Fully probabilistic deep models for forward and inverse problems in parametric PDEs

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional PDE discretization techniques, deep neural networks, probabilistic modelling, and variational inference to assemble a fully probabilistic coherent framework. In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks. The PDE residual is assumed to be an observed random vector of value zero, hence we model it as a random vector with a zero mean and a user-prescribed covariance. The model is trained by maximizing the probability, that is the evidence or marginal likelihood, of observing a residual of zero by maximizing the evidence lower bound (ELBO). Consequently, the proposed methodology does not require any independent PDE solves and is physics-informed at training time, allowing the real-time solution of PDE forward and inverse problems after training. The proposed framework can be easily extended to seamlessly integrate observed data to solve inverse problems and to build generative models. We demonstrate the efficiency and robustness of our method on finite element discretized parametric PDE problems such as linear and nonlinear Poisson problems, elastic shells with complex 3D geometries, and time-dependent nonlinear and inhomogeneous PDEs using a physics-informed neural network (PINN) discretization. We achieve up to three orders of magnitude speed-up after training compared to traditional finite element method (FEM), while outputting coherent uncertainty estimates

Simulated leaf litter addition causes opposite priming effects on natural forest and plantation soils

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. The conversion of natural forests to tree plantations alters the quality and decreases the quantity of litter inputs into the soil, but how the alteration of litter inputs affect soil organic matter (SOM) decomposition remain unclear. We examined SOM decomposition by adding 13C-labeled leaf-litter of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook) to soils from a natural evergreen broad-leaved forest and an adjacent Chinese fir plantation converted from a natural evergreen broad-leaved forest 42 years ago. Over 195 days, we monitored CO2 efflux and its δ13C, microbial biomass, and the composition of microbial groups by phospholipid fatty acids (PLFAs). To distinguish priming mechanisms, partitioning of C sources in CO2 and microbial biomass was determined based on δ13C. Leaf-litter addition to natural forest increased microbial biomass and induced up to 14% faster SOM decomposition (positive priming) than that in soil without litter. In contrast, negative priming in soils under plantation indicated preferential use of added leaf-litter rather than recalcitrant SOM. This preferential use of leaf-litter was supported by an increased fungal to bacterial ratio and litter-derived (13C) microbial biomass, reflecting increased substrate recalcitrance, the respective changes in microbial substrate utilization and increased C use efficiency. The magnitude and direction of priming effects depend on microbial preferential utilization of new litter or SOM. Concluding, the impact of coniferous leaf-litter inputs on the SOM priming is divergent in natural evergreen broad-leaved forests and plantations, an important consideration in understanding long-term C dynamics and cycling in natural and plantation forest ecosystems

Assessing Temperate Forest Growth and Climate Sensitivity in Response to a Long-Term Whole-Watershed Acidification Experiment

Acid deposition is a major biogeochemical driver in forest ecosystems, but the impacts of long-term changes in deposition on forest productivity remain unclear. Using a combination of tree ring and forest inventory data, we examined tree growth and climate sensitivity in response to 26 years of whole-watershed ammonium sulfate ((NH4)2SO4) additions at the Fernow Experimental Forest (West Virginia, USA). Linear mixed effects models revealed species-specific responses to both treatment and hydroclimate variables. When controlling for environmental covariates, growth of northern red oak (Quercus rubra), red maple (Acer rubrum), and tulip poplar (Liriodendron tulipifera) was greater (40%, 52%, and 42%, respectively) in the control watershed compared to the treated watershed, but there was no difference in black cherry (Prunus serotina). Stem growth was generally positively associated with growing season water availability and spring temperature and negatively associated with vapor pressure deficit. Sensitivity of northern red oak, red maple, and tulip poplar growth to water availability was greater in the control watershed, suggesting that acidification treatment has altered tree response to climate. Results indicate that chronic acid deposition may reduce both forest growth and climate sensitivity, with potentially significant implications for forest carbon and water cycling in deposition-affected regions

