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Rank-adaptive tensor methods for high-dimensional nonlinear PDEs
Alec Dektor, Abram Rodgers, Daniele Venturi
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansio…
Dynamic tensor approximation of high-dimensional nonlinear PDEs
Alec Dektor, Daniele Venturi
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial dif…
Improving neural network predictions of material properties with limited data using transfer learning
Schuyler Krawczuk, Daniele Venturi
We develop new transfer learning algorithms to accelerate prediction of material properties from ab initio simulations based on density functional theory (DFT). Transfer learning h…
Spectral methods for nonlinear functionals and functional differential equations
Daniele Venturi, Alec Dektor
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpos…