Adversarial attacks are a potential threat to machine learning models, as they can cause the model to make incorrect predictions by introducing imperceptible perturbations to the input data. While extensively studied in unstructured data like images, their application to structured data like tabular data presents unique challenges due to the heterogeneity and intricate feature interdependencies of tabular data. Imperceptibility in tabular data involves preserving data integrity while potentially causing misclassification, underscoring the need for tailored imperceptibility criteria for tabular data. However, there is currently a lack of standardised metrics for assessing adversarial attacks specifically targeted at tabular data. To address this gap, we derive a set of properties for evaluating the imperceptibility of adversarial attacks on tabular data. These properties are defined to capture seven perspectives of perturbed data: proximity to original inputs, sparsity of alterations, deviation to datapoints in the original dataset, sensitivity of altering sensitive features, immutability of perturbation, feasibility of perturbed values and intricate feature interdepencies among tabular features. Furthermore, we conduct both quantitative empirical evaluation and case-based qualitative examples analysis for seven properties. The evaluation reveals a trade-off between attack success and imperceptibility, particularly concerning proximity, sensitivity, and deviation. Although no evaluated attacks can achieve optimal effectiveness and imperceptibility simultaneously, unbounded attacks prove to be more promised for tabular data in crafting imperceptible adversarial examples. The study also highlights the limitation of evaluated algorithms in controlling sparsity effectively. We suggest incorporating a sparsity metric in future attack design to regulate the number of perturbed features.

Our recent intensive study has found that physics - informed neural networks (PINN) tend to be local approximators after training . This observation le d to th e development of a novel physics - informed rad ial basis network (PIRBN), which is capable of maintaining the local approximating property throughout the entire training process . Unlike deep neural networks, a PIRBN comprises 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, comprehens ive investigations regarding the initialisation strategies of PIRBN were conducted. Based on numerical examples, PIRBN has been demonstrated to be more effective than PINN in solving nonlinear partial differential equation s with high - frequency features and ill - posed computational domains. 2 Moreover, the existing PINN numerical techniques, such as adaptive learning, decomposition and different types of loss functions, are applicable to PIRBN.

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications, such as structural risk estimation and medical diagnosis. This presents a significant barrier to the practical implementation of DL in these fields. Physics-guided deep learning (PGDL) is a novel type of DL that can integrate physics laws to train neural networks. This can be applied to any systems that are controlled or governed by physics laws, such as mechanics, finance and medical applications. It has been demonstrated that, with the additional information provided by physics laws, PGDL achieves great accuracy and generalisation in the presence of data scarcity. This review provides a detailed examination of PGDL and offers a structured overview of its use in addressing data scarcity across various fields, including physics, engineering and medical applications. Moreover, the review identifies the current limitations and opportunities for PGDL in relation to data scarcity and offers a thorough discussion on the future prospects of PGDL.