Related papers: Neural network-enhanced integrators for simulating…

Deep neural networks (DNN) can be applied at the post-processing stage for the improvement of the results of quantum computations on noisy intermediate-scale quantum (NISQ) processors. Here, we propose a method based on this idea, which is…

Classical simulation is essential in quantum algorithm development and quantum device verification. With the increasing complexity and diversity of quantum circuit structures, existing classical simulation algorithms need to be improved and…

Deep neural networks (DNNs) have been proving the effectiveness in various computing fields. To provide more efficient computing platforms for DNN applications, it is essential to have evaluation environments that include assorted benchmark…

Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their…

Classical state estimation algorithms rely on predefined target's state-space model, which complicates model derivation and limits adaptability when system dynamics change. Neural network based estimators offer a data-driven alternative,…

We investigate the potential of combining the computational power of noisy quantum computers and of classical scalable convolutional neural networks (CNNs). The goal is to accurately predict exact expectation values of parameterized quantum…

Numerical integration (NI) packages commonly used in scientific research are limited to returning the value of a definite integral at the upper integration limit, also commonly referred to as numerical quadrature. These quadrature…

Optimizing recessed-gate AlGaN/GaN MIS-HEMTs requires accurate multi-characteristic models, but experimental semiconductor datasets remain costly and encode process-induced variability that simulations cannot faithfully reproduce. This work…

Hybrid Quantum Neural Networks (HQNNs) have gained attention for their potential to enhance computational performance by incorporating quantum layers into classical neural network (NN) architectures. However, a key question remains: Do…

We explore two classes of exponential integrators in this letter to design nonlinear Fourier transform (NFT) algorithms with a desired accuracy-complexity trade-off and a convergence order of $4$ on an equispaced grid. The integrating…

We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study two new classes of exponential Runge-Kutta (ERK) integrators…

Numerical simulation is a predominant tool for studying the dynamics in complex systems, but large-scale simulations are often intractable due to computational limitations. Here, we introduce the Neural Graph Simulator (NGS) for simulating…

In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is…

Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…

Applying deep neural networks (DNNs) in mobile and safety-critical systems, such as autonomous vehicles, demands a reliable and efficient execution on hardware. Optimized dedicated hardware accelerators are being developed to achieve this.…

This paper presents a novel approach to enhance the Binary-Addition-Tree algorithm (BAT) by integrating incremental learning techniques. BAT, known for its simplicity in development, implementation, and application, is a powerful implicit…

We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear…

Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to…