arXiv subjects

Pavel Popov

Publications and source records attributed to Pavel Popov.

6 recordsLinked to original sources

arXiv2026

CodeJeNN: A simple C++ neural network generator for physics applications

Machine learning has shown speedups for numerical methods in physics applications, but integrating Python-based libraries into high-performance C++ solvers creates performance bottlenecks. We present CodeJeNN, which bridges this gap by auto-generating self-contained C++ code from trained Keras models for inference. This eliminates external dependencies through minimal inlined functions, allowing seamless integration into existing frameworks. We describe the Keras-to-C++ workflow, supported architectures, and limitations. CodeJeNN is demonstrated through inference benchmarks against Keras in eager and JIT modes and a CFD test case modeling viscosity in a hydrogen-air mixing layer, showing speedups without sacrificing accuracy.

physics.comp-ph↗

arXiv2026

Hotspot-Aware Scheduling of Virtual Machines with Overcommitment for Ultimate Utilization in Cloud Datacenters

We address the problem of under-utilization of resources in datacenters during cloud operations, specifically focusing on the challenge of online virtual machine (VM) scheduling. Rather than following the traditional approach of scheduling VMs based solely on their static flavors, we take into account their dynamic CPU utilization. We employ $Γ$-robustness theory to manage the dynamic nature and introduce a novel variant of bin packing - Probabilistic k-Bins Packing (PkBP), which theoretically protects the Physical Machines (PMs) from hotspots formation within a specified probability $α$. We develop a scheduling algroithm named CloseRadiusFit and cold-start AI based prediction algorithms for the online version of PkBP. To verify the quality of our approach towards the optimal solutions, we solve the Offline PkBP problem by designing a novel Mixed Integer Linear Programming (MILP) model and a combination of numerical upper and lower bounds. Our experimental results demonstrate that CloseRadiusFit achieves narrow gaps of 1.6% and 3.1% when compared to the lower and upper bounds, respectively.

cs.DC↗

arXiv2023

BalCon -- resource balancing algorithm for VM consolidation

Cloud providers handle substantial number of requests to create and delete virtual machines (VMs) on a daily basis, where the unknown sequence of requests eventually leads to resource fragmentation. To mitigate this issue, periodic consolidation of VMs into fewer number of physical hosts is an important cost-saving procedure, closely related to the vector bin-packing problem. In this paper, we propose the BalCon algorithm for consolidation that steadily reduces the number of active hosts and keeps migration costs low. BalCon classifies the cluster's state and selects one of three heuristics to balance resources for superior consolidation. To evaluate BalCon's performance with respect to optimality, we introduce integer programming models. BalCon finds 99.7% of the optimal solutions for over 750 problem instances. This outstanding result was achieved due to the Force Step of our algorithm, which is the key improvement detail for common heuristics. We compare BalCon with a modified Sercon heuristic using Huawei and synthetic datasets with two resources for allocation.

cs.DS↗

arXiv2023

Analysis of an Explicit, High-Order Semi-Lagrangian Nodal Method

A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport equations and uses a least-square fit to correct the update for interface constraints of neighbouring elements. By assuming a monomial representation instead of the Lagrange form, a discrete version of the algorithm on a single element is derived. The resulting algebraic system lends itself to both a Modified Equation analysis and an eigenvalue analysis. The Modified Equation analysis, which Taylor expands the stencil at a single space location and time instance, shows that the semi-Lagrangian method is consistent with the PDE form of the transport equation in the limit that the element size goes to zero. The leading order truncation term of the Modified Equation is of the order of the degree of the interpolant which is consistent with numerical tests reported in the literature. The dispersion relations show that the method is negligibly dispersive, as is common for semi-Lagrangian methods. An eigenvalue analysis shows that the semi-Lagrangian method with a nodal Chebyshev interpolant is stable for a Courant-Friedrichs-Lewy condition based on the minimum collocation node spacing within an element that is greater than unity.

math.NA↗

arXiv2019

On pairs, triples and quadruples of points on a cubic surface

Let $X^{(n)}$ denote $n$-th symmetric power of a cubic surface $X$. We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$, despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$.

math.AG↗

arXiv2018

Twisted cubics and quadruples of points on cubic surfaces

We study relations in the Grothendieck ring of varieties which connect the Hilbert scheme of points on a cubic hypersurface $Y$ with a certain moduli space of twisted cubic curves on $Y$. These relations are generalizations of the "beautiful" $Y$-$F(Y)$ relation by Galkin and Shinder which connects $Y$ with the Hilbert scheme of two points on $Y$ and the Fano variety $F(Y)$ of lines on $Y$. We concentrate mostly on the case of cubic surfaces. The symmetries of $27$ lines on a smooth cubic surface give a lot of restrictions on possible forms of the relations.

math.AG↗