March 24, 2024Open Access

Efficient Learning of PDEs via Taylor Expansion and Sparse Decomposition into Value and Fourier Domains

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Reel accelerates the learning of partial differential equations, which may lead to faster scientific discovery.
Empirical evidence shows a 70-98% reduction in training time when data is compressed to just 1% of its original size.
Random projection and taylor series expansion are applied for effective sparse decomposition in both value and frequency domains, enhancing learning efficiency and applicability of models across different PDEs conditions. Theoretical derivation indicates a constant factor approximation between projected and original loss functions.

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Randomized trial investigates efficient PDE learning techniques, suggesting broader applications for scientific discovery.

Nasim et al. (2024) studied this question.

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