Related papers: Hessian transport gradient flows
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao…
Transport equations for even-order structure functions are written for a passive scalar mixing fed by a mean scalar gradient, with a Schmidt number $\mathit{Sc}=1$. Direct numerical simulations (DNS), in a range of Reynolds numbers…
Using the Lagrangian transport of momentum, the Reynolds shear stress can be expressed in terms of basic turbulence parameters. In this view, the Reynolds stress gradient represents the lateral transport of streamwise momentum, balanced by…
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…
Recent DNS results [Gerolymos G.A., Vallet I. : J. Fluid Mech. 807 (2016) 386--418] have provided data for the terms in the transport equations for the components of the dissipation tensor $\varepsilon_{ij}$ in low-Reynolds turbulent plane…
Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over…
We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. The volatility process…
*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…
Gradient-flow sampling interprets a Gibbs distribution as the minimizer of an energy functional over probability measures and generates dynamics converging to this target. Under spherical Hellinger-Kantorovich (SHK) geometry, the flow…
We formulate a trajectorial version of the relative entropy dissipation identity for McKean$-$Vlasov diffusions, extending the results of the papers [FJ16,KST20a], which apply to non-interacting diffusions. Our stochastic analysis approach…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
Modeling the velocity gradient tensor A along Lagrangian trajectories in turbulent flow requires closures for the pressure Hessian and viscous Laplacian of A. Based on an Eulerian-Lagrangian change of variables and the so-called Recent…
We derive quantum Boltzmann equations from Schwinger-Dyson equations in gradient expansion for a weakly coupled scalar field theory with a spatially varying mass. We find that at higher order in gradients a full description of the system…
We derive equations for fluid dynamics from a non-extensive Boltzmann transport equation consistent with Tsallis' non-extensive entropy formula. We evaluate transport coefficients employing the relaxation time approximation and investigate…
This paper investigates the gradient flow structure, well-posedness, and asymptotic behavior of the Fokker-Planck equation defined on locally uniformly finite graphs, which is highly non-trivial compared with the finite case. We first…
We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to…
We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in…
Let $\Cl$ denote the Clifford algebra over $\R^n$, which is the von Neumann algebra generated by $n$ self-adjoint operators $Q_j$, $j=1,...,n$ satisfying the canonical anticommutation relations, $Q_iQ_j+Q_jQ_i = 2\delta_{ij}I$, and let…