathan I. Tamir , Stella X. Yu , Michael Lustig

Deep learning, as a highly efficient method for metasurface inverse design, commonly use simulation data to train deep neural networks (DNNs) that can map desired functionalities to proper metasurface designs. However, the assumptions and…

Signal Processing · Electrical Eng. & Systems 2023-08-07 Jingxin Zhang , Jiawei Xi , Peixing Li , Ray C. C. Cheung , Alex M. H. Wong , Jensen Li

Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML)…

Computational Physics · Physics 2022-07-27 Rui Guo , Tianyao Huang , Maokun Li , Haiyang Zhang , Yonina C. Eldar

Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have…