In this paper, we investigate the generalization error of deep physical models with latent variables. Deep physical models, such as Hamiltonian Neural Networks, are neural network models for learning equations of motion from observational data of physical phenomena and have attracted much attention in recent years. In particular, in such cases, the data are not completely random, but rather given as random trajectories. We provide an error bound for the case where the training data are given in such a way. Our results show that it is important to collect data from many trajectories, rather than simply collecting a large number of data, to improve generalization performance. In addition, an important application of the combination of deep physics models with latent variables is the interpolation of images from videos while preserving the laws of physics, such as the energy conservation law. However, when the frame interval of the video is large, it can be difficult to preserve the laws of physics. In this paper, we show that it is possible to interpolate the images from videos so that the laws of physics are preserved, provided that the generalization error is sufficiently small.

In recent years, optoelectronic neural networks have garnered significant attention due to their potential to facilitate high-speed and efficient information processing by employing light-based signals to transmit and process data. This review provides an overview of the current state-of-the-art in optoelectronic neural networks, including their design principles, fabrication techniques, and applications. The article also presents five different methods for constructing optoelectronic neural networks, which offer insights into current ONN research and solutions to overcome the limitations of traditional neural networks. Furthermore, the review discusses three different applications of ONNs, including basic tasks such as data classification, speech recognition, and image recognition, as well as hardware accelerators and SNN algorithms for object detection. The promising potential of optoelectronic neural networks in transforming various fields, such as artificial intelligence, image recognition, and data processing, is also highlighted. As research in this area continues to advance, further breakthroughs in optoelectronic neural networks are anticipated.

Vegetation changes and factors have a profound influence on the local ecology, the economy, and the long-term durability of human construction. This study focuses on the impacts of climate change and human activity on vegetation changes on the Qinghai-Tibet Plateau and aims to develop a dataset of human activity levels on the plateau. Sen and Mann-Kendall trend analysis was used to evaluate the spatial distribution of vegetation NDVI and its trends, as well as the lagged response of plant growth to climatic circumstances. Using a geodetector model, the effects of meteorological and anthropogenic intensity data were examined. The study’s findings show that, although anthropogenic influences and ecosystem vulnerability caused a decline in the region’s vegetation, a stable climate and a healthy ecosystem supported the growth of vegetation. From 2000 to 2017, the area where vegetation grass improved significantly accounted for the highest proportion, reaching 34.22%. Different anthropogenic intensities are distributed spatially, and this interplay of anthropogenic intensities and climatic factors affects the distribution of vegetation greenness more than each element acting alone. The study of how human activity and climate change affect vegetation greenness can offer practical recommendations for maintaining the Qinghai-Tibet Plateau’s natural ecology. It is crucial to responsibly safeguard the Qinghai-Tibet Plateau’s environment in response to the nation’s ecological civilization.

Background and Aims Plant traits are the results of plant evolutionary and environmental drivers operating at different scales. Although the relationship between above- and below-ground traits of terrestrial plants has been advanced, little is known about above- and below-ground traits of wetland plants, their relationship and influencing factors across a large scale. Methods Species coverage, and above- and below-ground plant traits were measured in nine typical marsh wetlands of northern China. Differences in plant traits at both species- and community-level among wetlands and between low and high soil moisture conditions, correlations between above- and below-ground traits of clonal plants, and the influencing environmental factors were analyzed. Results Plant traits at both species- and community-level were significantly higher in Daihai and Qingtongxia wetlands than that in other wetlands, which was influenced by combined effects of precipitation, soil nutrients, and temperature. Plant traits at both levels were generally higher under high than low soil moisture conditions. At the species level, the coordinated relationships were found between above- and below-ground traits of clonal plants under both low and high soil moisture conditions across all wetlands; while a trade-off relationship was found between internode diameter and length of clonal plants. Conclusions Plant traits exhibited the similar pattern among wetlands at both levels, but performed better at high soil moisture conditions in marsh wetlands. Coordinated relationships between above- and below-ground traits will be further clarified whether such coordination can be also seen in other wetland ecosystems.

The modification of dissolved organic matter (DOM) degradation by plant carbon inputs represents a critical biogeochemical process that controls carbon dynamics. However, the priming effects (PEs) different plant tissues induce on the degradation of DOM pools with different stabilities remain unknown. In this study, PEs, induced by different tissue leachates of Phragmites australis, were evaluated via changes in DOM components and properties of both fresh and tidal water (with different stabilities). The results showed that DOM derived from different plant tissue leachates differed in composition and bioavailability. Inputs of tissue leachates induced PEs with different intensities and directions (negative or positive) on DOM degradation of fresh and tidal water. In fresh water, the PEs of leaf and root leachates were significantly higher than those of stem and rhizome leachates. The PE direction changed for DOM degradation between fresh and tidal water. The addition of leaf and root leachates tended to induce positive PEs on DOM degradation of fresh water, while resulting in negative PEs on DOM degradation of tidal water. Negative PEs for tidal water DOM may be due to preferential utilization of microbes, high salinity, and/or the promotion of exogenous DOM production from plant tissues. The results indicate that intensity and direction of PEs induced by plant leachates depend on both leachate type and water stability. The findings highlight the necessity to examine the nature of exogenous and native DOM when interpreting the interactive processes that regulate DOM degradation.

