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author = {Ermon, Stefano and Merchant, Amil and Selvam, Nikil},
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booktitle = {Advances in Neural Information Processing Systems 37},
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collection = {NeurIPS 2024},
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doi = {10.52202/079017-0176},
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pages = {5429–5453},
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publisher = {Neural Information Processing Systems Foundation, Inc. (NeurIPS)},
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series = {NeurIPS 2024},
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title = {Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations},
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url = {http://dx.doi.org/10.52202/079017-0176},
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year = {2024},
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}
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@unpublished{SouzaEtAl2024,
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abstract = {Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by distributing the computational load more effectively, time parallelization is essential. We introduce a high-order parallel-in-time method addressing the substantial computational challenges posed by the stiff, multiscale, and nonlinear nature of cardiac dynamics. Our method combines the semi-implicit and exponential spectral deferred correction methods, yielding a hybrid method that is extended to parallel-in-time employing the PFASST framework. We thoroughly evaluate the stability, accuracy, and robustness of the proposed parallel-in-time method through extensive numerical experiments, using practical ionic models such as the ten-Tusscher-Panfilov. The results underscore the method's potential to significantly enhance real-time and high-fidelity simulations in biomedical research and clinical applications.},
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author = {Giacomo Rosilho de Souza and Simone Pezzuto and Rolf Krause},
@@ -7608,7 +7608,16 @@ @article{AlesEtAl2025
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year = {2025},
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}
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@article{AppelEtAl2024,
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@article{AppelEtAl2025,
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author = {Appel, Magnus and Alexandersen, Joe},
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doi = {10.2139/ssrn.5256438},
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publisher = {Elsevier BV},
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title = {Space-Time Multigrid Methods Suitable for Topology Optimisation of Transient Heat Conduction},
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url = {http://dx.doi.org/10.2139/ssrn.5256438},
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year = {2025},
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}
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@article{AppelEtAl2025b,
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author = {Appel, Magnus and Alexandersen, Joe},
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doi = {10.1137/24m1696603},
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issn = {1095-7197},
@@ -7623,15 +7632,6 @@ @article{AppelEtAl2024
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year = {2025},
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}
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@article{AppelEtAl2025,
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author = {Appel, Magnus and Alexandersen, Joe},
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doi = {10.2139/ssrn.5256438},
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publisher = {Elsevier BV},
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title = {Space-Time Multigrid Methods Suitable for Topology Optimisation of Transient Heat Conduction},
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url = {http://dx.doi.org/10.2139/ssrn.5256438},
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year = {2025},
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}
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@unpublished{ArrarasEtAl2025,
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abstract = {In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods offer the possibility to optimize parallelization. In the present paper, we propose a new family of these methods, built as a combination of the well-known parareal algorithm and suitable splitting techniques which permit us to parallelize in space. In particular, dimensional and domain decomposition splittings are considered for partitioning the elliptic operator, and first-order splitting time integrators are chosen as the propagators of the parareal algorithm to solve the resulting split problem. The major contribution of these methods is that, not only does the fine propagator perform in parallel, but also the coarse propagator. Unlike the classical version of the parareal algorithm, where all processors remain idle during the coarse propagator computations, the newly proposed schemes utilize the computational cores for both integrators. A convergence analysis of the methods is provided, and several numerical experiments are performed to test the solvers under consideration.},
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author = {Andrés Arrarás and Francisco J. Gaspar and Iñigo Jimenez-Ciga and Laura Portero},
@@ -7696,7 +7696,7 @@ @article{BhattEtAl2025
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year = {2025},
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}
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@article{BossuytEtAl2023,
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@article{BossuytEtAl2025,
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author = {Bossuyt, Ignace and Vandewalle, Stefan and Samaey, Giovanni},
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doi = {10.1137/23m1609142},
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issn = {1095-7197},
@@ -7752,7 +7752,7 @@ @unpublished{DaiEtAl2025
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year = {2025},
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}
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@article{DanieliEtAl2023,
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@article{DanieliEtAl2025,
