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

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... arameters, 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.