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The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…

In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

Stormwater infrastructures are decentralized urban water-management systems that face highly unsteady hydraulic and pollutant loadings from episodic rainfall-runoff events. Accurately evaluating their in-situ treatment performance is…

Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…

Traditional fluid flow predictions require large computational resources. Despite recent progress in parallel and GPU computing, the ability to run fluid flow predictions in real-time is often infeasible. Recently developed machine learning…

This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes…

In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…

Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use…

This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…

In this paper, we present a novel approach for fluid dynamic simulations by harnessing the capabilities of Physics-Informed Neural Networks (PINNs) guided by the newly unveiled principle of minimum pressure gradient (PMPG). In a PINN…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited…

Optical flow estimation is a classical yet challenging task in computer vision. One of the essential factors in accurately predicting optical flow is to alleviate occlusions between frames. However, it is still a thorny problem for current…

This work investigates transfer learning strategies to accelerate deep reinforcement learning (DRL) for multifidelity control of chaotic fluid flows. Progressive neural networks (PNNs), a modular architecture designed to preserve and reuse…

The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…

We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the…

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear…

Understanding shock-solid interactions remains a central challenge in compressiblefluiddynamics. WepresentJAX-Shock: afully-differentiable,GPU-accelerated, high-order shock-capturing solver for efficient simulation of the compressible…

Machine Learning is beginning to provide state-of-the-art performance in a range of environmental applications such as streamflow prediction in a hydrologic basin. However, building accurate broad-scale models for streamflow remains…