Optical neural engine for solving scientific partial differential equations.

Area of Science:

• Computational Science
• Optical Computing
• Machine Learning

Background:

• Solving partial differential equations (PDEs) is crucial for scientific research but computationally intensive.
• Machine learning (ML) offers accelerated solutions, but optical hardware for ML-based PDE solving is underexplored.

Purpose of the Study:

• To introduce and demonstrate an optical neural engine (ONE) architecture for solving diverse PDEs.
• To leverage optical computing's advantages for efficient and high-performance PDE simulations.

Main Methods:

• The ONE architecture combines diffractive optical neural networks (for Fourier space) and optical crossbars (for real space).
• Numerical and experimental validations were performed across multiple scientific disciplines.

Main Results:

• The ONE architecture effectively solves time-dependent and time-independent PDEs, including Darcy flow, magnetostatic Poisson's, Navier-Stokes, and Maxwell's equations.
• It outperforms traditional solvers and matches state-of-the-art ML models in performance.
• Demonstrated low-energy, parallel, constant-time processing with real-time reconfigurability.

Conclusions:

• The ONE architecture provides a versatile platform for large-scale scientific and engineering computations.
• Optical computing hardware enables efficient, high-throughput solutions for complex scientific problems.