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The ability to inferring latent psychological traits from human behavior is key to developing personalized human-interacting machine learning systems. Approaches to infer such traits range from surveys to manually-constructed experiments…

A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat…

This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…

Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating…

This paper addresses the challenges of pricing exotic options and structured products, which traditional models often fail to handle due to their inability to capture real-world market phenomena like fat-tailed distributions and volatility…

This paper studies a class of approach-evasion differential games, in which one player aims to steer the state of a dynamic system to the given target set in minimum time, while avoiding some set of disallowed states, and the other player…

This work considers designing an unmanned target hunting system for a swarm of unmanned underwater vehicles (UUVs) to hunt a target with high maneuverability. Differential game theory is used to analyze combat policies of UUVs and the…

Diffusion Models~(DMs) have emerged as the dominant approach in Generative Artificial Intelligence (GenAI), owing to their remarkable performance in tasks such as text-to-image synthesis. However, practical DMs, such as stable diffusion,…

This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…

Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system…

We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Multi-agent games in dynamic nonlinear settings are challenging due to the time-varying interactions among the agents and the non-stationarity of the (potential) Nash equilibria. In this paper we consider model-free games, where agent…

Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory…

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…

Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…

The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more…

We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Existence and regularity of the optimal solutions for…

A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our…

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…