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Found 8 papers, 2 papers with code
Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEs
The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces.
Good Lattice Training: Physics-Informed Neural Networks Accelerated by Number Theory
However, the solutions to PDEs are inherently infinite-dimensional, and the distance between the output and the solution is defined by an integral over the domain.
FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities
However, these models incorporate the underlying structures, and in most situations where neural networks learn unknown systems, these structures are also unknown.
Neural Symplectic Form: Learning Hamiltonian Equations on General Coordinate Systems
In this study, we propose a model that learns the symplectic form from data using neural networks, thereby providing a method for learning Hamiltonian equations from data represented in general coordinate systems, which are not limited to the generalized coordinates and the generalized momenta.
KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss
To apply the KAM theory, we provide a generalization error bound for Hamiltonian neural networks by deriving an estimate of the covering number of the gradient of the multi-layer perceptron, which is the key ingredient of the model.
Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory
The symplectic adjoint method obtains the exact gradient (up to rounding error) with memory proportional to the number of uses plus the network size.
Method for estimating hidden structures determined by unidentifiable state-space models and time-series data based on the Groebner basis
As the parameters of unidentifiable models cannot be uniquely determined from the given data, it is difficult to examine the systems described by such models.
Deep Energy-Based Modeling of Discrete-Time Physics
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws.
