Publications related to Numerical cognition

An adaptive phase field approach to 3D internal crack growth in rocks

Alexandra Roma Larisa Kushnir, Tao Xu, Michael Heap

Modeling the 3D internal crack under compression entails complex fracture mechanics (mode I-II-III fracture), resulting in substantial computational costs and challenges in characterizing fracture morphology characterization for Phase Field Method (PFM) si ...

2024

Perturbed Utility Stochastic Traffic Assignment

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

Informs2024

Robust mass lumping and outlier removal strategies in isogeometric analysis

Annalisa Buffa, Espen Sande, Yannis Dirk Voet

Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysi ...

2024

Stochastic Simulations and Machine Learning Modeling to Predict Bedload Transport and Bed Topography

Mehrdad Kiani Oshtorjani

In computational hydraulics models, predicting bed topography and bedload transport with sufficient accuracy remains a significant challenge. An accurate assessment of a river's sediment transport rate necessitates a prior understanding of its bed topograp ...

EPFL2024

Improving SAM Requires Rethinking its Optimization Formulation

Volkan Cevher, Kimon Antonakopoulos, Thomas Michaelsen Pethick, Wanyun Xie, Fabian Ricardo Latorre Gomez

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. We argue that SAM shou ...

2024

On the use of Cramér-Rao Lower Bound for least-variance circuit parameters identification of Li-ion cells

Mario Paolone, Vladimir Sovljanski

Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models (ECMs) are widely used to characterize the impedance and estimate parameters of electrochemical systems such as batteries. We use a generic ECM with ten parameters grouped to model ...

2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

Ultra-broadband terahertz radiation by supercontinuum generation and optical rectification in a dispersion-engineered waveguide: a numerical study

Ileana-Cristina Benea-Chelmus, Aleksei Gaier

In this work, we propose a numerical approach based on forward coupled mode modeling to simultaneously evaluate second- and third-order nonlinearities inside a dispersion-engineered waveguide towards the goal of generating broadband terahertz (THz) radiati ...

New York2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Saddle-to-Saddle Dynamics in Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Scott William Pesme

In this paper we fully describe the trajectory of gradient flow over diagonal linear networks in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until reaching the minim ...

2023

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An adaptive phase field approach to 3D internal crack growth in rocks

Perturbed Utility Stochastic Traffic Assignment

Robust mass lumping and outlier removal strategies in isogeometric analysis

Stochastic Simulations and Machine Learning Modeling to Predict Bedload Transport and Bed Topography

Improving SAM Requires Rethinking its Optimization Formulation

On the use of Cramér-Rao Lower Bound for least-variance circuit parameters identification of Li-ion cells

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Ultra-broadband terahertz radiation by supercontinuum generation and optical rectification in a dispersion-engineered waveguide: a numerical study

Low-Rank Tensor Methods for High-Dimensional Problems

Saddle-to-Saddle Dynamics in Diagonal Linear Networks

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Improving SAM Requires Rethinking its Optimization Formulation

Perturbed Utility Stochastic Traffic Assignment

Saddle-to-Saddle Dynamics in Diagonal Linear Networks

Stochastic Simulations and Machine Learning Modeling to Predict Bedload Transport and Bed Topography

Robust mass lumping and outlier removal strategies in isogeometric analysis

Ultra-broadband terahertz radiation by supercontinuum generation and optical rectification in a dispersion-engineered waveguide: a numerical study

On the use of Cramér-Rao Lower Bound for least-variance circuit parameters identification of Li-ion cells

Low-Rank Tensor Methods for High-Dimensional Problems

An adaptive phase field approach to 3D internal crack growth in rocks