Physical neural networks (PNNs) are emerging paradigms for neural network acceleration due to their high-bandwidth, in-propagation analogue processing. Despite the advantages of PNN for inference, training remains a challenge. The imperfect information of the physical transformation means the failure of conventional gradient-based updates from backpropagation (BP). Here, we present the asymmetrical training (AT) method, which treats the PNN structure as a grey box. AT performs training while only knowing the last layer output and neuron topological connectivity of a deep neural network structure, not requiring information about the physical control-transformation mapping. We experimentally demonstrated the AT method on deep grey-box PNNs implemented by uncalibrated photonic integrated circuits (PICs), improving the classification accuracy of Iris flower and modified MNIST hand-written digits from random guessing to near theoretical maximum. We also showcased the consistently enhanced performance of AT over BP for different datasets, including MNIST, fashion-MNIST, and Kuzushiji-MNIST. The AT method demonstrated successful training with minimal hardware overhead and reduced computational overhead, serving as a robust light-weight training alternative to fully explore the advantages of physical computation.