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High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics

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Representing and machine learning complex electronic-structure properties of materials

Austin Jacob Zadoks

The rise of high-throughput first-principles calculations of materials since the turn of the millennium has gifted the fields of physics, quantum chemistry, and materials science with a mountainous and ever-growing pile of data ready to be mined for hidden ...

EPFL2025

Forall-exist statements in pseudopolynomial time

Friedrich Eisenbrand

Given a convex set Q ⊆ R m and an integer matrix W ∈ Z m×n , we consider statements of the form ∀b ∈ Q ∩ Z m ∃x ∈ Z n s.t. W x ≤ b. Such statements can be verified in polynomial time with the algorithm of Kannan and its improvements if n is fixed and Q is ...

Society for Industrial and Applied Mathematics2025

Wave attenuation by cultivated seaweeds: A linearized analytical model

Morgane Aline Elsa Marine Weiss

An analytical framework is presented to describe the attenuation of regular and irregular waves propagating over floating seaweed farms. Kelp blades suspended on longlines are modelled, as a first approximation, as rigid bars rotating around their upper en ...

2025

Quenches in the Sherrington-Kirkpatrick model

Lenka Zdeborová, Florent Gérard Krzakala, Freya Behrens, Vittorio Erba

The Sherrington-Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that local ...

2024

Rigorous Dynamical Mean-Field Theory for Stochastic Gradient Descent Methods

Lenka Zdeborová, Florent Gérard Krzakala, Emanuele Troiani

We prove closed-form equations for the exact high-dimensional asymptotics of a family of first-order gradient-based methods, learning an estimator (e.g., M-estimator, shallow neural network) from observations on Gaussian data with empirical risk minimizati ...

Society for Industrial & Applied Mathematics (SIAM)2024