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Found 4 papers, 4 papers with code
An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations
In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain using traditional methods due to limited computational resources.
Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations.
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
In this paper, we introduce a new structure-preserving deep learning architecture, the Lie group Forced Variational Integrator Network (LieFVIN), capable of learning controlled Lagrangian or Hamiltonian dynamics on Lie groups, either from position-velocity or position-only data.
Approximation of nearly-periodic symplectic maps via structure-preserving neural networks
This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability.
