  The fundamental task of classification given a limited number of training
data samples is considered for physical systems with known parametric
statistical models. The standalone learning-based and statistical model-based
classifiers face major challenges towards the fulfillment of the classification
task using a small training set. Specifically, classifiers that solely rely on
the physics-based statistical models usually suffer from their inability to
properly tune the underlying unobservable parameters, which leads to a
mismatched representation of the system's behaviors. Learning-based
classifiers, on the other hand, typically rely on a large number of training
data from the underlying physical process, which might not be feasible in most
practical scenarios. In this paper, a hybrid classification method -- termed
HyPhyLearn -- is proposed that exploits both the physics-based statistical
models and the learning-based classifiers. The proposed solution is based on
the conjecture that HyPhyLearn would alleviate the challenges associated with
the individual approaches of learning-based and statistical model-based
classifiers by fusing their respective strengths. The proposed hybrid approach
first estimates the unobservable model parameters using the available
(suboptimal) statistical estimation procedures, and subsequently use the
physics-based statistical models to generate synthetic data. Then, the training
data samples are incorporated with the synthetic data in a learning-based
classifier that is based on domain-adversarial training of neural networks.
Specifically, in order to address the mismatch problem, the classifier learns a
mapping from the training data and the synthetic data to a common feature
space. Simultaneously, the classifier is trained to find discriminative
features within this space in order to fulfill the classification task.
