This work investigates the behavior of impurities in edge plasma tokamaks using high-resolution numerical simulations based on Hasegawa–Wakatani equations. Specifically, it focuses inertial particles, which has not been extensively studied field physics. Our utilize one-way coupling a large number point model impurities. We observe that with Stokes (St), characterizes inertia particles being much less than one, such light closely track fluid flow without pronounced clustering. For...

Abstract Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system PDEs, the so-called system. This calls for tailored model order reduction techniques that allow and accurate while guaranteeing physical properties like mass conservation. In this paper, we develop first achieve is accomplished macro-micro decomposition into macroscopic (conservative) part microscopic (non-conservative) with subsequent either...

Abstract The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by three-dimensional direct numerical simulations, limited owing computational complexity. Here, we propose wavelet-based adaptive version the POD (the wPOD), order overcome this limitation. amount data be analyzed reduced compressing them using...

Abstract Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents data-driven approach using reduced order models (ROM) to efficiently model flows in kinetic by comparing two ROM approaches: proper orthogonal decomposition (POD) and autoencoder neural networks (AE). While AE initially demonstrate higher accuracy, POD’s precision improves as more modes considered. Notably, our work recognizes that the...

Abstract This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction–diffusion process. Such systems especially challenging since the transport cannot be captured linear methods. Moreover, topological changes, such as splitting merging of fronts pose difficulties many nonlinear methods and small non-vanishing support underlying partial differential equations dynamics makes most hyper-reduction infeasible. We propose new...

We investigate the SU(3) Yang Mills theory at small gradient flow time and short distances. Lattice spacings down to $a=0.015$ fm are simulated with open boundary conditions allow topology in out. study behaviour of action density $E(t)$ close boundaries, feasibility flow-time expansion extraction $\Lambda$-parameter from static force For latter, significant deviations 4-loop perturbative $\beta$-function visible $\alpha\approx 0.2\,$. still can extrapolate extract $r_0\Lambda$.

We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated by sum of co-moving data fields. proposed methods stem from but optimize fields directly and penalize their nuclear norm promote low rank individual in decomposition. Furthermore, we add robustness term can deal interpolation error noises. Leveraging tools convex optimization, derive three...

Transport-dominated systems are pervasive in both industrial and scientific applications. However, they provide a challenge for common mode-based model order reduction (MOR) approaches, as often require large number of linear modes to obtain sufficiently accurate reduced (ROM). In this work, we utilize the shifted proper orthogonal decomposition (sPOD), methodology tailored MOR transport-dominated systems, combine it with an interpolation based on artificial neural networks (ANN)...

Condensed matter physics of gauge theories coupled to fermions can exhibit a rich phase structure, but are nevertheless very difficult study in Monte Carlo simulations when they afflicted by sign problem. As an alternate approach, we use tensor network methods explore the finite density Abelian without dynamical matter. concrete example, consider U(1) invariant quantum link ladder with spin-1/2 fields external electric field which cause winding fluxes condense ground state. We demonstrate...

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system PDEs, the so-called system. This calls for tailored model order reduction techniques that allow and accurate while guaranteeing physical properties like mass conservation. In this paper, we develop first achieve is accomplished macro-micro decomposition into macroscopic (conservative) part microscopic (non-conservative) with subsequent either...

Parametric model order reduction techniques often struggle to accurately represent transport-dominated phenomena due a slowly decaying Kolmogorov n-width. To address this challenge, we propose non-intrusive, data-driven methodology that combines the shifted proper orthogonal decomposition (POD) with deep learning. Specifically, POD technique is utilized derive high-fidelity, low-dimensional of flow, which subsequently as input learning framework forecast flow dynamics under various temporal...

We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid.The flow map is evolved numerically and exponential resolution in linear time obtained.Global third-order convergence space shown conservation properties are assessed.For benchmarking, we consider nonlinear Landau damping two-stream instability.We compare results Fourier pseudo-spectral from literature.The extreme fine-scale...

This paper presents a neural network-based methodology for the decomposition of transport-dominated fields using shifted proper orthogonal (sPOD). Classical sPOD methods typically require an priori knowledge transport operators to determine co-moving fields. However, in many real-life problems, such is difficult or even impossible obtain, limiting applicability and benefits sPOD. To address this issue, our approach estimates both simultaneously networks. achieved by training two sub-networks...

This work introduces a generalized characteristic mapping method designed to handle non-linear advection with source terms. The semi-Lagrangian approach advances the flow map, incorporating term via Duhamel integral. We derive recursive formula for time decomposition of map and integral, enhancing computational efficiency. Benchmark computations are presented test case an exact solution two-dimensional ideal incompressible magnetohydrodynamics (MHD). Results demonstrate third-order accuracy...

This paper presents a neural network-based methodology for the decomposition of transport-dominated fields using shifted proper orthogonal (sPOD).Classical sPOD methods typically require an priori knowledge transport operators to determine co-moving fields.However, in many real-life problems, such is difficult or even impossible obtain, limiting applicability and benefits sPOD.To address this issue, our approach estimates both simultaneously networks.This achieved by training two...

This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems especially challenging since the transport cannot be captured linear methods. Moreover, topological changes, such as splitting merging of fronts pose difficulties many nonlinear methods and small non-vanishing support underlying partial differential equations dynamics makes most hyper-reduction infeasible. We propose new decomposition...

We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in linear time obtained. Global third-order convergence space shown conservation properties are assessed. For benchmarking, we consider nonlinear Landau damping two-stream instability. compare results Fourier pseudo-spectral method. extreme fine-scale features...

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents data-driven approach using reduced order models (ROM) to efficiently model flows in kinetic by comparing two ROM approaches: Proper Orthogonal Decomposition (POD) and autoencoder neural networks (AE). While AE initially demonstrate higher accuracy, POD's precision improves as more modes considered. Notably, our work recognizes that the classical POD-MOR...