Related papers: Neural networks for learning macroscopic chemotact…
Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
This paper deals with the micro-macro derivation of virus models coupled with a reaction diffusion models that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [5, 6] on a…
Inferring parameters of macro-kinetic growth models, typically represented by Ordinary Differential Equations (ODE), from the experimental data is a crucial step in bioprocess engineering. Conventionally, estimates of the parameters are…
We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased random walk. In order to take into account…
The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often the variability of…
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc.…
Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such hydrodynamic parameters are difficult to derive from microscopics. Seldom is this challenge more…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…
Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
In this paper we propose a numerical study of macroscopic models for collective cell migration, focusing on a multi-dimensional pressureless Euler-type model with non-local interactions coupled with chemotaxis, rigorously derived from…
We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…
We demonstrate a machine learning based approach which can learn the time-dependent electronic excitation dynamics of small molecules subjected to ion irradiation. Ensembles of recurrent neural networks are trained on data generated by…
Machine learning techniques including neural networks are popular tools for materials and chemical scientists with applications that may provide viable alternative methods in the analysis of structure and energetics of systems ranging from…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
The analysis of the size of nanoparticles is an essential task in plasma technology and dusty plasmas. Light scattering techniques, based on Mie theory, can be used as a non-invasive and in-situ diagnostic tool for this purpose. However,…