Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however, in practice, this requires an expensive tuning phase. We show through several numerical tests that modifying the output of the neural network to exactly match the prescribed values leads to more efficient and accurate solvers. The best results are achieved by exactly enforcing the Dirichlet boundary conditions by means of an approximate distance function. We also show that variationally imposing the Dirichlet boundary conditions via Nitsche's method leads to suboptimal solvers.

[The evaluation of women's health promotion services: the internal client, the external client]

OBJECTIVES

To find the opinion of internal and external customers of the Women's Health Promotion Services; to obtain information about the perceptions and suggestions of both midwives and users of the service.

DESIGN

An observational study of the qualitative evaluation of a service provided in Primary Health Care, through an open questionnaire to midwives and focus groups with users.

SETTING

Health Area 4 in the Community of Valencia.

PARTICIPANTS

15 midwives from Health Area 4, 3 groups of women using the Pregnancy Follow-up Programme and 3 groups from the Programme of Integrated Care for climacteric women, coming from two Health Districts, one urban and one rural.

MAIN RESULTS

For midwives, coordination with general practitioners was better in the urban setting, and with Family Planning Centres in the rural one. Absence of team work with gynaecologists, and gynaecologists' failure to value midwives' work, were identified as problems.

CONCLUSIONS

Different patterns for the organisation and use of women's health promotion services were identified between the urban and rural setting. The problems of coordination identified by the midwives are not perceived as such by the service's users, who evaluated as satisfactory the Primary Care services received.