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• W2972630188 abstract "The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($text{S}^3text{d}$), decides which physical terms are necessary and which can be removed (because they are physically negligible in the sense that they do not affect the dynamics too much) from a pool of candidate functions. The method is built on the recent development of Sparse Bayesian Learning; which enforces the sparsity in the to-be-identified PDEs, and therefore can balance the model complexity and fitting error with theoretical guarantees. Without leveraging prior knowledge or assumptions in the discovery process, we use an automated approach to discover ten types of PDEs, including the famous Navier-Stokes and sine-Gordon equations, from simulation data alone. Moreover, we demonstrate our data-driven discovery process with the Complex Ginzburg-Landau Equation (CGLE) using data measured from a traveling-wave convection experiment. Our machine discovery approach presents solutions that has the potential to inspire, support and assist physicists for the establishment of physical laws from measured spatiotemporal data, especially in notorious fields that are often too complex to allow a straightforward establishment of physical law, such as biophysics, fluid dynamics, neuroscience or nonlinear optics." @default.
• W2972630188 created "2019-09-19" @default.
• W2972630188 creator A5003035659 @default.
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• W2972630188 date "2019-09-15" @default.
• W2972630188 modified "2023-10-16" @default.
• W2972630188 title "Machine Discovery of Partial Differential Equations from Spatiotemporal Data" @default.
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• W2972630188 doi "https://doi.org/10.48550/arxiv.1909.06730" @default.
• W2972630188 hasPublicationYear "2019" @default.

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