Parallel-in-Time Probabilistic Solutions for Time-Dependent Nonlinear Partial Differential Equations
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A4 Artikkeli konferenssijulkaisussa
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Date
2024-11
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en
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6
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Abstract
We present an efficient probabilistic solver for time-dependent nonlinear partial differential equations. We formulate our method as the maximum a posteriori solver for a constrained risk problem on a reproducing kernel Hilbert space induced by a spatiotemporal Gaussian process prior. We show that for a suitable choice of temporal kernels, the risk objective can be minimized efficiently via a Gauss-Newton algorithm corresponding to an iterated extended Kalman smoother (IEKS). Furthermore, by leveraging a parallel-in-time implementation of IEKS, our algorithm can take advantage of massively parallel graphical processing units to achieve logarithmic instead of linear scaling with time. We validate our method numerically on popular benchmark problems.Description
Keywords
probabilistic numerics, partial differential equations, parallel algorithm
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Iqbal, S, Abdulsamad, H, Cator, T, Braga-Neto, U & Särkkä, S 2024, Parallel-in-Time Probabilistic Solutions for Time-Dependent Nonlinear Partial Differential Equations . in 2024 IEEE 34th International Workshop on Machine Learning for Signal Processing (MLSP) . IEEE, IEEE International Workshop on Machine Learning for Signal Processing, London, United Kingdom, 22/09/2024 . https://doi.org/10.1109/MLSP58920.2024.10734739