Related papers: A Neural PDE Solver with Temporal Stencil Modeling

Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…

Accurate simulation of turbulent flows remains a challenge due to the high computational cost of direct numerical simulations (DNS) and the limitations of traditional turbulence models. This paper explores a novel approach to augmenting…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Spatial-temporal forecasting and imputation are important for real-world intelligent systems. Most existing methods are tailored for individual forecasting or imputation tasks but are not designed for both. Additionally, they are less…

Reservoir computing (RC), is a class of computational methods such as Echo State Networks (ESN) and Liquid State Machines (LSM) describe a generic method to perform pattern recognition and temporal analysis with any non-linear system. This…

The modeling, computational cost, and accuracy of traditional Spatio-temporal networks are the three most concentrated research topics in video action recognition. The traditional 2D convolution has a low computational cost, but it cannot…

We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…

Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

The rapid advancement of Intelligent Transportation Systems (ITS) presents challenges, particularly with missing data in multi-modal transportation and the complexity of handling diverse sequential tasks within a centralized framework. To…

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…

Recursive reasoning models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) show that small, weight-shared networks can solve compute-heavy and NP puzzles by iteratively refining latent states, but their training…

Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes,…

Time series forecasting (TSF) is critical across domains such as finance, meteorology, and energy. While extending the lookback window theoretically provides richer historical context, in practice, it often introduces irrelevant noise and…

Sensing is a universal task in science and engineering. Downstream tasks from sensing include inferring full state estimates of a system (system identification), control decisions, and forecasting. These tasks are exceptionally challenging…

We develop time-series machine learning (ML) methods for closure modeling of the Unsteady Reynolds Averaged Navier Stokes (URANS) equations applied to stably stratified turbulence (SST). SST is strongly affected by fine balances between…

Deep learning has become a one-size-fits-all solution for technical and business domains thanks to its flexibility and adaptability. It is implemented using opaque models, which unfortunately undermines the outcome trustworthiness. In order…

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…

Finite-difference methods are widely used in solving partial differential equations. In a large problem set, approximations can take days or weeks to evaluate, yet the bulk of computation may occur within a single loop nest. The modelling…