Multilevel tensor approximation of PDEs with random data
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Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...
We consider one-dimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian motio ...
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We propose and numerically assess three segregated ( partitioned) algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to t ...
This paper examines the minimization of the cost for an expected random production output, given an assembly of finished goods from two random inputs, matched in two categories. We describe the optimal input portfolio, first using the standard normal appro ...
We consider the numerical approximation of lipid biomembranes at equilibrium described by the Canham-Helfrich model, according to which the bending energy is minimized under area and volume constraints. Energy minimization is performed via L-2-gradient flo ...
We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham-Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is perfo ...
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor ' in the tensor train fo ...
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...
An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at acousto-elastic interface require continuity of the normal component of particle velocity and traction, ...