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math.NA2026
Multilevel Sparse Tensor Approximation for High-Dimensional Parametric PDEs
Martin Eigel, Philipp Trunschke, Dana Wrischnig
In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the rec…
math.NA2025
Approximation and learning with compositional tensor trains
Martin Eigel, Charles Miranda, Anthony Nouy +1
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train form…
math.NA2025
Functional SDE approximation inspired by a deep operator network architecture
Martin Eigel, Charles Miranda
A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of…