Related papers: Pathwise estimates for effective dynamics: the cas…

We present a time dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off variational path sampling methodology…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the…

We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…

When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…

We apply the non-linear flow response formalism to the recently measured event plane correlations. We find that as a result of the combined effects of linear and non-linear flow response, the observed event plane correlations can be…

We present a new formulation of ab initio molecular dynamics which exploits the efficiency of plane waves in adaptive curvilinear coordinates, and thus provides an accurate treatment of first-row elements. The method is used to perform a…

We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong $L^1$-convergence of a suitable deterministic particle approximation to weak…

The article is devoted to the dynamics of systems with an anomalous scaling near a critical point. The fractional stochastic equation of a Lanvevin type with the $\varphi^3$ nonlinearity is considered. By analogy with the model A the field…

Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…

We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into…

Trajectory estimation of maneuvering objects is applied in numerous tasks like navigation, path planning and visual tracking. Many previous works get impressive results in the strictly controlled condition with accurate prior statistics and…

We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…

The direct effect of one eventon another can be defined and measured byholding constant all intermediate variables between the two.Indirect effects present conceptual andpractical difficulties (in nonlinear models), because they cannot be…

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional…

Nonlinear dynamics can impact the performance of a particle accelerator in a number of different ways, depending on the type of the accelerator and the parameter regime in which it operates. Effects can range from minor changes in beam…

Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social…

Sequential experimental design to discover interventions that achieve a desired outcome is a key problem in various domains including science, engineering and public policy. When the space of possible interventions is large, making an…