449 citations · 831 across the 30 of their papers we have counts for
7 papers · 1 filter
Rational neural networks for tracking complex singularities of nonlinear PDEs
Nadiia Derevianko, Hans-Joachim Bungartz, Felix Dietrich
We present a neural network-based method for numerical analytic continuation of solutions of nonlinear partial differential equations (PDEs) and detection of their complex singular…
Neural network-based singularity detection and applications
Nadiia Derevianko, Ioannis G. Kevrekidis, Felix Dietrich
We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on usin…
Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operator
Ioannis K. Gallos, Daniel Lehmberg, Felix Dietrich +1
We propose a machine-learning approach to model long-term out-of-sample dynamics of brain activity from task-dependent fMRI data. Our approach is a three stage one. First, we explo…
On the Use of Neural Networks for Full Waveform Inversion
Leon Herrmann, Tim Bürchner, Felix Dietrich +1
Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and…
Personalized Algorithm Generation: A Case Study in Learning ODE Integrators
Yue Guo, Felix Dietrich, Tom Bertalan +4
We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven a…
On the Koopman operator of algorithms
Felix Dietrich, Thomas N. Thiem, Ioannis G. Kevrekidis
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, acce…
Numerical Model Construction with Closed Observables
Felix Dietrich, Gerta Köster, Hans-Joachim Bungartz
Performing analysis, optimization and control using simulations of many-particle systems is computationally demanding when no macroscopic model for the dynamics of the variables of…