Related papers: Differentiable physics-enabled closure modeling fo…
Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
Data-driven turbulence modeling studies have reached such a stage that the fundamental framework is basically settled, but several essential issues remain that strongly affect the performance, including accuracy, smoothness, and…
This paper is a synopsis of the recent book A. Boritchev, S. Kuksin, \textit{One-Dimensional Turbulence and the Stochastic Burgers Equation}, AMS Publications, 2021 (to appear). The book is dedicated to the stochastic Burgers equation as a…
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…
We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of…
The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and…
The Burgers equation is a well-established test case in the computational modeling of several phenomena such as fluid dynamics, gas dynamics, shock theory, cosmology, and others. In this work, we present the application of Physics-Informed…
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers,…
We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on…
Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…
Filtered budgets for anelastic turbulence and a general expression of the turbulent sensible heat flux are derived for a multicomponent fluid with an arbitrary equation of state. A family of subgrid-scale closures is then found under the…
Learning to integrate non-linear equations from highly resolved direct numerical simulations (DNSs) has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock…
In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…
Burgers equation is one of the simplest nonlinear partial differential equations-it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a…
Accurate subgrid-scale closures are essential for weather/climate models, where predicting extreme events is critical. Traditional closures have structural errors, e.g., producing excessive diffusion that dampens extremes. Artificial…
The applicability of computational fluid dynamics (CFD) based design tools depend on the accuracy and complexity of the physical models, for example turbulence models, which remains an unsolved problem in physics, and rotor models that…
We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schr\"{o}dinger boundary data problem for the random matter transport. This entails…
Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This…