相关论文: Variational Analysis of Landscape Elevation and Dr…

Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been…

Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral…

The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is…

In this paper, we study the forcing of baroclinic critical levels, which arise in stratified fluids with horizontal shear flow along the surfaces where the phase speed of a wave relative to the mean flow matches a natural internal…

Rugged (or, rough) energy landscape (REL) with spatially distributed maxima and minima are often employed in applications of physics, chemistry and biology (enzyme kinetics, protein folding, diffusion in disordered solids, transport in…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms:…

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…

The dynamics of many natural systems is dominated by non-linear waves propagating through the medium. We show that the dynamics of non-linear wave fronts with positive surface tension can be formulated as a gradient system. The variational…

The landscape of computer graphics has undergone significant transformations with the recent advances of differentiable rendering models. These rendering models often rely on heuristic designs that may not fully align with the final…

We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…

The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that…

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…

Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different…

In this paper we follow up the study of 'complex complex landscapes,' rugged landscapes of many complex variables. Unlike real landscapes, the classification of saddles by index is trivial. Instead, the spectrum of fluctuations at…

Desert surfaces are typically non uniform, with individual sand dunes generally surrounded by gravel or non-erodible beds. Similarly, beaches vary in composition and moisture that enhances cohesion between the grains. These bed…