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With the continuous progress of technology, the subject of life science plays an increasingly important role, among which the application of artificial intelligence in the medical field has attracted more and more attention. Bell facial palsy, a neurological ailment characterized by facial muscle weakness or paralysis, exerts a profound impact on patients' facial expressions and masticatory abilities, thereby inflicting considerable distress upon their overall quality of life and mental well-being. In this study, we designed a facial attribute recognition model specifically for individuals with Bell's facial palsy. The model utilizes an enhanced SSD network and scientific computing to perform a graded assessment of the patients' condition. By replacing the VGG network with a more efficient backbone, we improved the model's accuracy and significantly reduced its computational burden. The results show that the improved SSD network has an average precision of 87.9% in the classification of light, middle and severe facial palsy, and effectively performs the classification of patients with facial palsy, where scientific calculations also increase the precision of the classification. This is also one of the most significant contributions of this article, which provides intelligent means and objective data for future research on intelligent diagnosis and treatment as well as progressive rehabilitation. [ABSTRACT FROM AUTHOR]

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning. [ABSTRACT FROM AUTHOR]