  This paper is aimed at using the newly developing field of physics informed
machine learning (PIML) to develop models for predicting the remaining useful
lifetime (RUL) aircraft engines. We consider the well-known benchmark NASA
Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) data as the main
data for this paper, which consists of sensor outputs in a variety of different
operating modes. C-MAPSS is a well-studied dataset with much existing work in
the literature that address RUL prediction with classical and deep learning
methods. In the absence of published empirical physical laws governing the
C-MAPSS data, our approach first uses stochastic methods to estimate the
governing physics models from the noisy time series data. In our approach, we
model the various sensor readings as being governed by stochastic differential
equations, and we estimate the corresponding transition density mean and
variance functions of the underlying processes. We then augment LSTM
(long-short term memory) models with the learned mean and variance functions
during training and inferencing. Our PIML based approach is different from
previous methods, and we use the data to first learn the physics. Our results
indicate that PIML discovery and solutions methods are well suited for this
problem and outperform previous data-only deep learning methods for this data
set and task. Moreover, the framework developed herein is flexible, and can be
adapted to other situations (other sensor modalities or combined multi-physics
environments), including cases where the underlying physics is only partially
observed or known.
