Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into neural networks. This transforms the process of solving PDEs into optimization problems for neural networks. To address a collection of advection-diffusion equations (ADE) in a range of difficult circumstances, this paper proposes a novel network structure. This architecture integrates the solver, a multi-scale deep neural networks (MscaleDNN) utilized in the PINN method, with a hard constraint technique known as HCPINN. This method introduces a revised formulation of the desired solution for ADE by utilizing a loss function that incorporates the residuals of the governing equation and penalizes any deviations from the specified boundary and initial constraints. By surpassing the boundary constraints automatically, this method improves the accuracy and efficiency of the PINN technique. To address the “spectral bias” phenomenon in neural networks, a subnetwork structure of MscaleDNN and a Fourier-induced activation function are incorporated into the HCPINN, resulting in a hybrid approach called SFHCPINN. The effectiveness of SFHCPINN is demonstrated through various numerical experiments involving ADE in different dimensions. The numerical results indicate that SFHCPINN outperforms both standard PINN and its subnetwork version with Fourier feature embedding. It achieves remarkable accuracy and efficiency while effectively handling complex boundary conditions and high-frequency scenarios in ADE

Solving a class of multi-scale elliptic PDEs by Fourier-based mixed physics informed neural networks

Deep neural networks have garnered widespread attention due to their simplicity and flexibility in the fields of engineering and scientific calculation. In this study, we probe into solving a class of elliptic partial differential equations (PDEs) with multiple scales by utilizing Fourier-based mixed physics informed neural networks (dubbed FMPINN), its solver is configured as a multi-scale deep neural network. In contrast to the classical PINN method, a dual (flux) variable about the rough coefficient of PDEs is introduced to avoid the ill-condition of neural tangent kernel matrix caused by the oscillating coefficient of multi-scale PDEs. Therefore, apart from the physical conservation laws, the discrepancy between the auxiliary variables and the gradients of multi-scale coefficients is incorporated into the cost function, obtaining a satisfactory solution of PDEs by minimizing the defined loss through some optimization methods. Additionally, a trigonometric activation function is introduced for FMPINN, which is suited for representing the derivatives of complex target functions. Handling the input data by Fourier feature mapping will effectively improve the capacity of deep neural networks to solve high-frequency problems. Finally, to validate the efficiency and robustness of the proposed FMPINN algorithm, we present several numerical examples of multi-scale problems in various dimensional Euclidean spaces. These examples cover low-frequency and high-frequency oscillation cases, demonstrating the effectiveness of our approach. All code and data accompanying this manuscript will be publicly available at https://github.com/Blue-Giant/FMPINN

Mining salt stress-related genes in Spartina alterniflora via analyzing co-evolution signal across 365 plant species using phylogenetic profiling

With the increasing number of sequenced species, phylogenetic profiling (PP) has become a powerful method to predict functional genes based on co-evolutionary information. However, its potential in plant genomics has not yet been fully explored. In this context, we combined the power of machine learning and PP to identify salt stress-related genes in a halophytic grass, Spartina alterniflora, using evolutionary information generated from 365 plant species. Our results showed that the genes highly co-evolved with known salt stress-related genes are enriched in biological processes of ion transport, detoxification and metabolic pathways. For ion transport, five identified genes coding two sodium and three potassium transporters were validated to be able to uptake Na+. In addition, we identified two orthologs of trichome-related AtR3-MYB genes, SaCPC1 and SaCPC2, which may be involved in salinity responses. Genes co-evolved with SaCPCs were enriched in functions related to the circadian rhythm and abiotic stress responses. Overall, this work demonstrates the feasibility of mining salt stress-related genes using evolutionary information, highlighting the potential of PP as a valuable tool for plant functional genomics

A New Hybrid Model FPA-SVM Considering Cointegration for Particular Matter Concentration Forecasting: A Case Study of Kunming and Yuxi, China

