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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. 

Abstract Bismuth ferrite has garnered considerable attention as a promising candidate for magnetoelectric spin-orbit coupled logic-in-memory. As model systems, epitaxial BiFeO₃thin films have typically been deposited at relatively high temperatures (650–800 °C), higher than allowed for direct integration with silicon-CMOS platforms. Here, we circumvent this problem by growing lanthanum-substituted BiFeO₃at 450 °C (which is reasonably compatible with silicon-CMOS integration) on epitaxial BaPb_0.75Bi_0.25O₃electrodes. Notwithstanding the large lattice mismatch between the La-BiFeO₃, BaPb_0.75Bi_0.25O₃, and SrTiO₃(001) substrates, all the layers in the heterostructures are well ordered with a [001] texture. Polarization mapping using atomic resolution STEM imaging and vector mapping established the short-range polarization ordering in the low temperature grown La-BiFeO₃. Current-voltage, pulsed-switching, fatigue, and retention measurements follow the characteristic behavior of high-temperature grown La-BiFeO₃, where SrRuO₃typically serves as the metallic electrode. These results provide a possible route for realizing epitaxial multiferroics on complex-oxide buffer layers at low temperatures and opens the door for potential silicon-CMOS integration.