A neural operator-based surrogate solver for free-form electromagnetic inverse design

• URL: http://arxiv.org/abs/2302.01934v2
• Date: Tue, 28 Mar 2023 07:22:31 GMT
• Title: A neural operator-based surrogate solver for free-form electromagnetic inverse design
• Authors: Yannick Augenstein, Taavi Rep\"an, Carsten Rockstuhl
• Abstract summary: We implement and train a modified Fourier neural operator as a surrogate solver for electromagnetic scattering problems. We demonstrate its application to the gradient-based nanophotonic inverse design of free-form, fully three-dimensional electromagnetic scatterers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural operators have emerged as a powerful tool for solving partial differential equations in the context of scientific machine learning. Here, we implement and train a modified Fourier neural operator as a surrogate solver for electromagnetic scattering problems and compare its data efficiency to existing methods. We further demonstrate its application to the gradient-based nanophotonic inverse design of free-form, fully three-dimensional electromagnetic scatterers, an area that has so far eluded the application of deep learning techniques.

Related papers

• DimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning [63.5925701087252]
  We introduce DimOL (Dimension-aware Operator Learning), drawing insights from dimensional analysis. To implement DimOL, we propose the ProdLayer, which can be seamlessly integrated into FNO-based and Transformer-based PDE solvers. Empirically, DimOL models achieve up to 48% performance gain within the PDE datasets.
  arXiv  Detail & Related papers  (2024-10-08T10:48:50Z)
• Physics aware machine learning for micromagnetic energy minimization: recent algorithmic developments [0.0]
  Building on Brown's bounds for magnetostatic self-energy, we revisit their application in the context of variational formulations of the transmission problems. We reformulate these bounds on a finite domain, making the method more efficient and scalable for numerical simulation. Results highlight the potential of mesh-free Physics-Informed Neural Networks (PINNs) and Extreme Learning Machines (ELMs) when integrated with hard constraints.
  arXiv  Detail & Related papers  (2024-09-19T16:22:40Z)
• Multi-frequency Neural Born Iterative Method for Solving 2-D Inverse Scattering Problems [3.171666227612361]
  We propose a deep learning-based imaging method for addressing the multi-frequency electromagnetic inverse scattering problem (ISP) By combining deep learning technology with EM physical laws, we have successfully developed a multi-frequency neural Born iterative method (Neural BIM) The effectiveness of the multi-frequency Neural BIM is validated through synthetic and experimental data, demonstrating improvements in accuracy and computational efficiency for solving ISP.
  arXiv  Detail & Related papers  (2024-09-02T15:16:07Z)
• Magnetic Hysteresis Modeling with Neural Operators [0.7817677116789855]
  This paper proposes neural operators for modeling laws that exhibit magnetic by learning a mapping between magnetic fields. Two prominent neural operators -- deep operator network and Fourier neural operator -- are employed to predict novel first-order reversal curves and minor loops.
  arXiv  Detail & Related papers  (2024-07-03T16:45:45Z)
• Mechanistic Neural Networks for Scientific Machine Learning [58.99592521721158]
  We present Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations. Central to our approach is a novel Relaxed Linear Programming solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs.
  arXiv  Detail & Related papers  (2024-02-20T15:23:24Z)
• Equivariant Graph Neural Operator for Modeling 3D Dynamics [148.98826858078556]
  We propose Equivariant Graph Neural Operator (EGNO) to directly models dynamics as trajectories instead of just next-step prediction. EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods.
  arXiv  Detail & Related papers  (2024-01-19T21:50:32Z)
• Waveformer for modelling dynamical systems [1.0878040851638]
  We propose "waveformer", a novel operator learning approach for learning solutions of dynamical systems. The proposed waveformer exploits wavelet transform to capture the spatial multi-scale behavior of the solution field and transformers. We show that the proposed Waveformer can learn the solution operator with high accuracy, outperforming existing state-of-the-art operator learning algorithms by up to an order.
  arXiv  Detail & Related papers  (2023-10-08T03:34:59Z)
• Neural Operators for Accelerating Scientific Simulations and Design [85.89660065887956]
  An AI framework, known as Neural Operators, presents a principled framework for learning mappings between functions defined on continuous domains. Neural Operators can augment or even replace existing simulators in many applications, such as computational fluid dynamics, weather forecasting, and material modeling.
  arXiv  Detail & Related papers  (2023-09-27T00:12:07Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Transformer Meets Boundary Value Inverse Problems [4.165221477234755]
  Transformer-based deep direct sampling method is proposed for solving a class of boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and reconstructed images.
  arXiv  Detail & Related papers  (2022-09-29T17:45:25Z)
• Physics informed neural networks for continuum micromechanics [68.8204255655161]
  Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $mu$CT-scans.
  arXiv  Detail & Related papers  (2021-10-14T14:05:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.