Related papers: Using ODE waveform-relaxation methods to efficient…

Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose…

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

With the remarkable progress that technology has made, the need for processing data near the sensors at the edge has increased dramatically. The electronic systems used in these applications must process data continuously, in real-time, and…

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections…

Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finite difference or finite element are computationally…

Neuromorphic computing offers an energy-efficient alternative to conventional deep learning accelerators for real-time time-series processing. However, many edge applications, such as wireless sensing and audio recognition, generate…

Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolution equations, the nature of multiscale spatio-temporal…

We are motivated to solve differential algebraic equations with new multi-stage and multisplitting methods. The multi-stage strategy of the waveform relaxation (WR) methods are given with outer and inner iterations. While the outer…

Spiking Neural Network (SNN) is a promising energy-efficient AI model when implemented on neuromorphic hardware. However, it is a challenge to efficiently train SNNs due to their non-differentiability. Most existing methods either suffer…

Current Deep Learning methods for environment segmentation and velocity estimation rely on Convolutional Recurrent Neural Networks to exploit spatio-temporal relationships within obtained sensor data. These approaches derive scene dynamics…

The information of spiking neural networks (SNNs) are propagated between the adjacent biological neuron by spikes, which provides a computing paradigm with the promise of simulating the human brain. Recent studies have found that the time…

A neural network model of a differential equation, namely neural ODE, has enabled the learning of continuous-time dynamical systems and probabilistic distributions with high accuracy. The neural ODE uses the same network repeatedly during a…

We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs). The core element of the method is a SNN, trained to use…

This study investigates the use of continuous-time dynamical systems for sparse signal recovery. The proposed dynamical system is in the form of a nonlinear ordinary differential equation (ODE) derived from the gradient flow of the Lasso…

Direct numerical simulations (DNS) are an indispensable tool for understanding the fundamental physics of turbulent flows. Because of their steep increase in computational cost with Reynolds number ($R_{\lambda}$), well-resolved DNS are…

Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more…

We designed a new artificial neural network by modifying the neural ordinary differential equation (NODE) framework to successfully predict the time evolution of the 2D mode profile in both the linear growth and nonlinear saturated stages.…

Real-time analysis and classification of bio-signals measured using wearable devices is computationally costly and requires dedicated low-power hardware. One promising approach is to use spiking neural networks implemented using in-memory…

This report describes a modification of the orthogonal function Poisson solver for n-body simulations that minimizes relaxation caused by small particle number fluctuations. With the standard algorithm, the noise leading to relaxation can…

Through the Non-Equilibrium Green's Function (NEGF) formalism, quantum-scale device simulation can be performed with the inclusion of electron-phonon scattering. However, the simulation of realistically sized devices under the NEGF…