This limits SNNs' capability of transmitting precise information in the network, which becomes worse for deeper SNNs.

Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties.

Although existing artistic style transfer methods have achieved significant improvement with deep neural networks, they still suffer from artifacts such as disharmonious colors and repetitive patterns. Motivated by this, we propose an internal-external style transfer method with two contrastive losses.

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models.

The adversarial training is a popular tool to remedy the vulnerability of deep learning models against adversarial attacks, and there is rich theoretical literature on the training loss of adversarial training algorithms. In contrast, this paper studies the algorithmic stability of a generic adversarial training algorithm, which can further help to establish an upper bound for generalization error. By figuring out the stability upper bound and lower bound, we argue that the non-differentiability issue of adversarial training causes worse algorithmic stability than their natural counterparts. To tackle this problem, we consider a noise injection method. While the non-differentiability problem seriously affects the stability of adversarial training, injecting noise enables the training trajectory to avoid the occurrence of non-differentiability with dominating probability, hence enhancing the stability performance of adversarial training. Our analysis also studies the relation between the algorithm stability and numerical approximation error of adversarial attacks.