TY - GEN
T1 - Machine learning structure preserving brackets for forecasting irreversible processes
AU - Lee, Kookjin
AU - Trask, Nathaniel
AU - Stinis, Panos
N1 - Funding Information:
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003530. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. SAND Number: SAND2021-7461 O. We thank Chris Eldred for his recommendation to consider Ottingers bracket formulation of GENERIC. The work of N. Trask, and P. Stinis is supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research under the Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project. N. Trask and K. Lee are supported by the Department of Energy early career program.
Funding Information:
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003530. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. SAND Number: SAND2021-7461 O.
Funding Information:
We thank Chris Eldred for his recommendation to consider Ottingers bracket formulation of GENERIC. The work of N. Trask, and P. Stinis is supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research under the Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project. N. Trask and K. Lee are supported by the Department of Energy early career program.
Publisher Copyright:
© 2021 Neural information processing systems foundation. All rights reserved.
PY - 2021
Y1 - 2021
N2 - Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve structure for systems with reversible dynamics. In this work we present a novel parameterization of dissipative brackets from metriplectic dynamical systems appropriate for learning irreversible dynamics with unknown a priori model form. The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively. Furthermore, for the case of added thermal noise, we guarantee exact preservation of a fluctuation-dissipation theorem, ensuring thermodynamic consistency. We provide benchmarks for dissipative systems demonstrating learned dynamics are more robust and generalize better than either "black-box" or penalty-based approaches.
AB - Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve structure for systems with reversible dynamics. In this work we present a novel parameterization of dissipative brackets from metriplectic dynamical systems appropriate for learning irreversible dynamics with unknown a priori model form. The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively. Furthermore, for the case of added thermal noise, we guarantee exact preservation of a fluctuation-dissipation theorem, ensuring thermodynamic consistency. We provide benchmarks for dissipative systems demonstrating learned dynamics are more robust and generalize better than either "black-box" or penalty-based approaches.
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M3 - Conference contribution
AN - SCOPUS:85126859855
T3 - Advances in Neural Information Processing Systems
SP - 5696
EP - 5707
BT - Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
A2 - Ranzato, Marc'Aurelio
A2 - Beygelzimer, Alina
A2 - Dauphin, Yann
A2 - Liang, Percy S.
A2 - Wortman Vaughan, Jenn
PB - Neural information processing systems foundation
T2 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
Y2 - 6 December 2021 through 14 December 2021
ER -