We discuss the possibility of learning a data-driven explicit model correction for inverse
problems and whether such a model correction can be used within a variational framework …

This paper deals with a parabolic–elliptic chemotaxis system with nonlinear sensitivity and
logistic source {ut= Δ u− χ∇⋅(ψ (u)∇ v)+ f (u),(x, t)∈ Ω×(0,∞), 0= Δ v− v+ g (u),(x, t)∈ …

The aim of this paper is to study a PDE model for two diffusing species interacting by local
size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion …

Chemotaxis is the physical phenomenon that bacteria adjust their motions according to
chemical stimulus. A classical model for this phenomenon is a kinetic equation that …

This study utilizes an ensemble of feedforward neural network models to analyze large-
volume and high-dimensional consumer touchpoints and their impact on purchase …

We consider the identifiability and stable numerical estimation of multiple parameters in a
Cahn–Hilliard model for phase separation. Spatially resolved measurements of the phase …

In this paper, we consider the fast numerical solution of an optimal control formulation of the
Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the …

We present a framework enabling variational data assimilation for gradient flows in general
metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) …

We consider the identification of nonlinear diffusion coefficients of the form $ a (t, u) $ or $ a
(u) $ in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is …

We discuss the control of a human crowd whose dynamics is governed by a regularized
version of Hughes' model, cf. Hughes (Transp Res Part B: Methodol 36 (6): 507–535, 2002 …