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author = {Danieli, Federico and Southworth, Ben S. and Schroder, Jacob B.},
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doi = {10.1002/nla.70034},
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issn = {1099-1506},
@@ -7824,7 +7824,7 @@ @article{FeketeEtAl2025
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year = {2025},
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}
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@article{FreeseEtAl2024,
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@article{FreeseEtAl2025,
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author = {Freese, Philip and Götschel, Sebastian and Lunet, Thibaut and Ruprecht, Daniel and Schreiber, Martin},
abstract = {We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordinary and partial) differential equations (ODEs, PDEs). The method employs Gaussian processes (GPs) to model the Parareal correction function, as GParareal does, further enabling the propagation of numerical uncertainty across time and yielding probabilistic forecasts of system's evolution. Furthermore, Prob-GParareal accommodates probabilistic initial conditions and maintains compatibility with classical numerical solvers, ensuring its straightforward integration into existing Parareal frameworks. Here, we first conduct a theoretical analysis of the computational complexity and derive error bounds of Prob-GParareal. Then, we numerically demonstrate the accuracy and robustness of the proposed algorithm on five benchmark ODE systems, including chaotic, stiff, and bifurcation problems. To showcase the flexibility and potential scalability of the proposed algorithm, we also consider Prob-nnGParareal, a variant obtained by replacing the GPs in Parareal with the nearest-neighbors GPs, illustrating its increased performance on an additional PDE example. This work bridges a critical gap in the development of probabilistic counterparts to established PinT methods.},
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author = {Guglielmo Gattiglio and Lyudmila Grigoryeva and Massimiliano Tamborrino},
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howpublished = {arXiv:2509.03945v1 [stat.CO]},
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title = {Prob-GParareal: A Probabilistic Numerical Parallel-in-Time Solver for Differential Equations},
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url = {http://arxiv.org/abs/2509.03945v1},
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year = {2025},
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}
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@article{GattiglioEtAl2025b,
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author = {Gattiglio, Guglielmo and Grigoryeva, Lyudmila and Tamborrino, Massimiliano},
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doi = {10.1137/24m1663648},
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issn = {1095-7197},
@@ -7898,15 +7907,6 @@ @article{GattiglioEtAl2024
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year = {2025},
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}
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@unpublished{GattiglioEtAl2025,
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abstract = {We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordinary and partial) differential equations (ODEs, PDEs). The method employs Gaussian processes (GPs) to model the Parareal correction function, as GParareal does, further enabling the propagation of numerical uncertainty across time and yielding probabilistic forecasts of system's evolution. Furthermore, Prob-GParareal accommodates probabilistic initial conditions and maintains compatibility with classical numerical solvers, ensuring its straightforward integration into existing Parareal frameworks. Here, we first conduct a theoretical analysis of the computational complexity and derive error bounds of Prob-GParareal. Then, we numerically demonstrate the accuracy and robustness of the proposed algorithm on five benchmark ODE systems, including chaotic, stiff, and bifurcation problems. To showcase the flexibility and potential scalability of the proposed algorithm, we also consider Prob-nnGParareal, a variant obtained by replacing the GPs in Parareal with the nearest-neighbors GPs, illustrating its increased performance on an additional PDE example. This work bridges a critical gap in the development of probabilistic counterparts to established PinT methods.},
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author = {Guglielmo Gattiglio and Lyudmila Grigoryeva and Massimiliano Tamborrino},
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howpublished = {arXiv:2509.03945v1 [stat.CO]},
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title = {Prob-GParareal: A Probabilistic Numerical Parallel-in-Time Solver for Differential Equations},
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url = {http://arxiv.org/abs/2509.03945v1},
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year = {2025},
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}
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@unpublished{GengEtAl2025,
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abstract = {While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned solution as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. To ensure such consistency, we propose to use the convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the traditional numerical scheme used as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen-Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNNs model is trained on trajectories-based on random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without re-training. This work demonstrates the potential of integrating neural network methods into the parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.},
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author = {Yuwei Geng and Junqi Yin and Eric C. Cyr and Guannan Zhang and Lili Ju},
journal = {Computer Methods in Applied Mechanics and Engineering},
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month = {March},
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pages = {118605},
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publisher = {Elsevier BV},
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title = {Large-scale topology optimisation of time-dependent thermal conduction using space-time finite elements and a parallel space-time multigrid preconditioner},
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