Related papers: Integrated photonic multigrid solver for partial d…
Analog photonic solutions offer unique opportunities to address complex computational tasks with unprecedented performance in terms of energy dissipation and speeds, overcoming current limitations of modern computing architectures based on…
Photonic computing has emerged as a promising solution for accelerating computation-intensive artificial intelligence (AI) workloads. However, limited reconfigurability, high electrical-optical conversion cost, and thermal sensitivity limit…
Photonic computing promises faster and more energy-efficient deep neural network (DNN) inference than traditional digital hardware. Advances in photonic computing can have profound impacts on applications such as autonomous driving and…
Optimization problems are central to many important cross-disciplinary applications.In their conventional implementations, the sequential nature of operations imposes strict limitations on the computational efficiency. Here, we discuss how…
The subset sum problem is a typical NP-complete problem that is hard to solve efficiently in time due to the intrinsic superpolynomial-scaling property. Increasing the problem size results in a vast amount of time consuming in…
Photonic computing, with potentials of high parallelism, low latency and high energy efficiency, have gained progressive interest at the forefront of neural network (NN) accelerators. However, most existing photonic computing accelerators…
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…
Multigrid methods are popular iterative methods for solving large-scale sparse systems of linear equations. We present a mixed precision formulation of the multigrid V-cycle with general assumptions on the finite precision errors coming…
Building on the scientific understanding and technological infrastructure of single-mode fibers, multimode fibers are being explored as a means of adding new degrees of freedom to optical technologies such as telecommunications, fiber…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…
Research in photonic computing has flourished due to the proliferation of optoelectronic components on photonic integration platforms. Photonic integrated circuits have enabled ultrafast artificial neural networks, providing a framework for…
With the increasing need for large volumes of data processing, transport, and storage, optimizing the trade-off between high-speed and energy consumption in today's optoelectronic devices is getting increasingly difficult. Heterogeneous…
The need for solving optimization problems is prevalent in a wide range of physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as…
Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
Photonic computing has emerged as a promising substrate for accelerating the dense linear-algebra operations at the heart of AI, yet adoption for large Transformer models remains in its infancy. We identify two bottlenecks: (1) costly…
A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems owing to optical processing with spatial parallelism. However, iterative feedback in the search for optimal solutions limits processing speed…
We present a multigrid algorithm for the solution of the linear systems of equations stemming from the $p-$version of the Virtual Element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed…