Abstract: The finite-difference time-domain (FDTD) method, which is important in photonic hardware design flow, is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost, taking minutes to hours to simulate a single device. Recently, AI has been applied to realize orders-of-magnitude speedup in partial differential equation (PDE) solving. However, AI-based FDTD solvers for photonic devices have not been clearly formulated. Directly applying off-the-shelf models to predict the optical field dynamics shows unsatisfying fidelity and efficiency since the model primitives are agnostic to the unique physical properties of Maxwell equations and lack algorithmic customization. In this work, we thoroughly investigate the synergy between neural operator designs and the physical property of Maxwell equations and introduce a physics-inspired AI-based FDTD prediction framework PIC2O-Sim which features a causality-aware dynamic convolutional neural operator as its backbone model that honors the space-time causality constraints via careful receptive field configuration and explicitly captures the permittivity-dependent light propagation behavior via an efficient dynamic convolution operator. Meanwhile, we explore the trade-offs among prediction scalability, fidelity, and efficiency via a multi-stage partitioned time-bundling technique in autoregressive prediction. Multiple key techniques have been introduced to mitigate iterative error accumulation while maintaining efficiency advantages during autoregressive field prediction. Extensive evaluations on three challenging photonic device simulation tasks have shown the superiority of our PIC2O-Sim method, showing 51.2% lower roll-out prediction error, 23.5 times fewer parameters than state-of-the-art neural operators, providing 300-600x higher simulation speed than an open-source FDTD numerical solver.

@article{10.1063/5.0242728,
  author = {Ma, Pingchuan and Yang, Haoyu and Gao, Zhengqi and Boning, Duane S. and Gu, Jiaqi},
  title = {PIC2O-Sim: A physics-inspired causality-aware dynamic convolutional neural operator for ultra-fast photonic device time-domain simulation},
  journal = {APL Photonics},
  volume = {10},
  number = {3},
  pages = {036104},
  year = {2025},
  month = {03},
  abstract = {Optical simulation plays an important role in photonic hardware design flow. The finite-difference time-domain (FDTD) method is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost as it iteratively solves Maxwell equations and takes minutes to hours to simulate a single device. Recently, AI has been applied to realize orders-of-magnitude speedup in partial differential equation solving. However, AI-based FDTD solvers for photonic devices have not been clearly formulated. Directly applying off-the-shelf models to predict the optical field dynamics shows unsatisfying fidelity and efficiency since the model primitives are agnostic to the unique physical properties of Maxwell equations and lack algorithmic customization. In this work, we thoroughly investigate the synergy between neural operator designs and the physical property of Maxwell equations and introduce a physics-inspired AI-based FDTD prediction framework PIC2O-Sim. PIC2O-Sim features a causality-aware dynamic convolutional neural operator as its backbone model that honors the space–time causality constraints via careful receptive field configuration and explicitly captures the permittivity-dependent light propagation behavior via an efficient dynamic convolution operator. Meanwhile, we explore the trade-offs among prediction scalability, fidelity, and efficiency via a multi-stage partitioned time-bundling technique in autoregressive prediction. Multiple key techniques have been introduced to mitigate iterative error accumulation while maintaining efficiency advantages during autoregressive field prediction. Extensive evaluations on three challenging photonic device simulation tasks have shown the superiority of our PIC2O-Sim method, showing 51.2\% lower roll-out prediction error, 23.5 times fewer parameters than state-of-the-art neural operators, providing 133–310× or 31–89× higher simulation speed than an open-source single-process or eight-process parallel FDTD numerical solver.},
  issn = {2378-0967},
  doi = {10.1063/5.0242728},
  url = {https://doi.org/10.1063/5.0242728},
  eprint = {https://pubs.aip.org/aip/app/article-pdf/doi/10.1063/5.0242728/20420133/036104\_1\_5.0242728.pdf},
}

