Deep-Picard iteration uses supervised neural networks trained on Monte Carlo labels from beta-stable subordinators and alpha-stable Levy walks to approximate solutions of high-dimensional fractional PDEs up to dimension 100.
Ten equivalent definitions of the fractional laplace operator
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Short-time rescalings of compression covariance defects E_s,t = V_s^* V_t yield tangent kernels F whose Kolmogorov spaces carry induced contraction semigroups whose representing vectors obey additive cocycle identities, restricting admissible positive kernels.
Improved global and local Gagliardo-Nirenberg inequalities with BMO terms are obtained by using fractional Laplacians in place of local derivatives.
citing papers explorer
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Deep-Picard Iteration for Space-time Fractional Diffusion PDEs
Deep-Picard iteration uses supervised neural networks trained on Monte Carlo labels from beta-stable subordinators and alpha-stable Levy walks to approximate solutions of high-dimensional fractional PDEs up to dimension 100.
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Compression Covariance and Tangent kernels
Short-time rescalings of compression covariance defects E_s,t = V_s^* V_t yield tangent kernels F whose Kolmogorov spaces carry induced contraction semigroups whose representing vectors obey additive cocycle identities, restricting admissible positive kernels.
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Gagliardo-Nirenberg type inequalities with a BMO term and fractional Laplacians
Improved global and local Gagliardo-Nirenberg inequalities with BMO terms are obtained by using fractional Laplacians in place of local derivatives.