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- W4315704946 abstract "Linear Partial Differential Equations (PDEs) govern the spatial-temporal dynamics of physical systems that are essential to building modern technology. When working with linear PDEs, designing a physical system for a specific outcome is difficult and costly due to slow and expensive explicit simulation of PDEs and the highly nonlinear relationship between a system's configuration and its behavior. In this work, we prove a parametric form that certain physical quantities in the Fourier domain must obey in linear PDEs, named the CZP (Constant-Zeros-Poles) framework. Applying CZP to antenna design, an industrial application using linear PDEs (i.e., Maxwell's equations), we derive a sample-efficient parametric surrogate model that directly predicts its scattering coefficients without explicit numerical PDE simulation. Combined with a novel image-based antenna representation and an attention-based neural network architecture, CZP outperforms baselines by 10% to 25% in terms of test loss and also is able to find 2D antenna designs verifiable by commercial software with $33%$ greater success than baselines, when coupled with sequential search techniques like reinforcement learning." @default.
- W4315704946 created "2023-01-12" @default.
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- W4315704946 date "2023-01-06" @default.
- W4315704946 modified "2023-09-23" @default.
- W4315704946 title "Sample-efficient Surrogate Model for Frequency Response of Linear PDEs using Self-Attentive Complex Polynomials" @default.
- W4315704946 doi "https://doi.org/10.48550/arxiv.2301.02747" @default.
- W4315704946 hasPublicationYear "2023" @default.
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