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Ghost States Underlying Spatial and Temporal Patterns: How Nonexistent Invariant Solutions Control Nonlinear Dynamics

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Light-Induced Density Waves in Strongly Interacting Fermions

Timo Zwettler

The manipulation of quantum materials by light constitutes a new emergent field in condensed matter systems. Strong light-matter coupling and ultrafast optics are powerful tools for inducing new quantum phases in strongly correlated systems, with one parti ...

EPFL2025

Learning Time-Scales in Two-Layers Neural Networks

Raphaël Jean Berthier

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes barely any progre ...

2024

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...

2020

Invariant solutions underlying small- and large-scale structures in turbulent boundary layers

Sajjad Azimi

Flows of gases and liquids interacting with solid objects are often turbulent within a thin boundary layer. As energy dissipation and momentum transfer are dominated by the boundary layer dynamics, many engineering applications can benefit from an improved ...

EPFL2020