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The Finite-Difference Time-Domain (FDTD) method is a numerical modeling technique used by researchers as one of the most accurate methods to simulate the propagation of an electromagnetic wave through an object over time. Due to the nature of the method, FDTD can be computationally expensive when used in complex setting such as light propagation in highly heterogenous object such as the imaging process of tissues. In this paper, we explore a Deep Learning (DL) model that predicts the evolution of an electromagnetic field in a heterogeneous medium. In particular, modeling for propagation of a Gaussian beam in skin tissue layers. This is relevant for the characterization of microscopy imaging of tissues. Our proposed model named FDTD-net, is based on the U-net architecture, seems to perform the prediction of the electric field (EF) with good accuracy and faster when compared to the FDTD method. A dataset of different geometries was created to simulate the propagation of the electric field. The propagation of the electric field was initially generated using the traditional FDTD method. This data set was used for training and testing of the FDTD-net. The experiments show that the FDTD-net learns the physics related to the propagation of the source in the heterogeneous objects, and it can capture changes in the field due to changes in the object morphology. As a result, we present a DL model that can compute a propagated electric field in less time than the traditional method.
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HoD-Net: High-Order Differentiable Deep Neural Networks and Applications
We introduce a deep architecture named HoD-Net to enable high-order differentiability for deep learning. HoD-Net is based on and generalizes the complex-step finite difference (CSFD) method. While similar to classic finite difference, CSFD approaches the derivative of a function from a higher-dimension complex domain, leading to highly accurate and robust differentiation computation without numerical stability issues. This method can be coupled with backpropagation and adjoint perturbation methods for an efficient calculation of high-order derivatives. We show how this numerical scheme can be leveraged in challenging deep learning problems, such as high-order network training, deep learning-based physics simulation, and neural differential equations.
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- PAR ID:
- 10350317
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 36
- Issue:
- 8
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 8249 to 8258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/aaai.v36i8.20799
