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20212026
most citedParareal with a physics-informed neural network as coarse propagator

12 citations · 29 across the 14 of their papers we have counts for

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10 papers · 1 filter

math.NA2026

Space-Time Parallel Direct Numerical Simulation of Rayleigh-Bénard Convection

Thomas Saupe, Thibaut Lunet, Mathis Bode +3

Rayleigh-Bénard convection (RBC) is a model for turbulent flow and challenging to simulate by direct numerical simulation (DNS). Adequate resolution of all relevant length scales r…

math.NA2026

Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor

Vamika Rathi, Fatima Sehar, Finn Sommer +4

Lagrangian sensors have shown promise to improve operator awareness of conditions inside a chemical reactor but three-dimensional tracking remains a mostly unsolved challenge. We e…

math.NA2026

Adjoint-based Perfusion Estimation from Dynamic Contrast-Enhanced Ultrasound: Advection-Diffusion and Two-Compartment Models

Sophie Externbrink, Ahmed El Kaffas, Dimitre Hristov +1

Tumor perfusion and vascular properties are important determinants of a cancer's response to therapy. In this paper, we discuss the estimation of spatially varying blood flow veloc…

math.NA2025

Enforcing boundary conditions for physics-informed neural operators

Niklas Göschel, Sebastian Götschel, Daniel Ruprecht

Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partia…

math.NA2024★ 2 cited

Space-time parallel scaling of Parareal with a physics-informed Fourier Neural Operator coarse propagator applied to the Black-Scholes equation

Abdul Qadir Ibrahim, Sebastian Götschel, Daniel Ruprecht

Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they re…

math.NA2024★ 7 cited

Improving Efficiency of Parallel Across the Method Spectral Deferred Corrections

Gayatri Čaklović, Thibaut Lunet, Sebastian Götschel +1

Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, wh…

math.NA2024★ 3 cited

Adaptive time step selection for Spectral Deferred Correction

Thomas Saupe, Sebastian Götschel, Thibaut Lunet +2

Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial…

math.NA2023★ 3 cited

Spectral deferred correction methods for second-order problems

Ikrom Akramov, Sebastian Götschel, Michael Minion +2

Spectral deferred corrections (SDC) are a class of iterative methods for the numerical solution of ordinary differential equations. SDC can be interpreted as a Picard iteration to…

math.NA2023★ 12 cited

Parareal with a physics-informed neural network as coarse propagator

Abdul Qadir Ibrahim, Sebastian Götschel, Daniel Ruprecht

Parallel-in-time algorithms provide an additional layer of concurrency for the numerical integration of models based on time-dependent differential equations. Methods like Parareal…

math.NA2021

Impact of spatial coarsening on Parareal convergence for the linear advection equation

Judith Angel, Sebastian Götschel, Daniel Ruprecht

The Parareal parallel-in-time integration method often performs poorly when applied to hyperbolic partial differential equations. This effect is even more pronounced when the coars…