Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks

2025-02-17

AI Summary

Addressing the challenge of training large-scale physics-informed neural networks (PINNs) on silicon photonic chips—hindered by the absence of on-chip photonic memory, large device footprints, and incompatibility with backpropagation—this work proposes the first photonic PINN training framework tailored for edge-deployable, real-time, low-power partial differential equation (PDE) solving. Our method eliminates backpropagation via a sparse-grid Stein derivative estimator for gradient-free training; employs tensor-train decomposition to enable dimensionality-reduced, zeroth-order optimization; and introduces a scalable photonic tensor kernel hardware architecture. Evaluated on both low- and high-dimensional PDE benchmarks, the framework demonstrates robust convergence. Circuit-level simulations show over 60% reduction in chip area, two orders-of-magnitude improvement in energy efficiency, and real-time latency—significantly advancing the feasibility of photonic acceleration for scientific machine learning at the edge.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs), with growing interest in their energy-efficient, real-time training on edge devices. Photonic computing offers a potential solution to achieve this goal because of its ultra-high operation speed. However, the lack of photonic memory and the large device sizes prevent training real-size PINNs on photonic chips. This paper proposes a completely back-propagation-free (BP-free) and highly salable framework for training real-size PINNs on silicon photonic platforms. Our approach involves three key innovations: (1) a sparse-grid Stein derivative estimator to avoid the BP in the loss evaluation of a PINN, (2) a dimension-reduced zeroth-order optimization via tensor-train decomposition to achieve better scalability and convergence in BP-free training, and (3) a scalable on-chip photonic PINN training accelerator design using photonic tensor cores. We validate our numerical methods on both low- and high-dimensional PDE benchmarks. Through circuit simulation based on real device parameters, we further demonstrate the significant performance benefit (e.g., real-time training, huge chip area reduction) of our photonic accelerator.

Problem

• BP-free training of PINNs
• Scalable photonic chip implementation
• Real-time PDE solving efficiency

Innovation

• Back-propagation-free training method
• Sparse-grid Stein derivative estimator
• On-chip photonic tensor cores