相关论文: NeuroPDE: A Neuromorphic PDE Solver Based on Spint…

The widely parallel, spiking neural networks of neuromorphic processors can enable computationally powerful formulations. While recent interest has focused on primarily machine learning tasks, the space of appropriate applications is wide…

We present a design-scheme for ultra-low power neuromorphic hardware using emerging spin-devices. We propose device models for 'neuron', based on lateral spin valves and domain wall magnets that can operate at ultra-low terminal voltage of…

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

Neuromorphic computing, commonly understood as a computing approach built upon neurons, synapses, and their dynamics, as opposed to Boolean gates, is gaining large mindshare due to its direct application in solving current and future…

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

Despite the promise of superior efficiency and scalability, real-world deployment of emerging nanoelectronic platforms for brain-inspired computing have been limited thus far, primarily because of inter-device variations and intrinsic…

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…

Stochastic diffusion processes are pervasive in nature, from the seemingly erratic Brownian motion to the complex interactions of synaptically-coupled spiking neurons. Recently, drawing inspiration from Langevin dynamics, neuromorphic…

Computing stands to be radically improved by neuromorphic computing (NMC) approaches inspired by the brain's incredible efficiency and capabilities. Most NMC research, which aims to replicate the brain's computational structure and…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…

In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existing methods are constrained by the properties of numerical…

Present day computers expend orders of magnitude more computational resources to perform various cognitive and perception related tasks that humans routinely perform everyday. This has recently resulted in a seismic shift in the field of…

Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.

Neuromorphic computing uses brain-inspired principles to design circuits that can perform computational tasks with superior power efficiency to conventional computers. Approaches that use traditional electronic devices to create artificial…

Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…