Math and Research

Stability of hyperbolic systems with non-symmetric partial dissipation By Timothée Crin-Barat Introduction In this post, we report new results for ...

Neural ODEs for interpolation and transport: From tight to shallow By Arselane Hadj Slimane, Internship. Master Student. ENS Paris-Saclay Introduction ...

Combined convection and diffusion in a network. A numerical analysis. By Dragoș Manea, Visiting PhD Student. Simion Stoilow Mathematical Institute ...

The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach By Yongcun Song, Postdoctoral Researcher at FAU DCN-AvH ...

Reinforcement learning as a new perspective into controlling physical systems By Theïlo Terrisse, Visiting PhD Student. L’Ecole des Ponts ParisTech ...

Null controllability for population dynamics with age, size structuring and diffusion By Yacouba Simpore, Visiting scientist from University of Fada ...

Breaking the symmetry with Robin boundary conditions By Alba Lia Masiello, Visiting PhD student from University of Naples Federico II ...

Convolutional autoencoders for very low-dimensional parametrizations of nonlinear fluid flow By Jan Heiland, MPI for Dynamics of Complex Technical Systems ...

Torsional Rigidity: Classical and new results By Gloria Paoli, Postdoctoral Researcher at FAU DCN-AvH Torsional rigidity is a key quantity ...

Analysis of a local-nonlocal polymer chain model By Jean-Daniel Djida, Postdoctoral Researcher at FAU DCN-AvH What does the mathematics of ...

Federated Learning: Protect your data and privacy By Ziqi Wang, PhD student at FAU DCN-AvH Code: A basic PyTorch implementation ...

Breaking the curse of dimensionality with Barron spaces By Antonio Álvarez López 1 Introduction Recent advances in computational hardware have ...

Stability results for the KdV equation with time-varying delay By Hugo Parada Ríos Introduction The Korteweg-de Vries equation (KdV), is ...

Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs) By Dania Sana Introduction Accurate and fast predictions of ...

Gas networks at stationary states: Analysis, software and visualization By Veronika Riedl Code: Files to run: nocircle.m, onecircle.m or twocircles.m ...

Author: Daniël Veldman, FAU DCN-AvH Code: A sheep herding game in MATLAB developed for the Long Night of Science #NdW22 ...

Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd's algorithm. Also called Voronoid iteration, ...

Using the support function for optimal shape design By Ilias Ftouhi 1 Motivation Led by problems of optimal placement and ...

Uniform Turnpike Property By Martín Hernández Salinas 1 Introduction In this post, we analyze a 1 − d heat equation ...

Author: Borjan Geshkovski, MIT The interplay of control and Deep Learning By Borjan Geshkovski It is superfluous to state the ...

Nonlinear hyperbolic systems: Modeling, controllabiliy and applications By Yue Wang The control theory of hyperbolic systems is an important topic ...

Kinetic theory of Bose Einstein Condensates By Minh-Binh Tran If a dilute gas of bosons, about one-hundred-thousandth the density of ...

Author: Martin Gugat, Enrique Zuazua, Aleksey Sikstel, FAU DCN-AvH Code:   [HINT] To run the software on your computer, you ...

Author: Carlos Esteve, Deusto CCM Code: In a previous post "Inverse Design For Hamilton-Jacobi Equations", described all the possible initial ...

Author: Daniel Veldman, FAU DCN-AvH Code: || Also available @Daniël's GitHub In a previous post "Randomized time-splitting in linear-quadratic optimal ...

Author: Alexei Gazca, FAU DCN-AvH Code:   Below is a description of the types of problems that can be tackled ...

Transition Layers in Elliptic Equations By Maicon Sônego Stable transition layers in an unbalanced bistable equation Consider the following semi-linear ...

Randomized time-splitting in linear-quadratic optimal control By Daniël Veldman Introduction Solving an optimal control problem for a large-scale dynamical system ...

Felix Klein: A Legacy of Innovation in Mathematics and Education By Roberto Rodríguez del Río, Complutense University of Madrid | ...

Control of Advection-Diffusion Equations on Networks and Singular Limits By Jon Asier Bárcena-Petisco, Márcio Cavalcante, Giuseppe Maria Coclite, Nicola de ...

Probabilistic Constrained Optimization on Flow Networks By Michael Schuster This research was funded by DFG in the SFB Transregio 154: ...

Perceptrons, Neural Networks and Dynamical Systems By Sergi Andreu // This post is last part of the "Deep Learning and ...

Deep Learning and Paradigms By Sergi Andreu // This post is the 2nd. part of the "Opening the black box ...

Opening the black box of Deep Learning By Sergi Andreu Deep Learning is one of the three main paradigms of ...

Averaged dynamics and control for heat equations with random diffusion By Jon Asier Bárcena Petisco, Enrique Zuazua Background and motivation ...

pyGasControls Framework By Martin Gugat, Enrique Zuazua, Aleksey Sikstel In order to optimize the operation of gas transportation networks, as ...

Model-based optimization of ripening processes with feedback modules By Michele Spinola 1 Important remark This contribution presents a proof of ...

Gas networks uncertainty and Probust constraints: model, distribution and optimization By Martin Gugat Gas transport and distribution systems are usually ...

Q-learning for finite-dimensional problems By Carlos Esteve Reinforcement Learning Reinforcement Learning (RL) is, together with Supervised Learning and Unsupervised Learning, ...

The interplay of control and Deep Learning By Borjan Geshkovski It is superfluous to state the impact deep (machine) learning ...

Neural networks and Machine Learning By Marius Yamakou Neural Networks with time delayed connections Neurons communicate with each other through ...

Stochastic Synchronization of Chaotic Neurons By Marius Yamakou Real biological neurons can show chaotic dynamics when excited by the certain ...

Nonlocal population balance equations and applications By Michele Spinola Motivational example: look ahead behavior of car drivers When analyzing traffic ...

Inverse Design For Hamilton-Jacobi Equations By Carlos Esteve, Enrique Zuazua In many evolution models, the reconstruction of the initial state ...

Stochastic Neural Dynamics By Marius Yamakou Neural activity shows fluctuations and unpredictable transitions in its dynamics. This randomness can be ...

Controllability properties of fractional PDE By Umberto Biccari Controllability of the fractional heat equation Let \omega\subset (-1,1) be an open ...

Flows on Networks By Enrique Zuazua, Nicola de Nitti PDE models on Networks In the last few decades, models based ...

Stochastic optimization for simultaneous control By Umberto Biccari What is a simultaneous control problem? Consider the following parameter-dependent linear control ...

Convexity and Starshapedness of feasible sets in Stationary Flow Networks By Martin Gugat, Michael Schuster This research was funded by ...

Collective dynamics modelling, Control and Simulation By Dongnam Ko Collective dynamics Herds, packs, bird flocks, and fish schools are common ...

Classical models By Cyprien Neverov Compartmental epidemiological models [1] where introduced almost a century ago and are still considered the ...

Non-local population balance equations By Michele Spinola Nichtlokale Populationsbilanzgleichungen. Der Verlauf des Weges wie zur Schule oder zur Arbeit hängt ...