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Found 8 papers, 4 papers with code
Hamiltonian Matching for Symplectic Neural Integrators
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science.
Parallel-in-Time Solutions with Random Projection Neural Networks
This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator.
Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach
Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks.
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.
Predictions Based on Pixel Data: Insights from PDEs and Finite Differences
We support our theoretical results with numerical experiments simulating the linear advection, heat, and Fisher equations.
Dynamical systems' based neural networks
The structure of the neural network is then inferred from the properties of the ODE vector field.
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
