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Simulations of large-scale plasma systems are typically based on a fluid approximation approach. These models construct a moment-based system of equations that approximate the particle-based physics as a fluid, but as a result lack the…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
When simulating multiscale systems, where some fields cannot be fully prescribed despite their effects on the simulation's accuracy, closure models are needed. This phenomenon is observed in turbulent fluid dynamics, where Large Eddy…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of…
Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers.…
Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…
We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is non-local both in space and time, i.e. the closure terms are…
Nonlinear plasma physics problems are usually simulated through comprehensive modeling of phase space. The extreme computational cost of such simulations has motivated the development of multi-moment fluid models. However, a major challenge…
Numerical simulations of turbulent flows are well known to pose extreme computational challenges due to the huge number of dynamical degrees of freedom required to correctly describe the complex multi-scale statistical correlations of the…
Turbulence in fluids, gases, and plasmas remains an open problem of both practical and fundamental importance. Its irreducible complexity usually cannot be tackled computationally in a brute-force style. Here, we combine Large Eddy…
We show how a complete mathematical description of a complicated physical phenomenon can be learned from observational data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality,…
Many phenomena in collisionless plasma physics require a kinetic description. The evolution of the phase space density can be modeled by means of the Vlasov equation, which has to be solved numerically in most of the relevant cases. One of…
Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually…
At the core of some of the most important problems in plasma physics -- from controlled nuclear fusion to the acceleration of cosmic rays -- is the challenge to describe nonlinear, multi-scale plasma dynamics. The development of reduced…
In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be…
The inclusion of kinetic effects into fluid models has been a long standing problem in magnetic reconnection and plasma physics. Generally the pressure tensor is reduced to a scalar which is an approximation used to aid in the modeling of…
The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics. Any simulation based on a fluid model inherently requires a closure relation for the high order plasma…
In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…