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The purpose of this study is to solve the Reynolds equation for finite journal bearings by using the physics-informed neural networks (PINNs) method. As a meshless method, it is unnecessary to use big data to train the neural networks, but to satisfy the Reynolds equation and the corresponding boundary conditions by using the known physics information.

Here, the boundary conditions are enforced through the loss function firstly, i.e. the soft constrain method. After this, an equation was constructed to build a surrogate model for satisfying the corresponding boundary conditions naturally, i.e. the hard constrain method.

For the soft one, in brief, the pressure results agree well with existing results, apart from the ones on the boundaries. While for the hard one, it can be noted that the discrepancies on the boundaries are reduced significantly.

The PINNs method is used to solve the Reynolds equation for finite journal bearings, and the error values on the boundaries for the results of the soft constrain method are improved by using the hard constrain method. Therefore, the hard constraint maybe also a good option when the pressure results on the boundaries are emphasized.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2023-0045/

This study aims to measure social enterprises’ (SEs’) social objectives under the United Nation’s 17 Sustainable Development Goals (SDGs) framework, and explore the impact of SEs’ social objectives on their choices of legal forms.

This study used semi-structured questionnaires followed up by field interviews and observations of the sampled SEs. The survey sample includes 80 participants of Social Entrepreneurs Stars Competition in Zhejiang Province of China. The authors conduct content analysis to measure the objectives of SEs. The authors also perform descriptive analysis, chi-square test and regression analysis on the data.

The findings confirm the theoretical discussions that SEs’ choices of legal forms reflect SEs’ strategies toward achieving social objectives. Similar to certain countries, some SEs in China register as nonprofit entities to concentrate on nonprofitable sustainability objectives, while others register as commercial enterprises or hybrid organizations to generate profits. However, some SEs focus on profitable non-sustainability issues and fail to prioritize social objectives over economic objectives. There are positive effects of social entrepreneurs’ background similarity and negative effects of social entrepreneurs’ educational level on their SEs’ choices to register as commercial enterprises.

Due to the small size and nonrepresentative sample this study is based on, the findings need be further tested by a larger sample. SEs in different service domains rely on different types of financial resources (Mair et al., 2012; Doherty et al., 2014). In future research, the model can be expanded to test the effects of service domains and types of financial sources on SEs’ choices of legal forms.

To encourage more societal resources being allocated toward achieving the United Nations’ SDGs, policymakers and SE certification programs are recommended to explicitly incorporate sustainability objectives into the evaluation standards and supportive policies for SEs. Social entrepreneurs who aim to balance the social and economic objectives in their business are suggested to target the population with whom they share similar community background. Training or consulting programs for social entrepreneurs are suggested to provide advice tailored to their socio-economic background and personal experiences.

To the best of the authors’ this study is the first quantitative analysis to identify factors that associate with SEs’ choice of legal forms in China. The authors developed new instruments to measure SEs’ social objectives and service targets, access to financial resources and social entrepreneurs’ social-economic backgrounds.