Many physical phenomena are described by Hamiltonian mechanics using an energy function (Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamiltonian by a neural network, and its extensions have attracted much attention. This is a very powerful method, but theoretical studies are limited. In this study, by combining the statistical learning theory and KAM theory, we provide a theoretical analysis of the behavior of Hamiltonian neural networks when the learning error is not completely zero. A Hamiltonian neural network with non-zero errors can be considered as a perturbation from the true dynamics, and the perturbation theory of the Hamilton equation is widely known as KAM theory. To apply KAM theory, we provide a generalization error bound for Hamiltonian neural networks by deriving an estimate of the covering number of the gradient of the multi-layer perceptron, which is the key ingredient of the model. This error bound gives a sup-norm bound on the Hamiltonian that is required in the application of KAM theory.

In recent years, substantial research on the methods for learning Hamiltonian equations has been conducted. Although these approaches are very promising, the commonly used representation of the Hamilton equation uses the generalized momenta, which are generally unknown. Therefore, the training data must be represented in this unknown coordinate system, and this causes difficulty in applying the model to real data. Meanwhile, Hamiltonian equations also have a coordinate-free expression that is expressed by using the symplectic 2-form. In this study, we propose a model that learns the symplectic form from data using neural networks, thereby providing a method for learning Hamiltonian equations from data represented in general coordinate systems, which are not limited to the generalized coordinates and the generalized momenta. Consequently, the proposed method is capable not only of modeling target equations of both Hamiltonian and Lagrangian formalisms but also of extracting unknown Hamiltonian structures hidden in the data. For example, many polynomial ordinary differential equations such as the Lotka-Volterra equation are known to admit non-trivial Hamiltonian structures, and our numerical experiments show that such structures can be certainly learned from data. Technically, each symplectic 2-form is associated with a skew-symmetric matrix, but not all skew-symmetric matrices define the symplectic 2-form. In the proposed method, using the fact that symplectic 2-forms are derived as the exterior derivative of certain differential 1-forms, we model the differential 1-form by neural networks, thereby improving the efficiency of learning.

Selection pressure of flooding promotes the development of phenotypic plasticity of riparian plants; however, whether the selection effects of flooding are elevation-dependent still remains unclear. Seeds of the riparian species Polygonum hydropiper were collected from 10 different locations each at low and high elevations in the Three Gorges Reservoir Region. Plants germinated from these seeds were subjected to control and flooding treatments. Flooding significantly increased both specific leaf area (SLA) and adventitious root biomass but decreased other growth traits of all progeny. In response to flooding, plasticity of all leaf and root traits except SLA varied significantly among seed families (seedlings emerged from the same mother plant) from low elevation. However, among seed families from high elevation, plasticity of only leaf number, total leaf area, and adventitious root biomass varied significantly. For low-elevation seed families, benefits of plasticity in leaf width, leaf number, average leaf area, and leaf biomass were detected across control and flooded conditions. However, in response to flooding, significant costs of plasticity in leaf length, leaf width, average and total leaf areas were found. Therefore, selection effects of flooding impose great pressure on plasticity of leaf and root traits of low-elevation seed families, which is elevation-dependent.

In plant communities, genetic diversity among dominant species can not only affect the fitness of the population, but also interactions with concomitant species. Soil salinity is a common factor that influences plant growth in estuarine wetlands. However, few studies have tested whether their high genetic diversity will be beneficial for the resistance of plant populations to salinity and the presence of concomitant plants. Four different genotypes of Phragmites australis, a dominant species of the Yellow River Delta in China, were selected to construct populations with three different genotypic levels. These populations were planted either with or without concomitant species and were subjected to control or salinity treatments. At the end of treatments, growth variables of P. australis populations were measured. In response to soil salinity, the total biomass of 1-, 2-, and 4-genotype populations decreased by 35%, 24%, and 13%, respectively, indicating higher resistance of P. australis populations with high genetic diversity. Correspondingly, 2-, and 4-genotype populations showed higher biomass allocation to roots, which can maintain adequate water uptake for plants. The biomass accumulation of 1-genotype populations with concomitant plants was significantly lower compared with populations without concomitant plants; however, no significant difference was found for 4-genotype populations between both control and salinity treatments, suggesting their higher capacities when coexisting with concomitant species. However, the genotypic level of populations did not significantly affect their biomass accumulation. High genetic diversity is greatly beneficial for the resistance of P. australis populations to salinity and coexistence with other plants. This information should be considered in the construction or restoration of this species in estuarine wetlands.

