Imre Fekete

He deals with the theory of numerical analysis and its applications. His research mainly focuses on numerical methods for ordinary differential equations. Particularly, he deals with stability, convergence and efficient implementation of Runge-Kutta, linear multistep, IMEX and SSP methods and their adaptive versions.

Keywords

Runge-Kutta methods, Linear multistep methods, Strong Stability Preserving (SSP) methods, Adaptivity, Deep learning

Scientific computing aspects of machine learning and deep learning

Application possibilities of temporal and spatial discreziazion techniques in neural differential equations.

Keywords

numerical methods, Machine learning, Deep learning, neural networks

Interactive notebook environments in scientific computing related courses

Opportunities applying ChatGPT in numerical methods' related courses.

Keywords

didactics of mathematics, higher education research, inquiry-based learning

Parallel-in-time discretization methods

When optimizing neural ordinary differential equations using the adjoint sensitivity method, we need to solve initial value problems both forward and backward in time. For computational efficiency, the effective use of a parallelized time integrator is essential.

Keywords

Multigrid Reduction in Time methods