Accelerated Time-Domain Simulation of Complex Photonic Structures with a Data-Aware Fourier Neural Operator

TL;DR

The paper tackles the challenge of slow time-domain photonic simulations by introducing the Data-Aware Fourier Neural Operator (DA-FNO), a physics-informed neural operator that autoregressively predicts the full time evolution of TM electromagnetic fields and terminates when the energy within the domain converges, removing CFL constraints. By incorporating a learnable 3×3 convolution to couple field components and a data-driven spectral mode selection, the model preserves high-frequency content essential for scattering phenomena and achieves robust generalization across complex/random geometries and wavelengths in the optical C-band (1525–1575 nm). Empirically, DA-FNO delivers around an 11× speedup over FDTD with approximately 95% accuracy, demonstrates strong frequency-domain fidelity, and shows promising 3D extrapolation, paving the way for faster photonic design and potential integration into inverse-design workflows. The work highlights the potential of physics-aware neural operators to replace or accelerate full-wave solvers in photonics, balancing accuracy and computational efficiency for practical device development.

Abstract

Efficient and accurate time-domain simulation of electromagnetic fields in complex photonic devices is critical for designing broadband and ultrafast optical components, yet it is often limited by the high computational cost of conventional numerical methods like FDTD. While machine learning approaches show promise in accelerating these simulations, existing models still struggle to simultaneously capture the dynamic field evolution and generalize to complex geometries. In this paper, we introduce a Data-Aware Fourier Neural Operator (DA-FNO) as an innovative neural operator for solving electromagnetic simulations. Applied autoregressively, the model iteratively predicts the time-domain evolution of all field components and automatically terminates upon energy convergence. Our model not only generalizes to complex and randomized geometries but also shows good predictive consistency across the optical C-band (1530-1565nm) when evaluated on the test set. In a representative configuration, it achieves an 11* speedup over conventional methods while maintaining about 95% accuracy across the C-band. This approach provides a new pathway for C-band photonic simulations, potentially facilitating the research, development, and inverse design of novel photonic devices.

Figures (10)

• Figure 1: Schematic diagram of the proposed model. Similar to the FDTD method, the DA-FNO model iteratively outputs all field components ($E_z$, $H_x$, $H_y$) over time until the energy converges. By eliminating CFL constraints, the DA-FNO allows for larger time steps ($m\Delta t$), thereby enabling faster simulations.
• Figure 2: (a) The full architecture of the vanilla FNO. $a(x)$ is lifted to a higher-dimensional space by network $P$, processed through $n$ Fourier layers and projected to the target function $u(x)$ by network $Q$. (b) The architecture of the Fourier layer in (a). The output $v_0(x)$ from network $P$ is Fourier-transformed into the spectral space, where a spectral weight $R$ is applied along with rectangular truncation. After an inverse Fourier transform, the result is added to $v_0(x)$ and passed through an activation function.
• Figure 3: (a) The full architecture of the DA-FNO model. The five input time-domain field states $\left \{ s_{t-4},\ldots,s_t \right \}$ is augmented by $S$ with permittivity distribution $\epsilon$ and spatial coordinates $(x,y)$, lifted to a higher-dimensional space by network $P$, processed through four DA Fourier layers and mapped to the next state $s_{t+1}$ by network $Q$. The new state and the last four time-domain states of the input form a new input $\left \{ s_{t-3},\ldots,s_{t+1} \right \}$, enabling the iteration to continue until the energy of the new state falls below a convergence factor, $\delta$, of the historical maximum. (b) The architecture of the DA Fourier layer. The convolutional processing establishes correlations among the three field components. Data-Aware mode selection is performed in the spectral space.
• Figure 4: (a) Ez field distributions at $t=5\Delta t,13\Delta t$ and $21\Delta t$. (b) The mode selection regions (white areas) of the vanilla FNO and DA-FNO. Average spectral image of all training data, normalized and displayed in logarithmic scale.
• Figure 5: Performance comparison among DA-FNO models with $\theta=0.6,0.7,0.8,0.9$, Conv-FNO and vanilla FNO models, based on 500 samples and 1000 epochs. (a) Training and test ARL1Es at the 1000th epoch of the six models. Each model is evaluated over multiple runs, and the five most stable results are presented. (b) Training and (c) test ARL1E curves (smoothed for clarity) of the six models, each corresponding to the run with the lowest training ARL1E among the five runs in (a). All original curves are provided in Supplementary material, Figure S2 and S3. (d) Average spectral image over the training subset. (e) Mode selection regions of the six models. (f) Absolute errors between the average spectral images of the outputs from the best run of each model in (a) and the spectral image of the training subset.