TRY plant trait database - enhanced coverage and open access

Plant traits-the morphological, anatomical, physiological, biochemical and phenological characteristics of plants-determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait-based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits-almost complete coverage for 'plant growth form'. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait-environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Distance travelled : Outcomes and evidence in flexible learning options

Flexible learning options (FLOs) provide individualised learning pathways for disengaged young people with strong emphasis on inclusivity and wellbeing support. Amidst a rapid expansion of Australia’s flexible learning sector, service providers are under increasing pressure to substantiate participant outcomes. This paper stems from a national study of the value of FLOs to young people and the broader Australian community. The study enumerates the outcomes valued by flexible learning practitioners, as well as the various evidence forms they cite to substantiate participant outcomes. Framing success as ‘distance travelled’ (i.e. an individual’s progress relative to his or her own starting point), practitioners demonstrate critical awareness of the social and structural mechanisms by which young people are marginalised from mainstream schooling. Holistic assessment practices also reveal practitioners’ efforts to expand the terms of reference by which educational outcomes may be validated in alternative education settings

Depth-related effects on a meiofaunal community dwelling in the periphyton of a mesotrophic lake

Kreuzinger B, Schroeder F, Majdi N, Traunspurger W. Depth-related effects on a meiofaunal community dwelling in the periphyton of a mesotrophic lake. PLoS One. 2015;10(9): e0137793.Periphyton is a complex assemblage of micro- and meiofauna embedded in the organic matrix that coats most submerged substrate in the littoral of lakes. The aim of this study was to better understand the consequences of depth-level fluctuation on a periphytic community. The effects of light and wave disturbance on the development of littoral periphyton were evaluated in Lake Erken (Sweden) using an experimental design that combined in situ shading with periphyton depth transfers. Free-living nematodes were a major contributor to the meiofaunal community. Their species composition was therefore used as a proxy to distinguish the contributions of light- and wave-related effects. The periphyton layer was much thicker at a depth of 30 cm than at 200 cm, as indicated by differences in the amounts of organic and phototrophic biomass and meiofaunal and nematode densities. A reduction of the depth-level of periphyton via a transfer from a deep to a shallow location induced rapid positive responses by its algal, meiofaunal, and nematode communities. The slower and weaker negative responses to the reverse transfer were attributed to the potentially higher resilience of periphytic communities to increases in the water level. In the shallow littoral of the lake, shading magnified the effects of phototrophic biomass erosion by waves, as the increased exposure to wave shear stress was not compensated for by an increase in photosynthesis. This finding suggests that benthic primary production will be strongly impeded in the shallow littoral zones of lakes artificially shaded by construction or embankments. However, regardless of the light constraints, an increased exposure to wave action had a generally positive short-term effect on meiofaunal density, by favoring the predominance of species able to anchor themselves to the substrate, especially the Chromadorid nematode Punctodora ratzeburgensis

Multifractal Spatial Patterns and Diversity in an Ecological Succession

We analyzed the relationship between biodiversity and spatial biomass heterogeneity along an ecological succession developed in the laboratory. Periphyton (attached microalgae) biomass spatial patterns at several successional stages were obtained using digital image analysis and at the same time we estimated the species composition and abundance. We show that the spatial pattern was self-similar and as the community developed in an homogeneous environment the pattern is self-organized. To characterize it we estimated the multifractal spectrum of generalized dimensions Dq. Using Dq we analyze the existence of cycles of heterogeneity during succession and the use of the information dimension D1 as an index of successional stage. We did not find cycles but the values of D1 showed an increasing trend as the succession developed and the biomass was higher. D1 was also negatively correlated with Shannon's diversity. Several studies have found this relationship in different ecosystems but here we prove that the community self-organizes and generates its own spatial heterogeneity influencing diversity. If this is confirmed with more experimental and theoretical evidence D1 could be used as an index, easily calculated from remote sensing data, to detect high or low diversity areas