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07/26/2023
Good Lattice Training: Physics-Informed Neural Networks Accelerated by Number Theory
Physics-informed neural networks (PINNs) offer a novel and efficient app...
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10/01/2022
FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities
Many real-world dynamical systems are associated with first integrals (a...
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12/28/2021
An Error Analysis Framework for Neural Network Modeling of Dynamical Systems
We propose a theoretical framework for investigating a modeling error ca...
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12/27/2021
Symplecticity of coupled Hamiltonian systems
We derived a condition under which a coupled system consisting of two fi...
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11/22/2021
Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics
Definite integrals with parameters of holonomic functions satisfy holono...
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02/22/2021
Universal Approximation Properties of Neural Networks for Energy-Based Physical Systems
In Hamiltonian mechanics and the Landau theory, many physical phenomena ...
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02/19/2021
Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory
A neural network model of a differential equation, namely neural ODE, ha...
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12/22/2020
Method for estimating hidden structures determined by unidentifiable state-space models and time-series data based on the Groebner basis
In this study, we propose a method for extracting the hidden algebraic s...
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05/21/2019