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Transformers excel at time series modelling through attention mechanisms that capture long-term temporal patterns. However, they assume uniform time intervals and therefore struggle with irregular time series. Neural Ordinary Differential…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…
Spike-based learning with memristive devices in neuromorphic computing architectures typically uses learning circuits that require overlapping pulses from pre- and post-synaptic nodes. This imposes severe constraints on the length of the…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
Complex envelope and reduced phase simulation models describing the dynamical behavior of an optoelectronic oscillator (OEO) under injection by an external source are described. The models are built on the foundations of a previously…
Simulation code for conventional supercomputers serves as a reference for neuromorphic computing systems. The present bottleneck of distributed large-scale spiking neuronal network simulations is the communication between compute nodes.…
Spiking Neural P systems, SNP systems for short, are biologically inspired computing devices based on how neurons perform computations. SNP systems use only one type of symbol, the spike, in the computations. Information is encoded in the…
Optical neural networks (ONNs), or optical neuromorphic hardware accelerators, have the potential to dramatically enhance the computing power and energy efficiency of mainstream electronic processors, due to their ultralarge bandwidths of…
Neural-ODE parameterize a differential equation using continuous depth neural network and solve it using numerical ODE-integrator. These models offer a constant memory cost compared to models with discrete sequence of hidden layers in which…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
Simulation is a third pillar next to experiment and theory in the study of complex dynamic systems such as biological neural networks. Contemporary brain-scale networks correspond to directed graphs of a few million nodes, each with an…
We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integrates Neural Ordinary Differential Equations (Neuro-ODEs) with Continuous Normalizing Flows (CNFs) for stochastic fluid simulation and…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
Spiking Neural Networks (SNNs) emulate the spiking behavior of biological neurons and are typically deployed on distributed-memory neuromorphic hardware. The deployment of a SNN usually requires partitioning the network and mapping these…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Neuromorphic computing systems emulate the electrophysiological behavior of the biological nervous system using mixed-mode analog or digital VLSI circuits. These systems show superior accuracy and power efficiency in carrying out cognitive…