Air pollution in China is becoming more serious especially for the particular matter (PM) because of rapid economic growth and fast expansion of urbanization. To solve the growing environment problems, daily PM2.5 and PM10 concentration data form January 1, 2015, to August 23, 2016, in Kunming and Yuxi (two important cities in Yunnan Province, China) are used to present a new hybrid model CI-FPA-SVM to forecast air PM2.5 and PM10 concentration in this paper. The proposed model involves two parts. Firstly, due to its deficiency to assess the possible correlation between different variables, the cointegration theory is introduced to get the input-output relationship and then obtain the nonlinear dynamical system with support vector machine (SVM), in which the parameters c and g are optimized by flower pollination algorithm (FPA). Six benchmark models, including FPA-SVM, CI-SVM, CI-GA-SVM, CI-PSO-SVM, CI-FPA-NN, and multiple linear regression model, are considered to verify the superiority of the proposed hybrid model. The empirical study results demonstrate that the proposed model CI-FPA-SVM is remarkably superior to all considered benchmark models for its high prediction accuracy, and the application of the model for forecasting can give effective monitoring and management of further air quality

A hybrid Autoformer framework for electricity demand forecasting

Electricity demand forecasting is of great significance to the electricity system and residents’ life, but it is difficult to forecast the electricity demand series because of the influence of cyclical factors. Electricity demand forecasting also faces the problem of small data amounts. Therefore, we need to design a model that is less affected by data volume and can cope with complex electricity demand series. Based on the Autoformer model, this paper establishes a novel forecasting framework with excellent performance. In the part of data preprocessing, multiple linear regression with 10 variables and Bootstrap processing are added. In the part of the model, the Auto Correlation mechanism is modified to better extract the historical and nonlinear characteristics of electricity demand series from different time spans. Using this framework, we further analyze the impact of working days and seasonal changes on the electricity demand in Taixing City and New South Wales. In addition, we propose a new electricity demand forecasting method, which can adjust the original sequence according to the actual situation. The experimental results show that this method can achieve good precision in demand forecasting. Taking Taixing of China and New South Wales of Australia as examples, the forecasting performance with the proposed framework is better than that of Autoformer, Reformer, Informer, and other mainstream models. The forecasting indexes with our proposed framework of the test set are MAE: 35.05, RMSE: 47.28, MAPE: 1.63 in Taixing and MAE: 193.17, RMSE: 239.96, MAPE: 2.43 in NS

Extreme Learning Machine-Assisted Solution of Biharmonic Equations via Its Coupled Schemes

Obtaining the solutions of partial differential equations based on various machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine (called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gauss, sine, and trigonometric (sin+cos) functions are introduced to assess our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing approaches for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equation in both regular and irregular domains

Assessing and predicting water quality index with key water parameters by machine learning models in coastal cities, China

The water quality index (WQI) is a widely used tool for comprehensive assessment of river environments. However, its calculation involves numerous water quality parameters, making sample collection and laboratory analysis time-consuming and costly. This study aimed to identify key water parameters and the most reliable prediction models that could provide maximum accuracy using minimal indicators. Water quality from 2020 to 2023 were collected including nine biophysical and chemical indicators in seventeen rivers in Yancheng and Nantong, two coastal cities in Jiangsu Province, China, adjacent to the Yellow Sea. Linear regression and seven machine learning models (Artificial Neural Network (ANN), Self-Organizing Maps (SOM), K-Nearest Neighbor (KNN), Support Vector Machines (SVM), Random Forest (RF), Extreme Gradient Boosting (XGB) and Stochastic Gradient Boosting (SGB)) were developed to predict WQI using different groups of input variables based on correlation analysis. The results indicated that water quality improved from 2020 to 2022 but deteriorated in 2023, with inland stations exhibiting better conditions than coastal ones, particularly in terms of turbidity and nutrients. The water environment was comparatively better in Nantong than in Yancheng, with mean WQI values of approximately 55.3–72.0 and 56.4–67.3, respectively. The classifications "Good" and "Medium" accounted for 80 % of the records, with no instances of "Excellent" and 2 % classified as "Bad". The performance of all prediction models, except for SOM, improved with the addition of input variables, achieving R2 values higher than 0.99 in models such as SVM, RF, XGB, and SGB. The most reliable models were RF and XGB with key parameters of total phosphorus (TP), ammonia nitrogen (AN), and dissolved oxygen (DO) (R2 = 0.98 and 0.91 for training and testing phase) for predicting WQI values, and RF using TP and AN (accuracy higher than 85 %) for WQI grades. The prediction accuracy for "Medium" and "Low" water quality grades was highest at 90 %, followed by the "Good" level at 70 %. The model results could contribute to efficient water quality evaluation by identifying key water parameters and facilitating effective water quality management in river basins

