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math.NA2026
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…
math.NA2026
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…
math.NA2024
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…