Related papers: A gradient flow approach to quantization of measur…
This paper introduces new methods to study the long time behaviour of the generalised gradient flow associated with a solution of the critical equation for mechanical Hamiltonian system posed on the flat torus $\mathbb{T}^d$. For this…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
We give a direct construction of invariant measures and global flows for the stochastic quantization equation to the quantum field theoretical $\Phi ^4_3$-model on the $3$-dimensional torus. This stochastic equation belongs to a class of…
In this manuscript, we show how flow equation methods can be used to study localisation in disordered quantum systems, and particularly how to use this approach to obtain the non-equilibrium dynamical evolution of observables. We review the…
We prove three related quantitative results for the relative isoperimetric problem outside a convex body $\Omega$ in the plane: (1) {\L}ojasiewicz estimates and quantitative rigidity for critical points, (2) rates of convergence for the…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary…
This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with…
We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…
Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult…
We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger…
Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…