  Although machine learning (ML) is increasingly employed recently for
mechanistic problems, the black-box nature of conventional ML architectures
lacks the physical knowledge to infer unforeseen input conditions. This implies
both severe overfitting during a dearth of training data and inadequate
physical interpretability, which motivates us to propose a new kinematically
consistent, physics-based ML model. In particular, we attempt to perform
physically interpretable learning of inverse problems in wave propagation
without suffering overfitting restrictions. Towards this goal, we employ long
short-term memory (LSTM) networks endowed with a physical,
hyperparameter-driven regularizer, performing penalty-based enforcement of the
characteristic geometries. Since these characteristics are the kinematical
invariances of wave propagation phenomena, maintaining their structure provides
kinematical consistency to the network. Even with modest training data, the
kinematically consistent network can reduce the $L_1$ and $L_\infty$ error
norms of the plain LSTM predictions by about 45% and 55%, respectively. It can
also increase the horizon of the plain LSTM's forecasting by almost two times.
To achieve this, an optimal range of the physical hyperparameter, analogous to
an artificial bulk modulus, has been established through numerical experiments.
The efficacy of the proposed method in alleviating overfitting, and the
physical interpretability of the learning mechanism, are also discussed. Such
an application of kinematically consistent LSTM networks for wave propagation
learning is presented here for the first time.
