Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R

Radar and DC resistivity 2.5D multi-physics inversion suite. Forward modeling, separate inversions, joint inversions.

The main project for the MATLAB / GNU Octave code of FESTUNG

Pytorch implementation of "DeepFlow: History Matching in the Space of Deep Generative Models"

Numerical Solutions for PDE's | Heat Equation, Poisson Equation, Wave Equation

A fast direct dense solver with machine accuracy for 2-D Laplace's equation

Hierarchical Model Reduction

Object-oriented constructor of finite difference schemes

Transmission-line Modeling Method applied to BioHeat Transfer Problems

Simulations for geometrically exact beams in different settings (e.g., validation problems, feedback stabilization problem). In 2021-2022.

PDE-based vector-valued image regularization routine.

Repository for: "Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers"

This Matlab code implements a branching diffusion method for solving partial differential equations (PDEs). The method uses Monte Carlo simulation and the branching process to approximate the solution of PDEs. The code provides a set of functions to calculate the mean, standard deviation, and L2 approximation error of the solution.

This MATLAB code implements the classical Monte Carlo method for solving partial differential equations (PDEs). The code uses the log function of the norm of a random vector as an example PDE and computes the solution at time T=1 and initial condition x0=0.

Comparing the error generated while solving a function using numerical discretization for 1st, 2nd and 4th order approximation.

Finite Difference Method for the Multi-Asset Black–Scholes Equations

Simulation of a conducting cylinder rotating inside a magnetic field. (Finite difference methods for non-linear systems of PDEs).

Multilevel solvers for the Helmholtz equation based on the shifted Laplace preconditioner

Codes for the paper "Control of the linearized Stefan problem in a periodic box".

Software for the book 'The Sequential Quadratic Hamiltonian Method' - CRC Press / Chapman & Hall (2023)