Related papers: Solving Sparse Finite Element Problems on Neuromor…
We introduce a methodology to implement the physiological transition {between distinct neuronal spiking modes} in electronic circuits composed of resistors, capacitors and transistors. The result is a simple neuromorphic device organized by…
Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational…
Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
All systolic or distributed neuromorphic architectures require power-efficient processing nodes. In this paper, a unifying tutorial is presented which implements multiple neuromorphic processing elements using a systematic analog approach…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Recent advances in memory technologies, devices and materials have shown great potential for integration into neuromorphic electronic systems. However, a significant gap remains between the development of these materials and the realization…
Machine learning applications that are implemented with spike-based computation model, e.g., Spiking Neural Network (SNN), have a great potential to lower the energy consumption when they are executed on a neuromorphic hardware. However,…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
Recent work suggests that synaptic plasticity dynamics in biological models of neurons and neuromorphic hardware are compatible with gradient-based learning (Neftci et al., 2019). Gradient-based learning requires iterating several times…
We introduce a new method for representing the low energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the…
The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anisotropic meshes for a test problem which combines several…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
Noisy intermediate-scale quantum (NISQ) devices offer unique platforms to test and evaluate the behavior of non-fault-tolerant quantum computing. However, validating programs on NISQ devices is difficult due to fluctuations in the…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
This paper introduces a novel approach in neuromorphic computing, integrating heterogeneous hardware nodes into a unified, massively parallel architecture. Our system transcends traditional single-node constraints, harnessing the neural…
We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
In this paper, finite element method is applied to Leland's model for numerical simulation of option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated in combination with a…