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math.DS2026
Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
Yeang Makara, Yusuke Tanaka, Takashi Matsubara +1
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational an…
math.DS2021
KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss
Yuhan Chen, Takashi Matsubara, Takaharu Yaguchi
Many physical phenomena are described by Hamiltonian mechanics using an energy function (the Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamilton…