Zhiguang Wang

Classical acoustic impedance inversion methods rely on mathematical and physical models to estimate subsurface acoustic impedance distribution. However, these methods face difficulties in accurately fitting complex impedance data. While deep learning methods have achieved higher accuracy and efficiency in impedance inversion, they remain black box models, lacking interpretability. So, it is difficult to analyze the reason why they are (or are not) effective. To address the limitations of both traditional and deep learning methods, this paper proposes a novel approach, AII-SR (Acoustic Impedance Inversion with Symbolic Regression), which discovers partial differential equations (PDEs) from impedance data to model acoustic impedance inversion. To discover these PDEs, AII-SR adopts a dual-learning framework. It employs a forward model based on the Robinson convolution principle to ensure the physical consistency and reliability of predictions. Subsequently, AII-SR creates an inversion model that combines a symbolic regression-based PDE generator with a physics-informed solving neural network (PSNN) to identify PDEs that accurately fit the impedance data. Experiments demonstrate that AII-SR outperforms deep learning methods, such as SSEI, TCN and Se-Unet, in terms of accuracy and interpretability. AII-SR generates concise, interpretable mathematical expressions in the form of PDEs, offering profound insights into the physical relationships between seismic and impedance data.

Grounded Situation Recognition (GSR) aims to generate structured image descriptions. For a given image, GSR needs to identify the key verb, the nouns corresponding to roles, and their bounding-box groundings. However, current GSR research demands numerous meticulously labeled images, which are labor-intensive and time-consuming, making it costly to expand detection categories. Our study enhances model accuracy in detecting and localizing under data scarcity, reducing dependency on large datasets and paving the way for broader detection capabilities. In this paper, we propose the Grounded Situation Recognition under Data Scarcity (GSRDS) model, which uses the CoFormer model as the baseline and optimizes three subtasks: image feature extraction, verb classification, and bounding-box localization, to better adapt to data-scarce scenarios. Specifically, we replace ResNet50 with EfficientNetV2-M for advanced image feature extraction. Additionally, we introduce the Transformer Combined with CLIP for Verb Classification (TCCV) module, utilizing features extracted by CLIP’s image encoder to enhance verb classification accuracy. Furthermore, we design the Multi-source Verb-Role Queries (Multi-VR Queries) and the Dual Parallel Decoders (DPD) modules to improve the accuracy of bounding-box localization. Through extensive comparative experiments and ablation studies, we demonstrate that our method achieves higher accuracy than mainstream approaches in data-scarce scenarios. Our code will be available at https://github.com/Zhou-maker-oss/GSRDS.

Symbolic regression (SR) is the task of discovering a symbolic expression that fits a given data set from the space of mathematical expressions. Despite the abundance of research surrounding the SR problem, there's a scarcity of works that confirm its NP-hard nature. Therefore, this paper introduces the concept of a symbol graph as a comprehensive representation of the entire mathematical expression space, effectively illustrating the NP-hard characteristics of the SR problem. Leveraging the symbol graph, we establish a connection between the SR problem and the task of identifying an optimally fitted degree-constrained Steiner Arborescence (DCSAP). The complexity of DCSAP, which is proven to be NP-hard, directly implies the NP-hard nature of the SR problem.