Transfer learning-assisted inverse modeling in nanophotonics based on mixture density networks

• URL: http://arxiv.org/abs/2401.12254v2
• Date: Tue, 21 May 2024 13:39:50 GMT
• Title: Transfer learning-assisted inverse modeling in nanophotonics based on mixture density networks
• Authors: Liang Cheng, Prashant Singh, Francesco Ferranti,
• Abstract summary: In this paper, we propose an inverse modeling method for nanophotonic structures based on a mixture density network model enhanced by transfer learning. The proposed approach allows overcoming these limitations using transfer learning-based techniques, while preserving a high accuracy in the prediction capability of the design solutions given an optical response as an input.
• Score: 0.840835093659811
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The simulation of nanophotonic structures relies on electromagnetic solvers, which play a crucial role in understanding their behavior. However, these solvers often come with a significant computational cost, making their application in design tasks, such as optimization, impractical. To address this challenge, machine learning techniques have been explored for accurate and efficient modeling and design of photonic devices. Deep neural networks, in particular, have gained considerable attention in this field. They can be used to create both forward and inverse models. An inverse modeling approach avoids the need for coupling a forward model with an optimizer and directly performs the prediction of the optimal design parameters values. In this paper, we propose an inverse modeling method for nanophotonic structures, based on a mixture density network model enhanced by transfer learning. Mixture density networks can predict multiple possible solutions at a time including their respective importance as Gaussian distributions. However, multiple challenges exist for mixture density network models. An important challenge is that an upper bound on the number of possible simultaneous solutions needs to be specified in advance. Also, another challenge is that the model parameters must be jointly optimized, which can result computationally expensive. Moreover, optimizing all parameters simultaneously can be numerically unstable and can lead to degenerate predictions. The proposed approach allows overcoming these limitations using transfer learning-based techniques, while preserving a high accuracy in the prediction capability of the design solutions given an optical response as an input. A dimensionality reduction step is also explored. Numerical results validate the proposed method.

Related papers

• Diffusion Models as Network Optimizers: Explorations and Analysis [71.69869025878856]
  generative diffusion models (GDMs) have emerged as a promising new approach to network optimization. In this study, we first explore the intrinsic characteristics of generative models. We provide a concise theoretical and intuitive demonstration of the advantages of generative models over discriminative network optimization.
  arXiv  Detail & Related papers  (2024-11-01T09:05:47Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems [0.0]
  We show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model.
  arXiv  Detail & Related papers  (2024-01-25T13:41:34Z)
• Compositional Generative Inverse Design [69.22782875567547]
  Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem. We show that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes.
  arXiv  Detail & Related papers  (2024-01-24T01:33:39Z)
• Diffusion Generative Inverse Design [28.04683283070957]
  Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. Recent developments in learned graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics. We show how denoising diffusion diffusion models can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency.
  arXiv  Detail & Related papers  (2023-09-05T08:32:07Z)
• Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks [0.0]
  This work explores the potential usage of graph neural networks (GNNs) for the simulation of time-dependent PDEs. We propose a systematic strategy to build surrogate models based on a data-driven time-stepping scheme. We show that GNNs can provide a valid alternative to traditional surrogate models in terms of computational efficiency and generalization to new scenarios.
  arXiv  Detail & Related papers  (2023-08-03T08:14:28Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers. We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Tackling Multimodal Device Distributions in Inverse Photonic Design using Invertible Neural Networks [0.0]
  Inverse design is the process of matching a device or process parameters to exhibit a desired performance. Most traditional optimization routines assume an invertible one-to-one mapping between the design parameters and the target performance. We show how a generative modeling approach based on invertible neural networks can provide the full distribution of possible solutions to the inverse design problem.
  arXiv  Detail & Related papers  (2022-08-29T08:46:17Z)
• Modeling Design and Control Problems Involving Neural Network Surrogates [1.1602089225841632]
  We consider nonlinear optimization problems that involve surrogate models represented by neural networks. We show how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence. We present two alternative formulations of these problems in the specific case of feedforward neural networks with ReLU activation.
  arXiv  Detail & Related papers  (2021-11-20T01:09:15Z)
• Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation [101.22379613810881]
  We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive process. We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
  arXiv  Detail & Related papers  (2021-02-16T06:04:27Z)
• Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems [83.98774574197613]
  We take one of the simplest inference methods, a truncated max-product Belief propagation, and add what is necessary to make it a proper component of a deep learning model. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs) The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.
  arXiv  Detail & Related papers  (2020-03-13T13:11:35Z)

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.