Abstract: Nanophotonic device design aims to optimize photonic structures to meet specific requirements across various applications. Inverse design has unlocked non-intuitive, high-dimensional design spaces, enabling the discovery of high-performance devices beyond heuristic or analytic methods. The adjoint method, which calculates gradients for all variables using just two simulations, enables efficient navigation of this complex space. However, many inverse-designed structures, while numerically plausible, are difficult to fabricate and sensitive to variations, limiting their practical use. The discrete nature with numerous local-optimal structures also pose significant optimization challenges, often causing gradient-based methods to converge on suboptimal designs. In this work, we formulate inverse design as a fabrication-restricted, discrete, probabilistic optimization problem and introduce BOSON^-1, an end-to-end, variation-aware subspace optimization framework to address the challenges of manufacturability, robustness, and optimizability. To overcome optimization difficulty, we propose dense target-enhanced gradient flows to mitigate misleading local optima and introduce a conditional subspace optimization strategy to create high-dimensional tunnels to escape local optima. Furthermore, we significantly reduce the runtime associated with optimizing across exponential variation samples through an adaptive sampling-based robust optimization, ensuring both efficiency and variation robustness. On three representative photonic device benchmarks, our proposed inverse design methodology BOSON^-1 delivers fabricable structures and achieves the best convergence and performance under realistic variations, outperforming prior arts with 74.3% post-fabrication performance.

@INPROCEEDINGS{10993227,
  author={Ma, Pingchuan and Gao, Zhengqi and Begovic, Amir and Zhang, Meng and Yang, Haoyu and Ren, Haoxing and Huang, Rena and Boning, Duane S. and Gu, Jiaqi},
  booktitle={2025 Design, Automation & Test in Europe Conference (DATE)}, 
  title={BOSON−1: Understanding and Enabling Physically-Robust Photonic Inverse Design with Adaptive Variation-Aware Subspace Optimization}, 
  year={2025},
  volume={},
  number={},
  pages={1-7},
  keywords={Performance evaluation;Optical losses;Runtime;Navigation;Optimization methods;Robustness;Topology;Numerical models;Optimization;Photonics},
  doi={10.23919/DATE64628.2025.10993227}}

Abstract: DONNs leverage light propagation for efficient analog AI and signal processing. Advances in nanophotonic fabrication and metasurface-based wavefront engineering have opened new pathways to realize high-capacity DONNs across various spectral regimes. Training such DONN systems to determine the metasurface structures remains challenging. Heuristic methods are fast but oversimplify metasurfaces modulation, often resulting in physically unrealizable designs and significant performance degradation. Simulation-in-the-loop optimizes implementable metasurfaces via adjoint methods, but is computationally prohibitive and unscalable. To address these limitations, we propose SP²RINT, a spatially decoupled, progressive training framework that formulates DONN training as a PDE-constrained learning problem. Metasurface responses are first relaxed into freely trainable transfer matrices with a banded structure. We then progressively enforce physical constraints by alternating between transfer matrix training and adjoint-based inverse design, avoiding per-iteration PDE solves while ensuring final physical realizability. To further reduce runtime, we introduce a physics-inspired, spatially decoupled inverse design strategy based on the natural locality of field interactions. This approach partitions the metasurface into independently solvable patches, enabling scalable and parallel inverse design with system-level calibration. Evaluated across diverse DONN training tasks, SP²RINT achieves digital-comparable accuracy while being 1825 times faster than simulation-in-the-loop approaches. By bridging the gap between abstract DONN models and implementable photonic hardware, SP²RINT enables scalable, high-performance training of physically realizable meta-optical neural systems.

@misc{ma2025sp2rintspatiallydecoupledphysicsinspiredprogressive,
  title={SP2RINT: Spatially-Decoupled Physics-Inspired Progressive Inverse Optimization for Scalable, PDE-Constrained Meta-Optical Neural Network Training}, 
  author={Pingchuan Ma and Ziang Yin and Qi Jing and Zhengqi Gao and Nicholas Gangi and Boyang Zhang and Tsung-Wei Huang and Zhaoran Huang and Duane S. Boning and Yu Yao and Jiaqi Gu},
  year={2025},
  eprint={2505.18377},
  archivePrefix={arXiv},
  primaryClass={physics.optics},
  url={https://arxiv.org/pdf/2505.18377}, 
}