Related papers: Relative Entropy Methods for the Approximation of …

Stochastic thermodynamics is a developing theory for systems out of thermal equilibrium. It allows to formulate a wealth of nontrivial relations among thermodynamic quantities such as heat dissipation, excess work, and entropy production in…

The committor functions are central to investigating rare but important events in molecular simulations. It is known that computing the committor function suffers from the curse of dimensionality. Recently, using neural networks to estimate…

This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…

Here we define and study the properties of retrodictive inference. We derive equations relating retrodiction entropy and thermodynamic entropy, and as a special case, show that under equilibrium conditions, the two are identical. We…

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

The main motivation of this work is to assess the validity of a LWR traffic flow model to model measurements obtained from trajectory data, and propose extensions of this model to improve it. A formulation for a discrete dynamical system is…

We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

Despite a long record of intense efforts, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude a complete understanding. In particular, no unique pathway from kinetic theory to…

Whereas the original Boltzmann's $H$-theorem applies to elastic collisions, its rigorous generalization to the inelastic case is still lacking. Nonetheless, it has been conjectured in the literature that the relative entropy of the velocity…

We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it…

The paradigmatic model of the directed percolation process is studied near its second order phase transition between an absorbing and an active state. The model is first expressed in a form of Langevin equation and later rewritten into a…

We consider systems of conservation laws endowed with a convex entropy. We show the contraction, up to a translation, to extremal entropic shocks, for a pseudo-distance based on the notion of relative entropy. The contraction holds for…

Trajectory optimization with contact-rich behaviors has recently gained attention for generating diverse locomotion behaviors without pre-specified ground contact sequences. However, these approaches rely on precise models of robot dynamics…

We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the…

In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the…

We use the entropy production variational method to associate a one particle distribution function to the assumed known energy-momentum and entropy currents describing a relativistic conformal fluid. Assuming a simple form for the collision…

We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time…

Reaction coordinates (RCs) are low-dimensional representations of complex dynamical systems that capture their long-term dynamics. In this work, we focus on the criteria of lumpability and decomposability, previously established for…