相关论文: Variational Analysis of Landscape Elevation and Dr…
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral triangulations, we rigorously derive the corresponding…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not…
Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima -- at least those discovered by gradient-based optimization -- turn out to be connected by simple paths on which the loss function is almost constant.…
This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…
We show convergence in the natural $L^{\infty}$- and $W^{1,\infty}$-norm for a semidiscretization with linear finite elements of a linear parabolic partial differential equations on evolving surfaces. To prove this we show error estimates…
We seek to establish qualitative convergence results to a general class of evolution PDEs described by gradient flows in optimal transportation distances. These qualitative convergence results come from dynamical systems under the general…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
Landscapes are meaningful ecological units that strongly depend on the environmental conditions. Such dependencies between landscapes and the environment have been noted since the beginning of Earth sciences and cast into conceptual models…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
We consider a linearized dynamical system modelling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model…
The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…
Earth and soils are indispensable elements of river environment. Dam-downstream environment and ecosystems have been severely affected by reduced or even stopped sediment supply from the upstream. Replenishing earth and soils from outside…
The fluctuation of dynamic variables in complex networks is known to depend on the dimension and the heterogeneity of the substrate networks. Previous studies, however, have reported inconsistent results for the scaling behavior of…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
Biological networks such as gene regulatory networks possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated…