Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs) Code: • See the complete report by Dania Sana Introduction Accurate and fast predictions of numerical solutions are of significant interest in many areas of science and industry. On one hand, most theoretical methods used in the industry are the result of deriving differential equations that are based…

Start with tutorials to get familiar with the code Tutorial 1: Train a neural ODE based network on point cloud data set and generating a gif of the resulting time evolution of the neural ODE Code: Code is based on GitHub: borjanG : 2021-dynamical-systems that uses the torchdiffeq package GitHub : rtqichen: torchdiffeq Code: || Go to the Math…

Derivation of the pressure function Code: Files to run: nocircle.m, onecircle.m or twocircles.m 1 Introduction This post presents the results of my Bachelor thesis about the modeling and implementation of gas networks at stationary states. Using the isothermal Euler equations to describe the gas flow through a single pipe, algebraic node conditions that require the conservation of mass and…

Author: Daniël Veldman, FAU DCN-AvH Code: A sheep herding game in MATLAB developed for the Long Night of Science #NdW22 (Lange Nacht der Wissenschaft) Erlangen-Furth-Nuernberg 2022. Main rules • The dog should drive sheep to the target (red). • You can steer the dog with the arrow keys. • The sheep are afraid of the dog and of the fences.…

Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd’s algorithm. Also called Voronoid iteration, this is an iterative algorithm finding for equispaced convex cells in euclidean space. Lloyd’s algorithm finds the distribution of the cells computing their center of mass and iteratively applying the Voronoid tessellation. Like the closely related K-means clustering algorithm, it…

The code implements the gradient regularization method of robust training in the setting of neural ODEs. Various jupyter notebooks are included that generate plots comparing standard to robust training for 2d point clouds. Code: A good starting point is robustness_plots.ipynb Code is based on GitHub: borjanG : 2021-dynamical-systems that uses the torchdiffeq package GitHub : rtqichen: torchdiffeq || Go…

Author: Borjan Geshkovski, MIT The interplay of control and Deep Learning By Borjan Geshkovski It is superﬂuous to state the impact deep (machine) learning has had on modern technology, as it powers many tools of modern society, ranging from web searches to content ﬁltering on social networks. It is also increasingly present in consumer products such as cameras, smartphones…

Author: Martin Gugat, Enrique Zuazua, Aleksey Sikstel, FAU DCN-AvH Code: [HINT] To run the software on your computer, you may have to install additional standard software packages (like cmake and a c++ compiler) and additional libraries (lapack, PETSc). In order to optimize the operation of gas transportation networks, as a first step a powerful simulation software is mandatory.…

Author: Carlos Esteve, Deusto CCM Code: In a previous post “Inverse Design For Hamilton-Jacobi Equations“, described all the possible initial states that agree with the given observation of the system at time on the reconstruction of the initial state in many evolution models. Our goal here is to study the inverse design problem associated to Hamilton Jacobi Equations (HJ). More…

Author: Daniel Veldman, FAU DCN-AvH Code: || Also available @Daniël’s GitHub In a previous post “Randomized time-splitting in linear-quadratic optimal control“, it was proposed to use the Random Batch Method (RBM) to solve classical Linear-Quadratic (LQ) optimal control problems. This contribution is concerned with the corresponding numerical implementation. We thus consider the classical LQ optimal control problem, in which the…

Author: Alexei Gazca, FAU DCN-AvH Code: Below is a description of the types of problems that can be tackled using the code contained in this repository. Solving linear systems arising from the discretisation of partial differential equations can be an extremely challenging and computationally intensive task, especially for problems posed in more than two spatial dimensions: employing iterative methods…