Related papers: Solving Sparse Finite Element Problems on Neuromor…
The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain,…
After several decades of continuously optimizing computing systems, the Moore's law is reaching itsend. However, there is an increasing demand for fast and efficient processing systems that can handlelarge streams of data while decreasing…
For over a decade, linear and symmetric weight updates have remained the elusive holy grail in neuromorphic computing. Here, we unveil a kinetically controlled molecular mechanism driving a near-ideal neuromorphic element, capable of…
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…
Mixed-signal neuromorphic systems represent a promising solution for solving extreme-edge computing tasks without relying on external computing resources. Their spiking neural network circuits are optimized for processing sensory data…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
The representation of images in the brain is known to be sparse. That is, as neural activity is recorded in a visual area ---for instance the primary visual cortex of primates--- only a few neurons are active at a given time with respect to…
In this work, we describe a simple finite element approach that is able to resolve weak discontinuities in interface problems accurately. The approach is based on a fixed patch mesh consisting of quadrilaterals, that will stay unchanged…
The scalability of modern computing hardware is limited by physical bottlenecks and high energy consumption. These limitations could be addressed by neuromorphic hardware (NMH) which is inspired by the human brain. NMH enables physically…
Neuromorphic computing offers a transformative pathway to overcome the computational and energy challenges faced in deploying robotic localization and navigation systems at the edge. Visual place recognition, a critical component for…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
It is currently not clear what the potential is of neuromorphic hardware beyond machine learning and neuroscience. In this project, a problem is investigated that is inherently difficult to fully implement in neuromorphic hardware by…
Sparse tiling is a technique to fuse loops that access common data, thus increasing data locality. Unlike traditional loop fusion or blocking, the loops may have different iteration spaces and access shared datasets through indirect memory…
We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in the local space on each mesh cell are evaluated via…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…