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<pre class="abstract">@inproceedings{HamdanEtAl2025,
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title = {Leveraging Continuous-Time Echo State Networks to Accelerate Computing Nonlinear Stiff Dynamics through Parareal in Time Simulation},
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author = {Hamdan, Juman and Riahi, Mohamed Kamel},
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booktitle = {Journal of Physics: Conference Series},
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volume = {3027},
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number = {1},
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organization = {IOP Publishing},
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pages = {012036},
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year = {2025},
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organization = {IOP Publishing}
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title = {Leveraging Continuous-Time Echo State Networks to Accelerate Computing Nonlinear Stiff Dynamics through Parareal in Time Simulation},
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volume = {3027},
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year = {2025}
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}
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LjósheimEtAl2025
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<span id="LjósheimEtAl2025">H. W. Ljósheim, D. Kalise, J. W. Pearson, and F. J. Silva, “Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games,” arXiv:2507.01958v1 [math.NA], 2025 [Online]. Available at: <a href="http://arxiv.org/abs/2507.01958v1" target="_blank">http://arxiv.org/abs/2507.01958v1</a></span>
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author = {Ljósheim, Heidi Wolles and Kalise, Dante and Pearson, John W. and Silva, Francisco J.},
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howpublished = {arXiv:2507.01958v1 [math.NA]},
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title = {Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games},
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url = {http://arxiv.org/abs/2507.01958v1},
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We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference discretization and solve the resulting finite-dimensional optimization problem using the Chambolle–Pock primal–dual algorithm. As this involves computing proximal operators and solving ill-conditioned linear systems at each iteration, we propose a general class of parallel-in-time preconditioners based on diagonalization techniques using discrete Fourier transforms. These enable efficient, scalable iterative solvers with robustness across a wide range of viscosities. We further develop fast solvers for the resulting ill-conditioned systems arising at each time step, using exact recursive schemes for structured grids while allowing for other geometries. Numerical experiments confirm the improved performance and parallel scalability of our approach.
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