Related papers: A Neural PDE Solver with Temporal Stencil Modeling

Spiking Neural Networks (SNNs) are considered naturally suited for temporal processing, with membrane potential propagation widely regarded as the core temporal modeling mechanism. However, existing research lack analysis of its actual…

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has…

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

With the fast development of various positioning techniques such as Global Position System (GPS), mobile devices and remote sensing, spatio-temporal data has become increasingly available nowadays. Mining valuable knowledge from…

The ability to simulate the partial differential equations (PDE's) that govern multi-phase flow in porous media is essential for different applications such as geologic sequestration of CO2, groundwater flow monitoring and hydrocarbon…

Spiking Neural Networks (SNNs), with their brain-inspired spatiotemporal dynamics and spike-driven computation, have emerged as promising energy-efficient alternatives to Artificial Neural Networks (ANNs). However, existing SNNs typically…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…

Recent years have witnessed Spiking Neural Networks (SNNs) gaining attention for their ultra-low energy consumption and high biological plausibility compared with traditional Artificial Neural Networks (ANNs). Despite their distinguished…

In several practical applications, particularly healthcare, clinical data of each patient is individually recorded in a database at irregular intervals as required. This causes a sparse and irregularly sampled time series, which makes it…

Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…

Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing. Often, this requires high-resolution or adaptive discretization grids to capture relevant spatio-temporal features in…

Deep learning models have enjoyed great success for image related computer vision tasks like image classification and object detection. For video related tasks like human action recognition, however, the advancements are not as significant…

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study…

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current…

Spatial-temporal Map (STMap)-based methods have shown great potential to process high-angle videos for vehicle trajectory reconstruction, which can meet the needs of various data-driven modeling and imitation learning applications. In this…