LordNet: An efficient neural network for learning to solve parametric partial differential equations without simulated data.

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information in the MSR loss, which we called long-range entanglements, and identify the challenge that the neural network requires the capacity to model the long-range entanglements in the spatial domain of the PDE, whose patterns vary in different PDEs. To tackle the challenge, we propose LordNet, a tunable and efficient neural network for modeling various entanglements. Inspired by the traditional solvers, LordNet models the long-range entanglements with a series of matrix multiplications, which can be seen as the low-rank approximation to the general fully-connected layers and extracts the dominant pattern with reduced computational cost. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements from the MSR loss can be well modeled by the LordNet, yielding better accuracy and generalization ability than other neural networks. The results show that the Lordnet can be 40× faster than traditional PDE solvers. In addition, LordNet outperforms other modern neural network architectures in accuracy and efficiency with the smallest parameter size.

Physics-informed neural wavefields with Gabor basis functions.

Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be computationally demanding, especially for intricate functions like wavefields. This is primarily due to the neural-based (learned) basis functions, biased toward low frequencies, as they are dominated by polynomial calculations, which are not inherently wavefield-friendly. In response, we propose an approach to enhance the efficiency and accuracy of neural network wavefield solutions by modeling them as linear combinations of Gabor basis functions that satisfy the wave equation. Specifically, for the Helmholtz equation, we augment the fully connected neural network model with an adaptable Gabor layer constituting the final hidden layer, employing a weighted summation of these Gabor neurons to compute the predictions (output). These weights/coefficients of the Gabor functions are learned from the previous hidden layers that include nonlinear activation functions. To ensure the Gabor layer's utilization across the model space, we incorporate a smaller auxiliary network to forecast the center of each Gabor function based on input coordinates. Realistic assessments showcase the efficacy of this novel implementation compared to the vanilla PINN, particularly in scenarios involving high-frequencies and realistic models that are often challenging for PINNs.

Longitudinal measurement invariance of the meaning in life questionnaire in Chinese college students.

The Meaning in Life Questionnaire (MLQ) is a popular tool to measure the presence of and one's search for meaning in life. Although the validity of the MLQ has been verified in previous studies, the evidence from longitudinal measurement invariance (LMI) of the MLQ is still lacking. The current study aimed to examine the LMI of the MLQ in a sample of Chinese college students (N = 328) at a 1-year interval. Multigroup confirmatory factor analysis (MCFA) was used to examine the LMI of the MLQ over four time points (over the course of 1 year). Results indicate that the MLQ has strict longitudinal invariance across 1-year in Chinese college students, and the latent means difference of MLQ-P is not significant differences across time, while the latent means difference of MLQ-S show significant differences between Time 1 and the other time points. Moreover, the internal consistency reliabilities (e.g., alpha and omega) of the MLQ scores were acceptable at all four time points, and the stability coefficients across time were moderate. These findings provide preliminary evidence that the MLQ has satisfactory longitudinal properties in Chinese college students.

The effect of subjective age on loneliness in the old adults: The chain mediating role of resilience and self-esteem.

Objectives: This study aimed to explore the effect of subjective age on loneliness in old adults, and the mediating role of resilience and self-esteem in subjective age and loneliness. Methods: Approximately 450 old adults from Jiangxi, Hunan, Henan provinces completed the third edition of the Loneliness Scale (UCLA-LS III), Age Decade Scale (ADS), Connor-Davidson Resilience Scale (CD-RISC), and Self-Esteem Scale (SES). Results: (1) Subjective age was significantly positively correlated with loneliness. (2) Resilience, self-esteem, and loneliness were significantly negatively correlated. (3) Subjective age affected loneliness through the mediating effects of resilience and self-esteem, respectively. (4) Resilience and self-esteem played a chain mediating role between subjective age and loneliness. Conclusion: Resilience and self-esteem can directly affect the loneliness of the old adults alone and can also affect the loneliness of the old adults through the chain mediating effect of resilience and self-esteem.

Family functioning and adolescent depression: A moderated mediation model of self-esteem and peer relationships.

In consideration of family system theory, the vulnerability model of depression, and the stress buffering model of social support, the current study examined the effect of family functioning on adolescent depression, the mediating effect of self-esteem, and the moderating effect of peer relationships. A sample of Chinese adolescents (n = 562, 47.15% male, 52.85% female, mean age 14.33 years, SD = 1.81 years) completed questionnaires regarding family functioning, depression, self-esteem, and peer relationships. The results showed that: (1) family functioning had a significant negative predictive effect on adolescent depression; (2) self-esteem plays a mediating role between family functioning and adolescent depression; and (3) peer relationships have a moderating effect on the relationship between self-esteem and adolescent depression, supporting the moderated mediation model. These results reveal the influence mechanism of family functioning on adolescent depression and have implications for adolescent depression intervention.

A systematic review and meta-analysis of acupuncture combined with Tuina in the treatment of insomnia.

BACKGROUND: Insomnia is a sleep disorder with insufficient sleep time or/and poor sleep quality. Relevant epidemiological studies have shown that insomnia symptoms occur in about 35% to 50% of the adult population, and it is one of the most common diseases in the elderly. Patients who often suffer from insomnia are prone to symptoms such as fatigue, weakened cognitive function, depression, and even mental illness, which bring serious physical and mental damage to individuals and a heavy economic burden to social medical care and families. Traditional Chinese medicine and modern medicine have their own advantages in the treatment of insomnia, and there is currently a lack of reports on the comparison of acupuncture combined with massage and conventional medicine. OBJECTIVE: To evaluate the clinical efficacy of acupuncture combined with Tuina in the treatment of insomnia. METHODS: Search for clinical randomized controlled trials (RCTs) of acupuncture combined with Tuina in the treatment of insomnia from PubMed, Cochrane Library, Web of Science, China National Knowledge Infrastructure, Wan Fang Database, and China Science and Technology Journal Database. The RevMan5.4 software was used for Meta- analysis after literature screening, data extraction and quality evaluation. RESULTS: A total of 29 studies were included with a total of 2688 cases. Compared with drugs or acupuncture alone, acupuncture combined with Tuina has advantages in the total clinical effectiveness, as well as the Pittsburgh Sleep Quality Index (PSQI) and Statistical Self-Rating Anxiety Scale score (SAS) (OR = 3.59, 95% confidence interval [CI] [2.77, 4.66], Z = 9.62 [P < .00001]) (MD = -2.44, 95% CI [-2.93, -1.95], Z = 9.72 [P < .00001]) (MD = -8.42, 95% CI [-10.23, -6.61], Z = 9.09 [P < .00001]). There was no statistically significant difference in Statistical Self-rating Depression Scale score (SDS) (MD = -5.26, 95% CI [-11.29, 0.78], Z = 1.71 [P > .05]). CONCLUSION: Acupuncture combined with Tuina has obvious clinical advantages in the treatment of insomnia. This result is expected to provide a reference for the clinical treatment of insomnia, but the long-term effect of clinical efficacy still needs further study.