ベイズデータ同化によるハミルトン力学系の学習
Learning Hamiltonian Dynamics with Bayesian Data Assimilation
ハミルトニアンを保存するニューラルネットワークで未知の力学系を学習し、自己回帰予測誤差の導入とベイズデータ同化によるリアルタイム補正で長期予測精度を高める手法を提案した。
著者: Taehyeun Kim, Tae-Geun Kim, Anouck Girard, Ilya Kolmanovsky
分類: cs.LG, cs.RO, cs.SY, eess.SY
原文アブストラクト
In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions) and their conjugate momenta while preserving a constant Hamiltonian. To further enhance long-term prediction accuracy, we introduce an Autoregressive Hamiltonian Neural Network, which incorporates autoregressive prediction errors into the training objective. Additionally, we employ Bayesian data assimilation to refine predictions in real-time using online measurement data. Numerical experiments on a spring-mass system and highly elliptic orbits under gravitational perturbations demonstrate the effectiveness of the proposed method, highlighting its potential for accurate and robust long-term predictions.
