The next phase of LHC Operations-High Luminosity LHC (HL-LHC), which is aimed at ten-fold increase in the luminosity of proton-proton collisions at the energy of 14 TeV, is expected to start operation in 2027-2028 and...
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High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorith...
High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naïvely, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. In addition, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods.
High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorith...
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The numerical method based on the discontinuous Galerkin (DG) approach for perfect inviscid compressible gas dynamics modelling is developed. The approximate Riemann solvers in combination with gas dynamics equations ...
The numerical method based on the discontinuous Galerkin (DG) approach for perfect inviscid compressible gas dynamics modelling is developed. The approximate Riemann solvers in combination with gas dynamics equations system characteristic properties are used to calculate the numerical fluxes on the cells interfaces and inside the cells. A number of approximate Riemann solvers are considered. The solution characteristic decomposition is used in the similar to PPML way. The developed algorithm is tested using problems with smooth and discontinuous solutions. Both one-dimensional and two-dimensional test problems are considered. The method provides accurate discontinuity resolution and ability to compute gas-dynamic instabilities with minimal artificial distortion.
The paper presents results of simulation and optimization of the processes taking place in a fuel system injector. Simula-tion has been carried using tools of the OpenFOAM system. The problem of differential pressure ...
The paper presents results of simulation and optimization of the processes taking place in a fuel system injector. Simula-tion has been carried using tools of the OpenFOAM system. The problem of differential pressure minimization at the injector inlet and outlet was set and solved. This problem was considered as a Lipschitz optimization problem with a black-box type objective function. To solve it, we used an efficient global search algorithm implemented in the Globalizer system.
– In this paper, we study the black box optimization problem under the Polyak–Lojasiewicz (PL) condition, assuming that the objective function is not just smooth, but has higher smoothness. By using "kernel-bas...
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Formation of the platelet plug represents a primary response to the vessel wall injury, but may also result in vessel occlusion. The decrease of the local blood flow due to platelet thrombus formation may lead to seri...
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The work presents results of the application of a new OpenFOAM® solver QGDFoam for the numerical simulation of viscous compressible flows in a wide range of Mach numbers. The new solver is based on the explicit a...
The work presents results of the application of a new OpenFOAM® solver QGDFoam for the numerical simulation of viscous compressible flows in a wide range of Mach numbers. The new solver is based on the explicit approximation of regularized, or quasi-gas dynamic (QGD) equations. The mixed finite-volume and finite-difference approximation is constructed on unstructured spatial grids with co-located variables storage. The solver has been tested for a number of 1D Riemann problems (Sod’s problem, Noh test and others) and 2D cases (Mach 3 forward step, Ladenburg supersonic jet flow with Mach reflection, NASA Langley supersonic overexpanded jet flow and subsonic laminar flow over a backward-facing step). Results of numerical simulations were compared with analytic solutions and OpenFOAM® implementation of the Kurganov-Tadmor scheme, known as rhoCentralFoam. The testing procedure has shown that whereas QGD algorithm is more diffusive than Godunov-type methods with 2nd order TVD schemes with limiters, it is far less diffusive compared with pure upwind schemes as HLL. It was shown that OpenFOAM implementation of the QGD algorithm allows to compute successfully subsonic, sonic and supersonic flows, while other OpenFOAM® solvers have a very limited operational Mach number range. Preliminary results of QGDFoam application for large-scale 3D problems are presented. Scaling tests for up to 768 cores showed good scalability of QGDFoam solver.
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