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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…
cs.LG2025
Multi-level Neural Networks for high-dimensional parametric obstacle problems
Martin Eigel, Cosmas HeiÃ, Janina E. Schütte
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differenti…