GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems

@article{Zhang2022GFINNsGF,
  title={GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems},
  author={Zhen Zhang and Yeonjong Shin and George Em Karniadakis},
  journal={Philosophical Transactions of the Royal Society A},
  year={2022},
  volume={380}
}
We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a neural network whose architecture is designed to satisfy the required conditions. The component-wise architecture design provides flexible ways of leveraging available physics information into neural networks. We prove theoretically that GFINNs are… 

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References

SHOWING 1-10 OF 45 REFERENCES

Structure-preserving neural networks

Lagrangian Neural Networks

LNNs are proposed, which can parameterize arbitrary Lagrangians using neural networks, and do not require canonical coordinates, and thus perform well in situations where canonical momenta are unknown or difficult to compute.

OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle

The proposed systematic method for learning stable and interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle validates the basic approach of Lorenz, although it is discovered that the dimension of the learned autonomous model required for faithful representation increases with the Rayleigh number.

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems

This work puts forth a machine learning approach for identifying nonlinear dynamical systems from data that combines classical tools from numerical analysis with powerful nonlinear function approximators to distill the mechanisms that govern the evolution of a given data-set.

Hamiltonian Neural Networks

Inspiration from Hamiltonian mechanics is drawn to train models that learn and respect exact conservation laws in an unsupervised manner, and this model trains faster and generalizes better than a regular neural network.

Machine learning structure preserving brackets for forecasting irreversible processes

This work presents a novel parameterization of dissipative brackets from metriplectic dynamical systems appropriate for learning irreversible dynamics with unknown a priori model form, and guarantees exact preservation of a fluctuation-dissipation theorem, ensuring thermodynamic consistency.

Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks

This work demonstrates through several simulations that PNNs are capable of handling very accurately several challenging tasks, including the motion of a particle in the electromagnetic potential, the nonlinear Schrödinger equation, and pixel observations of the two-body problem.