A comparative study of physicsinformed neural network models for learning unknown dynamics and constitutive relations
Abstract
We investigate the use of discrete and continuous versions of physicsinformed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the dynamics with a deep neural network (DNN). When the dynamics of the system are known up to the specification of constitutive relations (that can depend on the state of the system), we represent these constitutive relations with a DNN. The discrete versions combine classical multistep discretization methods for dynamical systems with neural network based machine learning methods. On the other hand, the continuous versions utilize deep neural networks to minimize the residual function for the continuous governing equations. We use the case of a fedbatch bioreactor system to study the effectiveness of these approaches and discuss conditions for their applicability. Our results indicate that the accuracy of the trained neural network models is much higher for the cases where we only have to learn a constitutive relation instead of the whole dynamics. This finding corroborates the wellknown fact from scientific computing that building as much structural information is available into an algorithm can enhance its efficiency and/or accuracy.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.04058
 Bibcode:
 2019arXiv190404058T
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Numerical Analysis;
 Mathematics  Dynamical Systems;
 Mathematics  Numerical Analysis;
 Physics  Computational Physics