Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Here, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems. The rapidly developing field of physics-informed learning integrates data and mathematical models seamlessly, enabling accurate inference of realistic and high-dimensional multiphysics problems. This Review discusses the methodology and provides diverse examples and an outlook for further developments.

Physics-informed machine learning

Deep learning in environmental remote sensing: Achievements and challenges

https://eartharxiv.org/repository/object/149/download/296/

A comprehensive review of deep learning applications in hydrology and water resources

Interest in statistical analysis of remote sensing data to produce measurements of environment, agriculture, and sustainable development is established and continues to increase, and this is leading to a growing interaction between the earth science and statistical domains. With this in mind, we reviewed the literature on statistical machine learning methods commonly applied to remote sensing data. We focus particularly on applications related to the United Nations World Bank Sustainable Development Goals, including agriculture (food security), forests (life on land), and water (water quality). We provide a review of useful statistical machine learning methods, how they work in a remote sensing context, and examples of their application to these types of data in the literature. Rather than prescribing particular methods for specific applications, we provide guidance, examples, and case studies from the literature for the remote sensing practitioner and applied statistician. In the supplementary material, we also describe the necessary steps pre and post analysis for remote sensing data; the pre-processing and evaluation steps.

Statistical machine learning methods and remote sensing for sustainable development goals: A review

A review of computer vision technologies for plant phenotyping

Understanding and analyzing the changes in vegetation cover is very important in several aspects including climatic changes, water budget, ecological balance and specially to undertake necessary conservation measures. The concept of neural network has gained much significance in the analysis of vegetation dynamics using remote sensing satellite data. In the current study an attempt has been made to predict the vegetation dynamics using MODIS NDVI time series data sets and long short term memory network, an advanced technique adapted from the artificial neural network. The dataset of 861 NDVI images from January 2000 to June 2016 is used for making the time series. The data is segregated into three sets which comprises of training set (70%), validation set (20%), and testing set (10%). To check the reliability of the experiment we have finalised two different regions after extensive research for investigation. These include different terrains in the Great Nicobar Islands, one region along the coast where vegetation has severe ecological damage due to 2004 Indian Ocean tsunami and the other, an interior region which remained imperturbable during the tsunami. Long short term memory network, an advanced neural network is trained with these NDVI values for both the regions separately to predict the future vegetation dynamics. To measure the accuracy of the LSTM network, root mean square error is calculated. The resulting plots from both the experiments indicate that the long short-term memory neural network follows the series in addition to coinciding with the required time series. Also, an unanticipated change in the trend of the NDVI series were well adapted by the network and was able to predict the future NDVI values with good accuracy maintaining RMSE less than 0.03 without providing any supplementary data. By adopting the prescribed method in the paper, anticipation of vegetation changes can be done accurately much ahead of time and take proactive measures accordingly to safeguard and improve the vegetation in any area.

D. Sushma Reddy

Papers

Prediction of vegetation dynamics using NDVI time series data and LSTM