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Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Training

Yequan Zhao, Xian Xiao, Antoine Descos, Yuan Yuan, Xinling Yu, Geza Kurczveil, Marco Fiorentino, Zheng Zhang, Raymond G. Beausoleil

TL;DR

This work tackles the challenge of solving PDEs with physics-informed neural networks on photonic hardware by removing the need for backpropagation and pre-calibration through zeroth-order, BP-free training. The proposed approach implements PINNs on a photonic chip using a 1×4 micro-ring resonator weight bank and wavelength-division multiplexing to perform forward passes, demonstrated on the 1D heat equation with $u_t=\frac{1}{\pi^2}u_{xx}$, initial condition $u(x,0)=\sin(\pi x)$, and boundary conditions. The experimental results achieve an $\,\ell_2$ error of $5\times 10^{-3}$ after 1000 iterations, showing robustness to fabrication variations and noise, while highlighting the impact of bit precision (8–10 bits) on accuracy; simulations indicate 8-bit precision is insufficient. The work outlines scaling strategies to real-size PINNs via tensor-train PINN (TT-PINN) on tensorized ONN (TONN) inference accelerators, enabling real-time PDE Solving on edge devices.

Abstract

Partial differential equation (PDE) is an important math tool in science and engineering. This paper experimentally demonstrates an optical neural PDE solver by leveraging the back-propagation-free on-photonic-chip training of physics-informed neural networks.

Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Training

TL;DR

This work tackles the challenge of solving PDEs with physics-informed neural networks on photonic hardware by removing the need for backpropagation and pre-calibration through zeroth-order, BP-free training. The proposed approach implements PINNs on a photonic chip using a 1×4 micro-ring resonator weight bank and wavelength-division multiplexing to perform forward passes, demonstrated on the 1D heat equation with , initial condition , and boundary conditions. The experimental results achieve an error of after 1000 iterations, showing robustness to fabrication variations and noise, while highlighting the impact of bit precision (8–10 bits) on accuracy; simulations indicate 8-bit precision is insufficient. The work outlines scaling strategies to real-size PINNs via tensor-train PINN (TT-PINN) on tensorized ONN (TONN) inference accelerators, enabling real-time PDE Solving on edge devices.

Abstract

Partial differential equation (PDE) is an important math tool in science and engineering. This paper experimentally demonstrates an optical neural PDE solver by leveraging the back-propagation-free on-photonic-chip training of physics-informed neural networks.
Paper Structure (4 sections, 3 figures)

This paper contains 4 sections, 3 figures.

Table of Contents

  1. Introduction
  2. Principle and Architecture
  3. Experimental Demonstration
  4. Conclusion

Figures (3)

  • Figure 1: (a) PINN framework. (b) Comparison between first-order training and zeroth-order training. (c) First-order training framework of PINN. (d) Zeroth-order training framework of PINN proposed in this work.
  • Figure 2: (a) Schematic of the 1$\times$4 MRR weight bank. (b) Microscope image of the weight bank and the schematic of the experimental setup for on-chip training. (c) Weight curves of the four MRRs.
  • Figure 3: Comparison between the ground truth solution and learned solutions of (a) BP-free training simulation and (b) experimentally demonstrated BP-free on-chip training. (c) The $\ell_2$ error curve of on-chip training. (d) The $\ell_2$ error curve comparison between on-chip training and different simulation setups.