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Found 12 papers, 6 papers with code
Designing Stable Neural Networks using Convex Analysis and ODEs
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the weights are appropriately constrained.
Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integrators
We introduce the mean inverse integrator (MII), a novel approach to increase the accuracy when training neural networks to approximate vector fields of dynamical systems from noisy data.
Predictions Based on Pixel Data: Insights from PDEs and Finite Differences
Neural networks are the state-of-the-art for many approximation tasks in high-dimensional spaces, as supported by an abundance of experimental evidence.
Dynamical systems' based neural networks
The structure of the neural network is then inferred from the properties of the ODE vector field.
Deep neural networks on diffeomorphism groups for optimal shape reparameterization
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes.
Learning Hamiltonians of constrained mechanical systems
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks.
Lie Group integrators for mechanical systems
Finally, we show how Lie group integrators can be applied to model the controlled path of a payload being transported by two rotors.
Image Registration
Numerical Analysis
Numerical Analysis
Dynamical Systems
65L05, 70E55
Equivariant neural networks for inverse problems
In this work, we demonstrate that group equivariant convolutional operations can naturally be incorporated into learned reconstruction methods for inverse problems that are motivated by the variational regularisation approach.
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 slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers.
Fluid Dynamics Numerical Analysis Numerical Analysis
Structure preserving deep learning
Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks.
Signatures in Shape Analysis: an Efficient Approach to Motion Identification
Signatures provide a succinct description of certain features of paths in a reparametrization invariant way.
Deep learning as optimal control problems: models and numerical methods
We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation.
