We survey current developments in the approximation theory of sequence modelling in
machine learning. Particular emphasis is placed on classifying existing results for various …

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for
modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the …

A Transformer-based deep direct sampling method is proposed for electrical impedance
tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A …

Reservoir computing approximation and generalization bounds are proved for a new
concept class of input/output systems that extends the so-called generalized Barron …

Stochastic partial differential equations (SPDEs) are crucial for modelling dynamics with
randomness in many areas including economics, physics, and atmospheric sciences …

We present a novel probabilistic deep learning approach, the “stochastic latent
transformer”(SLT), designed for the efficient reduced‐order modeling of stochastic partial …

Recently, neural networks have been extensively employed to solve partial differential
equations (PDEs) in physical system modeling. While major studies focus on learning …