Related papers: Integrated photonic multigrid solver for partial d…
The problem of finding the solution of Partial Differential Equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high…
Photonic integrated circuits offer a compact and stable platform for generating, manipulating, and detecting light. They are instrumental for classical and quantum applications. Imperfections stemming from fabrication constraints,…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
The spectra of silicon integrated waveguides are tailored to process analog computing (i.e.,differential and integral) in optical domain with huge bandwidth.With the theory of signal and system, we design some silicon integrated devices to…
As electronic computing approaches its performance limits, photonic accelerators have emerged as promising alternatives. Photonic accelerators exploiting semiconductor-laser synchronization have been studied for decision-making. While…
Modern problems in high-performance computing, ranging from training and inferencing deep learning models in computer vision and language models to simulating complex physical systems with nonlinearly-coupled equations, require exponential…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
Here we show a photonic computing accelerator utilizing a system-level thin-film lithium niobate circuit which overcomes this limitation. Leveraging the strong electro-optic (Pockels) effect and the scalability of this platform, we…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
The rapid surge in data generated by Internet of Things (IoT), artificial intelligence (AI), and machine learning (ML) applications demands ultra-fast, scalable, and energy-efficient hardware, as traditional von Neumann architectures face…
The rapid growth of artificial intelligence, coupled with the slowing of Moore's law, is straining computing infrastructure, as CMOS electronics face inherent limits in bandwidth, energy efficiency, and parallelism. Integrated photonic…
Optical approaches have made great strides towards the goal of high-speed, energy-efficient computing necessary for modern deep learning and AI applications. Read-in and read-out of data, however, limit the overall performance of existing…
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…
As computing resource demands continue to escalate in the face of big data, cloud-connectivity and the internet of things, it has become imperative to develop new low-power, scalable architectures. Neuromorphic photonics, or photonic neural…
In recent decades, the demand for computational power has surged, particularly with the rapid expansion of artificial intelligence (AI). As we navigate the post-Moore's law era, the limitations of traditional electrical digital computing,…
We propose advancing photonic in-memory computing through three-dimensional photonic-electronic integrated circuits using phase-change materials (PCM) and AlGaAs-CMOS technology. These circuits offer high precision (greater than 12 bits),…
Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce a novel architecture of photonic circuits…
For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…