Math and Research

Torsional Rigidity: Classical and new results By Gloria Paoli Torsional rigidity is a key quantity to characterize how a beam ...
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Analysis of a local-nonlocal polymer chain model By Jean-Daniel Djida What does the mathematics of partial differential equations have to ...
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Federated Learning: Protect your data and privacy By Ziqi Wang Code: A basic PyTorch implementation of the FedAvg algorithm (GitHub) ...
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Breaking the curse of dimensionality with Barron spaces By Antonio Álvarez López 1 Introduction Recent advances in computational hardware have ...
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Stability results for the KdV equation with time-varying delay By Hugo Parada Ríos Introduction The Korteweg-de Vries equation (KdV), is ...
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Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs) By Dania Sana Code: • See the complete report ...
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Derivation of the pressure function By Veronika Riedl Code: Files to run: nocircle.m, onecircle.m or twocircles.m 1 Introduction This post ...
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Author: Daniël Veldman, FAU DCN-AvH Code: A sheep herding game in MATLAB developed for the Long Night of Science #NdW22 ...
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Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd's algorithm. Also called Voronoid iteration, ...
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Using the support function for optimal shape design By Ilias Ftouhi 1 Motivation Led by problems of optimal placement and ...
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Uniform Turnpike Property By Martín Hernández Salinas 1 Introduction In this post, we analyze a 1 − d heat equation ...
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Author: Borjan Geshkovski, MIT The interplay of control and Deep Learning By Borjan Geshkovski It is superfluous to state the ...
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Nonlinear hyperbolic systems: Modeling, controllabiliy and applications By Yue Wang The control theory of hyperbolic systems is an important topic ...
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Kinetic theory of Bose Einstein Condensates By Minh-Binh Tran If a dilute gas of bosons, about one-hundred-thousandth the density of ...
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Author: Martin Gugat, Enrique Zuazua, Aleksey Sikstel, FAU DCN-AvH Code:   [HINT] To run the software on your computer, you ...
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Author: Carlos Esteve, Deusto CCM Code: In a previous post "Inverse Design For Hamilton-Jacobi Equations", described all the possible initial ...
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Author: Daniel Veldman, FAU DCN-AvH Code: || Also available @Daniël's GitHub In a previous post "Randomized time-splitting in linear-quadratic optimal ...
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Author: Alexei Gazca, FAU DCN-AvH Code:   Below is a description of the types of problems that can be tackled ...
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Transition Layers in Elliptic Equations By Maicon Sônego Stable transition layers in an unbalanced bistable equation Consider the following semi-linear ...
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Randomized time-splitting in linear-quadratic optimal control By Daniël Veldman Introduction Solving an optimal control problem for a large-scale dynamical system ...
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Felix Klein: A Legacy of Innovation in Mathematics and Education By Roberto Rodríguez del Río, Complutense University of Madrid | ...
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Control of Advection-Diffusion Equations on Networks and Singular Limits By Jon Asier Bárcena-Petisco, Márcio Cavalcante, Giuseppe Maria Coclite, Nicola de ...
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Probabilistic Constrained Optimization on Flow Networks By Michael Schuster This research was funded by DFG in the SFB Transregio 154: ...
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Perceptrons, Neural Networks and Dynamical Systems By Sergi Andreu // This post is last part of the "Deep Learning and ...
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Deep Learning and Paradigms By Sergi Andreu // This post is the 2nd. part of the "Opening the black box ...
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Opening the black box of Deep Learning By Sergi Andreu Deep Learning is one of the three main paradigms of ...
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Averaged dynamics and control for heat equations with random diffusion By Jon Asier Bárcena Petisco, Enrique Zuazua Background and motivation ...
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pyGasControls Framework By Martin Gugat, Enrique Zuazua, Aleksey Sikstel In order to optimize the operation of gas transportation networks, as ...
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Model-based optimization of ripening processes with feedback modules By Michele Spinola 1 Important remark This contribution presents a proof of ...
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Gas networks uncertainty and Probust constraints: model, distribution and optimization By Martin Gugat Gas transport and distribution systems are usually ...
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Q-learning for finite-dimensional problems By Carlos Esteve Reinforcement Learning Reinforcement Learning (RL) is, together with Supervised Learning and Unsupervised Learning, ...
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The interplay of control and Deep Learning By Borjan Geshkovski It is superfluous to state the impact deep (machine) learning ...
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Neural networks and Machine Learning By Marius Yamakou Neural Networks with time delayed connections Neurons communicate with each other through ...
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Stochastic Synchronization of Chaotic Neurons By Marius Yamakou Real biological neurons can show chaotic dynamics when excited by the certain ...
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Nonlocal population balance equations and applications By Michele Spinola Motivational example: look ahead behavior of car drivers When analyzing traffic ...
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Inverse Design For Hamilton-Jacobi Equations By Carlos Esteve, Enrique Zuazua In many evolution models, the reconstruction of the initial state ...
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Stochastic Neural Dynamics By Marius Yamakou Neural activity shows fluctuations and unpredictable transitions in its dynamics. This randomness can be ...
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Controllability properties of fractional PDE By Umberto Biccari Controllability of the fractional heat equation Let \omega\subset (-1,1) be an open ...
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Flows on Networks By Enrique Zuazua, Nicola de Nitti PDE models on Networks In the last few decades, models based ...
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Stochastic optimization for simultaneous control By Umberto Biccari What is a simultaneous control problem? Consider the following parameter-dependent linear control ...
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Convexity and Starshapedness of feasible sets in Stationary Flow Networks By Martin Gugat, Michael Schuster This research was funded by ...
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Collective dynamics modelling, Control and Simulation By Dongnam Ko Collective dynamics Herds, packs, bird flocks, and fish schools are common ...
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Classical models By Cyprien Neverov Compartmental epidemiological models [1] where introduced almost a century ago and are still considered the ...
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Non-local population balance equations By Michele Spinola Nichtlokale Populationsbilanzgleichungen. Der Verlauf des Weges wie zur Schule oder zur Arbeit hängt ...
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