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Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations. 

With the ever-increasing hardware design complexity comes the realization that efforts required for hardware verification increase at an even faster rate. Driven by the push from the desired verification productivity boost and the pull from leap-ahead capabilities of machine learning (ML), recent years have witnessed the emergence of exploiting ML-based techniques to improve the efficiency of hardware verification. In this article, we present a panoramic view of how ML-based techniques are embraced in hardware design verification, from formal verification to simulation-based verification, from academia to industry, and from current progress to future prospects. We envision that the adoption of ML-based techniques will pave the road for more scalable, more intelligent, and more productive hardware verification.