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Graph neural networks (GNNs) are increasingly applied to physical design tasks such as congestion prediction and wirelength estimation, yet progress is hindered by inconsistent circuit representations and the absence of controlled…

We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…

Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…

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…

We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…

In light of the challenges surrounding convergence and error propagation encountered in Reynolds-averaged Navier-Stokes (RANS) equations with data-driven Reynolds stress closures, researchers commonly attribute these issues to…

Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based…

Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a…

Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this…

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

We investigate what can be learned from translating numerical algorithms into neural networks. On the numerical side, we consider explicit, accelerated explicit, and implicit schemes for a general higher order nonlinear diffusion equation…

An equation for the evolution of mean kinetic energy, $ E $, in a 2-D or 3-D Rayleigh-B\'enard system with domain height $ L $ is derived. Assuming classical Nusselt number scaling, $ Nu \sim Ra^{1/3} $, and that mean enstrophy, in the…

Transformer architectures rely on position encodings to model the spatial structure of input data. Rotary Position Encoding (RoPE) is a widely used method in language models that encodes relative positions through fixed, block-diagonal,…

We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…

A novel approach to simulate dynamic, recurrent flows with very large time steps is presented. Data-driven forecasts based on the method of analogues are made employing a set of precomputed time series segments of flow fields. These…

In recent years, sub-grid models for turbulent mixing have been developed by data-driven methods for large eddy simulation (LES). Super-resolution is a data-driven deconvolution technique in which deep convolutional neural networks are…

In this paper, we investigate the nonlinear stability of the Couette flow for the two-dimensional compressible Navier--Stokes equations at high Reynolds numbers ($Re$) regime. It was proved that if the initial data $(\rho_{in},u_{in})$…

A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number $Re$. We consider active, predetermined strategies based…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are…