Machine learning for fast and reliable solution of time-dependent differential equations
Graph Chatbot
Chattez avec Graph Search
Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.
AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.
We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of th ...
We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the ...
The segmentation of Drosophila is a prime model to study spatial patterning during embryogenesis. The spatial expression of segment polarity genes results from a complex network of interacting proteins whose expression products are maintained after success ...
We prove the existence of quasi-stationary symmetric solutions with exactly n >= 0 zeros and uniqueness for n = 0 for the Schrodinger-Newton model in one dimension and in two dimensions along with an angular momentum m >= 0. Our result is based on an analy ...
Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We descr ...
Modern experimental techniques for the quantitative, time-course measurement of protein concentrations and gene activation levels enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appr ...
Implicit Ordinary or Partial Differential Equations have been widely studied in recent times, essentially from the existence of solutions point of view. One of the main issues is to select a meaningful solution among the infinitely many ones. The most cele ...
The modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupl ...
The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this has the drawbacks of assuming continuous populatio ...
Systems and synthetic biology are two emerging disciplines that hold promise to revolutionize our understanding of biological systems and to herald a new era of programmable hardware, respectively. Mathematical abstraction and today's abundance of quantita ...