KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory

Orbital-free density functional theory (OF-DFT) holds the promise to compute ground state molecular properties at minimal cost. However, it has been held back by our inability to compute the kinetic energy as a functional of the electron density only. We here set out to learn the kinetic energy functional from ground truth provided by the more expensive Kohn-Sham density functional theory. Such learning is confronted with two key challenges: Giving the model sufficient expressivity and spatial context while limiting the memory footprint to afford computations on a GPU; and creating a sufficiently broad distribution of training data to enable iterative density optimization even when starting from a poor initial guess. In response, we introduce KineticNet, an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. Important contributions include convolution filters with sufficient spatial resolution in the vicinity of the nuclear cusp, an atom-centric sparse but expressive architecture that relays information across multiple bond lengths; and a new strategy to generate varied training data by finding ground state densities in the face of perturbations by a random external potential. KineticNet achieves, for the first time, chemical accuracy of the learned functionals across input densities and geometries of tiny molecules. For two electron systems, we additionally demonstrate OF-DFT density optimization with chemical accuracy.Comment: 10 pages, 8 figure

Future and potential spending on health 2015-40: development assistance for health, and government, prepaid private, and out-of-pocket health spending in 184 countries

Background The amount of resources, particularly prepaid resources, available for health can affect access to health care and health outcomes. Although health spending tends to increase with economic development, tremendous variation exists among health financing systems. Estimates of future spending can be beneficial for policy makers and planners, and can identify financing gaps. In this study, we estimate future gross domestic product (GDP), all-sector government spending, and health spending disaggregated by source, and we compare expected future spending to potential future spending. Methods We extracted GDP, government spending in 184 countries from 1980–2015, and health spend data from 1995–2014. We used a series of ensemble models to estimate future GDP, all-sector government spending, development assistance for health, and government, out-of-pocket, and prepaid private health spending through 2040. We used frontier analyses to identify patterns exhibited by the countries that dedicate the most funding to health, and used these frontiers to estimate potential health spending for each low-income or middle-income country. All estimates are inflation and purchasing power adjusted. Findings We estimated that global spending on health will increase from US$9·21 trillion in 2014 to$24·24 trillion (uncertainty interval [UI] 20·47–29·72) in 2040. We expect per capita health spending to increase fastest in upper-middle-income countries, at 5·3% (UI 4·1–6·8) per year. This growth is driven by continued growth in GDP, government spending, and government health spending. Lower-middle income countries are expected to grow at 4·2% (3·8–4·9). High-income countries are expected to grow at 2·1% (UI 1·8–2·4) and low-income countries are expected to grow at 1·8% (1·0–2·8). Despite this growth, health spending per capita in low-income countries is expected to remain low, at $154 (UI 133–181) per capita in 2030 and$195 (157–258) per capita in 2040. Increases in national health spending to reach the level of the countries who spend the most on health, relative to their level of economic development, would mean $321 (157–258) per capita was available for health in 2040 in low-income countries. Interpretation Health spending is associated with economic development but past trends and relationships suggest that spending will remain variable, and low in some low-resource settings. Policy change could lead to increased health spending, although for the poorest countries external support might remain essential.</p