Publications related to Backpropagation-Friendly Eigendecomposition

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

Randomized flexible GMRES with deflated restarting

Laura Grigori, Emeric Martin

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Springer2024

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

Randomized low-rank approximation and its applications

Ulf David Persson

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

EPFL2024

Reliable data-driven decision-making through optimal transport

Bahar Taskesen

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

EPFL2024

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Marco Picasso, Maude Girardin, Alexandre Caboussat

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Elsevier Science Sa2024

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

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 ...

Nature Portfolio2024

Validation and Application of Hysteresis Loss Model for HTS Stacks and Conductors for Fusion Applications

Nikolay Bykovskiy

Numerous conductor designs for pulsed magnets based on High Temperature Superconductors (HTS), featuring stacks of tapes are currently being proposed. A major contribution to the AC losses is expected to be given by hysteresis losses. Several numerical mod ...

IEEE Institute of Electrical and Electronics Engineers2024

Nanoindentation hardness and modulus of Al2O3-SiO2-CaO and MnO-SiO2-FeO inclusions in iron

Andreas Mortensen, David Hernandez Escobar, Léa Deillon, Alejandra Inés Slagter, Eva Luisa Vogt, Jonathan Aristya Setyadji

Dataset corresponding to the following manuscript: Slagter, A., Setyadji, J.A., Vogt, E.L. et al. Nanoindentation Hardness and Modulus of Al2O3–SiO2–CaO and MnO–SiO2–FeO Inclusions in Iron. Metall Mater Trans A (2024). https://doi.org/10.1007/s11661-024-0 ...

Zenodo2024

Understanding generalization and robustness in modern deep learning

Maksym Andriushchenko

In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

EPFL2024