Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal Ma-tErials Graph Network (MEGNet) models for accurate property prediction in both molecules and crystals. We demonstrate that the MEGNet models outperform prior ML models such as the SchNet in 11 out of 13 properties of the QM9 molecule data set. Similarly, we show that MEGNet models trained on ∼ 60, 000 crystals in the Materials Project substantially outperform prior ML models in the prediction of the formation energies, band gaps and elastic moduli of crystals, achieving better than DFT accuracy over a much larger data set. We present two new strategies to address data limitations common in materials science and chemistry. First, we demonstrate a physically-intuitive approach to unify four separate molecular MEGNet models for the internal energy at 0 K and room temperature, enthalpy and Gibbs free energy into a single free energy MEGNet model by incorporating the temperature, pressure and entropy as global state inputs. Second, we show that the learned element embeddings in MEGNet models encode periodic chemical trends and can be transfer-learned from arXiv:1812.05055v2 [cond-mat.mtrl-sci] a property model trained on a larger data set (formation energies) to improve property models with smaller amounts of data (band gaps and elastic moduli).

Vegetation controls the exchange of carbon, water, momentum and energy between the land and the atmosphere, and provides food, fibre, fuel and other valuable ecosystem services 1,2. Changes in vegetation structure and function are driven by climatic and environmental changes, and by human activities such as land-use change. Given that increased carbon storage in vegetation, such as through afforestation, could combat climate change 3,4 , quantifying vegetation change and its impact on carbon storage and climate has elicited considerable interest from scientists and policymakers. However, it is not possible to detect vegetation changes at the global scale using ground-based observations due to the heterogeneity of change and the lack of observations that can detect these changes both spatially and temporally. While monitoring the changes in some vegetation properties (for example, stem-size distribution and below-ground biomass) at the global scale remains impossible, satellite-based remote sensing has enabled continuous estimation of a few important metrics, including vegetation greenness, since the 1980s (Box 1). In 1986, a pioneering study by Tucker et al. 5 on remotely sensed normalized difference vegetation index (NDVI; a radiometric measure of vegetation greenness) (Box 1) revealed a close connection between vegetation canopy greenness and photosynthesis acti vity (as inferred from seasonal variations in atmospheric CO 2 concentration). This index was successfully used to constrain vegetation primary production globally 6. Using NDVI data from 1981 to 1991, Myneni et al. 7 reported an increasing trend in vegetation greenness in the Northern Hemisphere, which was subsequently observed across the globe 8-13. This 'vegetation greening' is defined as a statistically signi ficant increase in annual or seasonal vegetation greenness at a location resulting, for instance, from increases in average leaf size, leaf number per plant, plant density, species composition, duration of green-leaf presence due to changes in the growing season and increases in the number of crops grown per year. There has also been considerable interest in understanding the mechanisms or drivers of greening 11,14. Lucht et al. 14 and Xu et al. 10 revealed that warming has eased climatic constraints, facilitating increasing vegetation greenness over the high latitudes. Zhu et al. 11 further investigated key drivers of greenness trends and concluded that CO 2 fertilization is a major factor driving vegetation greening at the global scale. Subsequent studies based on fine-resolution and medium-resolution satel lite data 13 have shown the critical role of land-surface history, including afforestation and agricultural intensification, in enhancing vegetation greenness. The large spatial scale of vegetation greening and the robustness of its signal have led the Intergovernmental Panel on Climate Change (IPCC) special report on climate change Afforestation The conversion of treeless lands to forests through planting trees.

This predictive model allows an individualized assessment of prostate cancer risk and risk of high-grade disease for men who undergo a prostate biopsy.