Estimation of Sediment Transport Parameters From Measured Suspended Concentration Time Series Under Waves and Currents With a New Conceptual Model

In-situ observations of hydrodynamics and suspended sediment concentrations (SSCs) were conducted on an abandoned lobe in the northern part of the modern Yellow River Delta, China. The SSC record at the site is found to be the superposition of a general trend (fast increase and slow decrease cycle) caused by storm waves (SubSSC1) and relatively smaller fluctuations caused by tidal currents (SubSSC2). Physically, this indicates that storm waves eroded the bottom sediments while tidal currents then re-suspended and advected the suspended sediments in the study area. To further obtain the suspended sediment transport parameters, first, SubSSC1 is modeled with significant wave height which incorporates a “memory curve” to consider the remaining impacts of historical waves. It is detected that waves in the past 75 hr still influence the present SSC which is reasonable because 75 hr is roughly the typical duration of a normal storm. Second, SubSSC2 is modeled with tidal excursion and trigonometric functions with measured periodicities. Finally, some sediment transport parameters, for example, the background SSC, the horizontal SSC gradient, the tidal constituents that advect it, and their relative time lags are optimized from the best fits of the measured and modeled SSC time series. The proposed framework for model construction and parameter optimization can be extended to other sea areas for inferring sediment transport parameters from field SSC time series at a specific station

Asiaticoside Mitigates Alzheimer’s Disease Pathology by Attenuating Inflammation and Enhancing Synaptic Function

Alzheimer’s disease (AD) is a prevalent neurodegenerative disorder, hallmarked by the accumulation of amyloid-β (Aβ) plaques and neurofibrillary tangles. Due to the uncertainty of the pathogenesis of AD, strategies aimed at suppressing neuroinflammation and fostering synaptic repair are eagerly sought. Asiaticoside (AS), a natural triterpenoid derivative derived from Centella asiatica, is known for its anti-inflammatory, antioxidant, and wound-healing properties; however, its neuroprotective function in AD remains unclear. Our current study reveals that AS, when administered (40 mg/kg) in vivo, can mitigate cognitive dysfunction and attenuate neuroinflammation by inhibiting the activation of microglia and proinflammatory factors in Aβ1-42-induced AD mice. Further mechanistic investigation suggests that AS may ameliorate cognitive impairment by inhibiting the activation of the p38 MAPK pathway and promoting synaptic repair. Our findings propose that AS could be a promising candidate for AD treatment, offering neuroinflammation inhibition and enhancement of synaptic function

A highly efficient rice green tissue protoplast system for transient gene expression and studying light/chloroplast-related processes

<p>Abstract</p> <p>Background</p> <p>Plant protoplasts, a proven physiological and versatile cell system, are widely used in high-throughput analysis and functional characterization of genes. Green protoplasts have been successfully used in investigations of plant signal transduction pathways related to hormones, metabolites and environmental challenges. In rice, protoplasts are commonly prepared from suspension cultured cells or etiolated seedlings, but only a few studies have explored the use of protoplasts from rice green tissue.</p> <p>Results</p> <p>Here, we report a simplified method for isolating protoplasts from normally cultivated young rice green tissue without the need for unnecessary chemicals and a vacuum device. Transfections of the generated protoplasts with plasmids of a wide range of sizes (4.5-13 kb) and co-transfections with multiple plasmids achieved impressively high efficiencies and allowed evaluations by 1) protein immunoblotting analysis, 2) subcellular localization assays, and 3) protein-protein interaction analysis by bimolecular fluorescence complementation (BiFC) and firefly luciferase complementation (FLC). Importantly, the rice green tissue protoplasts were photosynthetically active and sensitive to the retrograde plastid signaling inducer norflurazon (NF). Transient expression of the GFP-tagged light-related transcription factor OsGLK1 markedly upregulated transcript levels of the endogeneous photosynthetic genes <it>OsLhcb1</it>, <it>OsLhcp</it>, <it>GADPH </it>and <it>RbcS</it>, which were reduced to some extent by NF treatment in the rice green tissue protoplasts.</p> <p>Conclusions</p> <p>We show here a simplified and highly efficient transient gene expression system using photosynthetically active rice green tissue protoplasts and its broad applications in protein immunoblot, localization and protein-protein interaction assays. These rice green tissue protoplasts will be particularly useful in studies of light/chloroplast-related processes.</p