Related papers: Multitime hybrid differential games with curviline…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
This paper concerns the design of a multidimensional Chebyshev interpolation based method for a differential game theory problem. In continuous game theory problems, it might be difficult to find analytical solutions, so numerical methods…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been…
Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…
Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…
Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…
Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the…
The properties of value functions of time inhomogeneous optimal stopping problem and zero-sum game (Dynkin game) are studied through time dependent Dirichlet form. Under the absolute continuity condition on the transition function of the…
Game theory offers an interpretable mathematical framework for modeling multi-agent interactions. However, its applicability in real-world robotics applications is hindered by several challenges, such as unknown agents' preferences and…
This paper is dealing with another multiple person game model under the antagonistic duel type setup. The most flexible multiple person duel game is analytically solved and the explicit formulas are solved to determine the time dependent…
Due to their complex dynamics, combinatorial games are a key test case and application for algorithms that train game playing agents. Among those algorithms that train using self-play are coevolutionary algorithms (CoEAs). However, the…
In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence…
We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary.…
We extend the constructive differential game logic (CdGL) of hybrid games with a refinement connective that relates two hybrid games. We use this connective to prove a folk theorem relating hybrid games to hybrid systems.
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
In the present paper invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations (FPDEs) involving both time and space fractional derivatives. Further the method has also been…
In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are…