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Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

Numerical Analysis · Mathematics 2020-10-27 Bryce Chudomelka , Youngjoon Hong , Hyunwoo Kim , Jinyoung Park

Diffractive neural network (DNN), which can perform machine learning tasks based on the light propagation and diffraction, has recently emerged as a promising optical computing paradigm due to its high parallel processing speed and low…

Optics · Physics 2026-01-27 Yudong Tian , Haifeng Xu , Yuqing Liu , Xiangyu Zhao , Jierong Cheng , Chongzhao Wu

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

Computation · Statistics 2025-09-30 Noah Yi-Ting Hung , Li-Hsiang Lin , Vince D. Calhoun

Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than…

Machine Learning · Computer Science 2022-03-22 Patrick Schnell , Philipp Holl , Nils Thuerey

Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…

Machine Learning · Computer Science 2021-07-23 Gaetan Rensonnet , Louise Adam , Benoit Macq

The Schr\"{o}dinger equation with random potentials is a fundamental model for understanding the behaviour of particles in disordered systems. Disordered media are characterised by complex potentials that lead to the localisation of…

Disordered Systems and Neural Networks · Physics 2023-07-13 Liam Harcombe , Quanling Deng

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Machine Learning · Statistics 2023-10-23 Tomoharu Iwata , Yusuke Tanaka , Naonori Ueda

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

Machine Learning · Computer Science 2022-04-01 Mike Y. Michelis , Robert K. Katzschmann

Evolutional deep neural networks (EDNN) solve partial differential equations (PDEs) by marching the network representation of the solution fields, using the governing equations. Use of a single network to solve coupled PDEs on large domains…

Numerical Analysis · Mathematics 2024-07-18 Hadden Kim , Tamer A. Zaki

Deep Neural Networks (DNNs) have gained immense success in cognitive applications and greatly pushed today's artificial intelligence forward. The biggest challenge in executing DNNs is their extremely data-extensive computations. The…

Computer Vision and Pattern Recognition · Computer Science 2019-09-10 Fuqiang Liu , C. Liu

Maxwell's equations govern light propagation and its interaction with matter. Therefore, the solution of Maxwell's equations using computational electromagnetic simulations plays a critical role in understanding light-matter interaction and…

Optics · Physics 2024-06-12 Joowon Lim , Demetri Psaltis

This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical…

Computational Engineering, Finance, and Science · Computer Science 2025-02-13 T. R. F. Phillips , C. E. Heaney , C. Boyang , A. G. Buchan , C. C. Pain

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…

Optimization and Control · Mathematics 2025-10-29 Fuat Can Beylunioglu , P. Robert Duimering , Mehrdad Pirnia

The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…

Disordered Systems and Neural Networks · Physics 2021-05-12 Chen-Yu Liu , Daw-Wei Wang

Physics-constrained neural networks are commonly employed to enhance prediction robustness compared to purely data-driven models, achieved through the inclusion of physical constraint losses during the model training process. However, one…

Machine Learning · Computer Science 2024-02-06 Hao Zhou , Sibo Cheng , Rossella Arcucci

Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…

Quantum Physics · Physics 2025-01-22 Abhishek Setty , Rasul Abdusalamov , Felix Motzoi

Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning,…

Strongly Correlated Electrons · Physics 2018-10-03 Xiao Liang , Wen-Yuan Liu , Pei-Ze Lin , Guang-Can Guo , Yong-Sheng Zhang , Lixin He

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schr\"odinger equation, where the control variable…

Numerical Analysis · Mathematics 2023-05-31 Yating Wang , Liu Liu

Conditional computation for Deep Neural Networks (DNNs) reduce overall computational load and improve model accuracy by running a subset of the network. In this work, we present a runtime throttleable neural network (TNN) that can…

Machine Learning · Computer Science 2020-11-06 Hengyue Liu , Samyak Parajuli , Jesse Hostetler , Sek Chai , Bir Bhanu

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

Materials Science · Physics 2021-03-17 Jaber Rezaei Mianroodi , Nima H. Siboni , Dierk Raabe