Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs

Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the local property throughout the entire training process. Compared to deep neural networks, a PIRBN comprises of only one hidden layer and a radial basis "activation" function. Under appropriate conditions, we demonstrated that the training of PIRBNs using gradient descendent methods can converge to Gaussian processes. Besides, we studied the training dynamics of PIRBN via the neural tangent kernel (NTK) theory. In addition, comprehensive investigations regarding the initialisation strategies of PIRBN were conducted. Based on numerical examples, PIRBN has been demonstrated to be more effective and efficient than PINN in solving PDEs with high-frequency features and ill-posed computational domains. Moreover, the existing PINN numerical techniques, such as adaptive learning, decomposition and different types of loss functions, are applicable to PIRBN. The programs that can regenerate all numerical results can be found at https://github.com/JinshuaiBai/PIRBN.

Physics-guided deep learning for data scarcity

Data are the core of deep learning (DL), and the quality of data significantly affects the performance of DL models. However, high-quality and well-annotated databases are hard or even impossible to acquire for use in many applications, such as structural risk estimation and medical diagnosis, which is an essential barrier that blocks the applications of DL in real life. Physics-guided deep learning (PGDL) is a novel type of DL that can integrate physics laws to train neural networks. It can be used for any systems that are controlled or governed by physics laws, such as mechanics, finance and medical applications. It has been shown that, with the additional information provided by physics laws, PGDL achieves great accuracy and generalisation when facing data scarcity. In this review, the details of PGDL are elucidated, and a structured overview of PGDL with respect to data scarcity in various applications is presented, including physics, engineering and medical applications. Moreover, the limitations and opportunities for current PGDL in terms of data scarcity are identified, and the future outlook for PGDL is discussed in depth.

MedNet: Pre-trained Convolutional Neural Network Model for the Medical Imaging Tasks

Deep Learning (DL) requires a large amount of training data to provide quality outcomes. However, the field of medical imaging suffers from the lack of sufficient data for properly training DL models because medical images require manual labelling carried out by clinical experts thus the process is time-consuming, expensive, and error-prone. Recently, transfer learning (TL) was introduced to reduce the need for the annotation procedure by means of transferring the knowledge performed by a previous task and then fine-tuning the result using a relatively small dataset. Nowadays, multiple classification methods from medical imaging make use of TL from general-purpose pre-trained models, e.g., ImageNet, which has been proven to be ineffective due to the mismatch between the features learned from natural images (ImageNet) and those more specific from medical images especially medical gray images such as X-rays. ImageNet does not have grayscale images such as MRI, CT, and X-ray. In this paper, we propose a novel DL model to be used for addressing classification tasks of medical imaging, called MedNet. To do so, we aim to issue two versions of MedNet. The first one is Gray-MedNet which will be trained on 3M publicly available gray-scale medical images including MRI, CT, X-ray, ultrasound, and PET. The second version is Color-MedNet which will be trained on 3M publicly available color medical images including histopathology, taken images, and many others. To validate the effectiveness MedNet, both versions will be fine-tuned to train on the target tasks of a more reduced set of medical images. MedNet performs as the pre-trained model to tackle any real-world application from medical imaging and achieve the level of generalization needed for dealing with medical imaging tasks, e.g. classification. MedNet would serve the research community as a baseline for future research.