Journal
MACHINE LEARNING AND KNOWLEDGE DISCOVERY IN DATABASES, ECML PKDD 2019, PT I
Volume 1167, Issue -, Pages 217-228Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-030-43823-4_19
Keywords
Neural networks; Equation discovery; Hamiltonian systems
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Funding
- U.S. Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344]
- LLNL-LDRD Program [19-ERD-009]
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We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network model of the potential and then applies an equation discovery technique to extract from the neural potential a closed-form algebraic expression. We demonstrate this approach for several systems, including oscillators, a central force problem, and a problem of two charged particles in a classical Coulomb potential. Through these test problems, we show close agreement between learned neural potentials, the interpreted potentials we obtain after training, and the ground truth. In particular, for the central force problem, we show that our approach learns the correct effective potential, a reduced-order model of the system.
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