50 citations · 159 across the 31 of their papers we have counts for
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Explicit and Effectively Symmetric Runge-Kutta Methods
Daniil Shmelev, Kurusch Ebrahimi-Fard, Nikolas Tapia +1
Symmetry is a key property of numerical methods. The geometric properties of symmetric schemes make them an attractive option for integrating Hamiltonian systems, whilst their abil…
Sparse Signature Coefficient Recovery via Kernels
Daniil Shmelev, Cristopher Salvi
Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effe…
A path-dependent PDE solver based on signature kernels
Alexandre Pannier, Cristopher Salvi
We develop a kernel-based solver for path-dependent PDEs (PPDEs) along with a convergence theory. Our numerical scheme leverages signature kernels, a recently introduced class of k…