This article provides a method that combines Taylor expansion and neural network technology to accelerate the solution of an isogeometric acoustic model with ground reflection. The Helmholtz equation for the acoustic problem is solved by the boundary element method (BEM), and the model structure shape is optimized by combining the isogeometric method. In addition, to mitigate the high computational cost arising from repeated evaluations at each discrete frequency point, the Hankel function is approximated via a Taylor series expansion. This approach enables the decoupling of the boundary element method equation into frequency-dependent and frequency-independent terms. After using the deep neural network (DNN) training simulation results, the acoustic results are predicted. The DNN model can effectively analyze the sound field problem. Finally, the accuracy and feasibility of the proposed algorithm are verified by a two-dimensional numerical example.

Computing the minimal axiom sets (MinAs) for an unsatisfiable class is an important task in incoherent ontology debugging. Ddebugging ontologies based on patterns (DOBP) is a pattern-based debugging method that uses a set of heuristic strategies based on four patterns. Each pattern is represented as a directed graph and the depth-first search strategy is used to find the axiom paths relevant to the MinAs of the unsatisfiable class. However, DOBP is inefficient when a debugging large incoherent ontology with a lot of unsatisfiable classes. To solve the problem, we first extract a module responsible for the erroneous classes and then compute the MinAs based on the extracted module. The basic idea of module extraction is that rather than computing MinAs based on the original ontology $ \mathcal{O} $, they are computed based on a module $ \mathcal{M} $ extracted from $ \mathcal{O} $. $ \mathcal{M} $ provides a smaller search space than $ \mathcal{O} $ because $ \mathcal{M} $ is considerably smaller than $ \mathcal{O} $. The experimental results on biological ontologies show that the module extracted using the Module-DOBP method is smaller than the original ontology. Lastly, our proposed approach optimized with the module extraction algorithm is more efficient than the DOBP method both for large-scale ontologies and numerous unsatisfiable classes.

Prompt tuning has shown impressive performance in the domain of few-shot text classification tasks, yet the coverage of its crucial module, i.e., the verbalizer, has a considerable effect on the results. Existing methods have not addressed breadth and depth in constructing the verbalizer. Specifically, breadth refers to the cross-granularity issue of label words, while depth refers to the number of elements within a granularity that make a positive contribution to classification. This study proposes a dynamic search tree (DST) method to enhance the coverage of the verbalizer further. The core idea is to utilize the hierarchical relationships within the tree to automatically unearth concealed high-quality words, thereby ensuring that the constructed verbalizer possesses both higher breadth and depth. DST involves amalgamating knowledgeable prompt tuning (KPT) by leveraging the breadth of the KPT’s label word space, which encompasses characteristics at various granularities and from various perspectives, thereby addressing the problem of the verbalizer’s breadth. Subsequently, a method that is capable of measuring the interrelation between words on a designated feature is proposed by analyzing the word vector, which successfully eradicates the noise introduced by irrelevant dimensions during the process of extending the verbalizer and effectively enhances the quality of the verbalizer in terms of depth. Extensive experiments were conducted on zero- and few-shot text classification tasks to demonstrate the effectiveness of our method. Our source code is publicly available at https://github.com/XianliangXia/VerbalizerConstrucionByDynamicSearchTree.