In a secret communication system using chaotic synchronization, the communication information is embedded in a signal that behaves as chaos and is sent to the receiver to retrieve the information. In a previous study, a chaotic synchronous system was developed by integrating the wave equation with the van der Pol boundary condition, of which the number of the parameters are only three, which is not enough for security. In this study, we replace the nonlinear boundary condition with an artificial neural network, thereby making the transmitted information difficult to leak. The neural network is divided into two parts; the first half is used as the left boundary condition of the wave equation and the second half is used as that on the right boundary, thus replacing the original nonlinear boundary condition. We also show the results for both monochrome and color images and evaluate the security performance. In particular, it is shown that the encrypted images are almost identical regardless of the input images. The learning performance of the neural network is also investigated. The calculated Lyapunov exponent shows that the learned neural network causes some chaotic vibration effect. The information in the original image is completely invisible when viewed through the image obtained after being concealed by the proposed system. Some security tests are also performed. The proposed method is designed in such a way that the transmitted images are encrypted into almost identical images of waves, thereby preventing the retrieval of information from the original image. The numerical results show that the encrypted images are certainly almost identical, which supports the security of the proposed method. Some security tests are also performed. The proposed method is designed in such a way that the transmitted images are encrypted into almost identical images of waves, thereby preventing the retrieval of information from the original image. The numerical results show that the encrypted images are certainly almost identical, which supports the security of the proposed method.

Aims Flooding and soil nutrients are the main environmen tal factors that affect plant growth in the hydro-fluctuation belt of the Three Gorges Reservoir Region (TGRR). Flooding intensity and concentration of soil nutrients experienced by riparian plants at different elevations of the hydro-fluctuation belt are different; therefore, we hypothesized that growth and reproductive responses of plants of the same species from different elevations to waterlogging and increased soil nutrients are also different. Methods In this study, the riparian species Polygonum hydropiper, which is widely distributed at low and high elevations of the hydro-fluctuation belt of the TGRR, was selected and its seeds were collected from natural populations. Effects of waterlogging and soil nutrients on growth and reproductive traits of P. hydropiper from high- and low-elevation areas were studied in a common-garden greenhouse experiment. length and of functional treatment significantly or marginal significantly decreased total node number, total branch number, root biomass, flower biomass, and total biomass of plants, indicating that both waterlogging and low soil nutrients inhibited growth and reproduction of P. hydropiper . Moreover, the interaction between waterlogging and soil nutrients significantly affected root biomass, showing higher root biomass accumulation at high soil nutrient conditions upon waterlogging. The high-elevation plants had significantly or marginal significantly higher leaf and root biomass than those from low elevation; however, flowering time of the low-elevation plants was significantly earlier, and reproduction allocation was higher than the high-elevation plants, indicating that resource allocation strategy was different between the high- and the low-elevation plants. The results indicate that growth and reproduction of P. hydropiper are inhibited by both waterlogging and soil nutrients, and this species has high adaptability at high soil nutrient conditions to waterlogging; meanwhile, low-elevation plants can adjust their growth and reproductive characteristics to improve their fitness under environmental stress.

Fluctuation range and frequency are two important components of water level fluctuation, but their effects on wetland plants have not been evaluated separately. We subjected eight wetland species to a control treatment with static water level and fluctuation treatments with different ranges or frequencies to examine their effects on plant growth. Acorus calamus, Butomus umbellatus and Iris wilsonii showed high survival rates in all treatments with various fluctuation ranges and frequencies. Their survival rates were higher at the medium fluctuation frequency than at the low and high frequencies, suggesting beneficial effects of the medium frequency. In the experiment comparing the fluctuation ranges, A. calamus and I. wilsonii could maintain the capacity for asexual propagation and accumulate higher biomass compared with the control plants, while biomass of the other six species dramatically decreased. In the experiment comparing fluctuation frequency, species with relatively high survival rates (≥ 50%) maintained or increased the capacity of asexual propagation, and A. calamus and I. wilsonii allocated relatively more biomass to roots, which may enhance plant growth and survival. In contrast, these species did not show increased biomass allocation to shoots in response to both fluctuation range and frequency, presumably because shoots are prone to mechanical damage caused by streaming floodwater. Taken together, biomass accumulation in roots rather than in shoots and the ability to asexually propagate are important for the survival of these species during water fluctuation.