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08/16/2023
B-stability of numerical integrators on Riemannian manifolds
We propose a generalization of nonlinear stability of numerical one-step...
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06/29/2023
Designing Stable Neural Networks using Convex Analysis and ODEs
Motivated by classical work on the numerical integration of ordinary dif...
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06/06/2023
Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integrators
We introduce the mean inverse integrator (MII), a novel approach to incr...
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05/01/2023
Predictions Based on Pixel Data: Insights from PDEs and Finite Differences
Neural networks are the state-of-the-art for many approximation tasks in...
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10/05/2022
Dynamical systems' based neural networks
Neural networks have gained much interest because of their effectiveness...
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09/02/2022
Using aromas to search for preserved measures and integrals in Kahan's method
The numerical method of Kahan applied to quadratic differential equation...
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07/22/2022
Deep learning of diffeomorphisms for optimal reparametrizations of shapes
In shape analysis, one of the fundamental problems is to align curves or...
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01/31/2022
Learning Hamiltonians of constrained mechanical systems
Recently, there has been an increasing interest in modelling and computa...
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09/25/2021
Dynamics of the N-fold Pendulum in the framework of Lie Group Integrators
Since their introduction, Lie group integrators have become a method of ...
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02/25/2021
Lie Group integrators for mechanical systems
Since they were introduced in the 1990s, Lie group integrators have beco...
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02/23/2021
Equivariant neural networks for inverse problems
In recent years the use of convolutional layers to encode an inductive b...
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12/21/2020
An integral model based on slender body theory, with applications to curved rigid fibers
We propose a novel integral model describing the motion of curved slende...
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08/31/2020
Discrete conservation laws for finite element discretisations of multisymplectic PDEs
In this work we propose a new, arbitrary order space-time finite element...
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06/05/2020
Structure preserving deep learning
Over the past few years, deep learning has risen to the foreground as a ...
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07/27/2019
Computational methods for tracking inertial particles in discrete incompressible flows
Calculating trajectories of small particles in numerical simulations of ...
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06/14/2019
Signatures in Shape Analysis: an Efficient Approach to Motion Identification
Signatures provide a succinct description of certain features of paths i...
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04/11/2019
Deep learning as optimal control problems: models and numerical methods
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018...
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06/02/2015