From the 1 of 5 linked papers with an AI index.
5 papers
The Financial Bubble Model with Lévy Jump Processes
Avetik Arakelyan, Rafayel Barkhudaryan, Vigen Khalatyan +1
The paper extends the Berestycki‑Monneau‑Scheinkman model for speculative financial bubbles by adding Lévy jump processes, and develops a viscosity solution theory and a convergent…
A Mean-Field Game Model For Large-Scale Attrition in Attacker-Defender Systems
Avetik Arakelyan, Tigran Bakaryan, Davit Alaverdyan +2
This paper proposes a novel Mean-Field Game (MFG) framework for large-scale attacker-defender systems aimed at protecting one or multiple High-Value Units (HVUs). Motivated by clas…
Numerical Algorithms for Partially Segregated Elliptic Systems
Farid Bozorgnia, Avetik Arakelyan, Vyacheslav Kungurtsev +1
We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise prod…
Gamma Convergence of Partially Segregated Elliptic Systems
Farid Bozorgnia, Avetik Arakelyan
We study partially segregated elliptic systems through the use of penalized energy functionals. These systems arise from the minimization of Gross-Pitaevskii-type energies that cap…
Convergence of Physics-Informed Neural Networks for Fully Nonlinear PDE's
Avetik Arakelyan, Rafayel Barkhudaryan
The present work is focused on exploring convergence of Physics-informed Neural Networks (PINNs) when applied to a specific class of second-order fully nonlinear Partial Differenti…