252 citations · 629 across the 33 of their papers we have counts for
8 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…
Efficient and Scalable Kernel Matrix Approximations using Hierarchical Decomposition
Keerthi Gaddameedi, Severin Reiz, Tobias Neckel +1
With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to co…
Multi-fidelity No-U-Turn Sampling
Kislaya Ravi, Tobias Neckel, Hans-Joachim Bungartz
Markov Chain Monte Carlo (MCMC) methods often take many iterations to converge for highly correlated or high-dimensional target density functions. Methods such as Hamiltonian Monte…
Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification
Ionut-Gabriel Farcas, Benjamin Peherstorfer, Tobias Neckel +2
Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating t…
Model Order Reduction based on Runge-Kutta Neural Network
Qinyu Zhuang, Juan Manuel Lorenzi, Hans-Joachim Bungartz +1
Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection…
Quasi-Newton Waveform Iteration for Partitioned Fluid-Structure Interaction
Benjamin Rüth, Benjamin Uekermann, Miriam Mehl +3
We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast…