arXiv subjects

Thibaut Lunet

Publications and source records attributed to Thibaut Lunet.

5 recordsLinked to original sources

arXiv2026

Fourier Neural Operators for Rayleigh-Bénard Convection

We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-Bénard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline. The resulting model is compact (314k parameters, 1.26 MB) and fast (7 ms inference), while maintaining similar accuracy as demonstrated in previous benchmarks. We show that although FNOs generalize to finer meshes, accuracy remains limited by the resolution of the training data.

cs.LG↗

arXiv2026

Parallel performance of shared memory parallel spectral deferred corrections

We investigate the parallel performance of Parallel Spectral Deferred corrections, a numerical approach that provides small-scale parallelism for the numerical solution of initial value problems. The scheme is applied to the shallow-water equation and uses an implicit-explicit splitting that, in order to be efficient, integrates fast modes implicitly and slow modes explicitly. We describe parallel \OpenMP-based implementations of parallel Spectral Deferred Corrections for two well established simulation codes: the finite volume based operational ocean model \ICON and the spherical harmonics based research code \SWEET. We also develop a performance model and benchmark our implementations on a single node of the JUSUF (\SWEET) and JUWELS (\ICON) system at Jülich Supercomputing Centre. A reduction of time-to-solution across a range of accuracies is demonstrated. For \ICON, we show speedup over the currently used Adams--Bashforth-2 integrator with \OpenMP loop parallelization. For \SWEET, we show speedup over serial Spectral Deferred Corrections and a second order implicit-explicit integrator.

cs.CE↗

arXiv2025

Resilience Against Soft Faults through Adaptivity in Spectral Deferred Correction

As supercomputers grow in hardware complexity, their susceptibility to faults increases and measures need to be taken to ensure the correctness of results. Some numerical algorithms have certain characteristics that allow them to recover from some types of faults. It has been demonstrated that adaptive Runge-Kutta methods provide resilience against transient faults without adding computational cost. Using recent advances in adaptive step size selection for spectral deferred correction (SDC), an iterative numerical time stepping scheme that can produce methods of arbitrary order, we show that adaptive SDC can also detect and correct transient faults. Its performance is found to be comparable to that of the dedicated resilience strategy Hot Rod.

cs.DC↗

arXiv2024

Improving Efficiency of Parallel Across the Method Spectral Deferred Corrections

Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods proposed by Van der Houwen and Sommeijer, can use a number of threads equal to the number of quadrature nodes in the underlying collocation method. However, convergence speed, efficiency and stability depends critically on the used coefficients. Previous approaches have used numerical optimization to find good parameters. Instead, we propose an ansatz that allows to find optimal parameters analytically. We show that the resulting parallel SDC methods provide stability domains and convergence order very similar to those of well established serial SDC variants. Using a model for computational cost that assumes 80% efficiency of an implementation of parallel SDC we show that our variants are competitive with serial SDC, previously published parallel SDC coefficients as well as Picard iteration, explicit RKM-4 and an implicit fourth-order diagonally implicit Runge-Kutta method.

math.NA↗

arXiv2024

Adaptive time step selection for Spectral Deferred Correction

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 value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.

math.NA↗