dataesr/scientific-paragraphs-categorization huggingface dataset:
This system cannot be solved analytically; we use a dichotomy algorithm to obtain the post-mortality values. 3. 5 Models of individual tree diameter distribution 3. 5. 1 Data. We worked with the same NFI plots as those used to calibrate our growth models, i. e. with NFI data collected between 2006 and 2013 in pure stands (Table  2 ). We used the tree diameter measurements to calibrate our distribution models.
Thanks to the properties of the normal distribution, the arithmetic mean Dm and the quadratic mean Dg are linked by the following equation: 2 2 D Dg = - m σ (17) 3. 6 Models of individual tree height 3. 6. 1 Data. We calibrated our height-circumference relationship models using the same data used to calibrate our growth models, i. e. French NFI data collected between 2006 and 2013 in pure stands. However, here we excluded trees with defects: broken trees and pollards. Differences in the number of plots used to calibrate our growth models and our height-circumference relationship models is due to the fact that (1) here we removed a few plots consisting solely of broken trees and/or pollards and (2) here we considered pure stands excluded for growth modelling: those with missing environmental variables and P.
Species Models Qu. ro. The dataset originally included 52 species, but some of them were scarce and therefore we focused on those for which we had at least 30 volume observations. After discarding the scarce species, the dataset that was used to fit the species-specific models contained 42,959 observations shared among 30 species. The characteristics of the dataset for the species relevant to Salem are shown in Table  12. The information on the other species can be found in Table  A. 3 of the supplementary information (see extended data;  Aussenac et al. , 2021). (α + a 1. 1 (1 -e -a 1. 2 Dg ) + a 2 SI)(1 - - γ c β e 130 ) + 1. 3 Qu. pe. (α + a 1 Dg + a 2. 1 SI + a 2. 2 SI 2 )(1 - - γ c β e 130 ) + 1. 3 Qu. pu. (α + a 2. 1 SI + a 2. 2 SI 2 )(1 - - γ c β e 130 ) + 1. 3 Fa. sy. (α + a 1. 1 (1 -e -a 1.
, 2015) , as predicted by the stress gradient hypothesis  (Bertness & Callaway, 1994). A major limitation of Salem is due to its phenomenological nature which implies that its predictions may be less reliable as we move further away from its calibration range. Salem is therefore intended to be used above all over the French territory. Similarly, Salem being calibrated on the past climate, the validity of its predictions in the future remains uncertain. However, the great diversity of ecological and climate conditions found in the French NFI dataset, which spans over four biogeographical regions  (mediterranean, alpine, continental and atlantic; Roekaerts, 2002) , could make Salem predictions robust over a larger area and in a wide range of climate conditions. In fact, some preliminary results indicate Salem remains reliable at various locations in Europe (Mats Mahnken, unpublished report).
Extended data Zenodo: Salem 2. 0 extended data. https://doi. org/10. 5281/zenodo. 4742559 (Aussenac et al. , 2021). This project contains the following extended data within the file 'Salem 2 0 extended data. pdf': • Table  A. 1 (Estimates of the s 0 parameter in Equation  10 )  In Abstract, Introduction, and Discussion -the authors suggest the improved productivity is the main motivation for the transition from monospecific to mixed stands. However, these motivations are much broader, including risk reduction (insurance hypothesis), creating more diverse habitats, etc. In my opinion, the effort to reduce the high risk of failure of monospecific stands is currently even a higher priority than fostering productivity. I suggest highlighting these aspects in the text and supporting these statements by references.
isimip. org/). Salem is ranked n°1 for the accuracy of its predictions. Following the ORE guidelines, we alluded to this work in our paper (p. 25): « […] some preliminary results indicate Salem remains reliable at various locations in Europe (Mats Mahnken, unpublished report) ». In this forthcoming publication, the evaluation dataset is completely independent from the calibration dataset, which makes the evaluation particularly robust. Splitting the data into calibration and testing samples as suggested by the reviewer would not be as robust for two main reasons: (1) being calibrated on less data, Salem will lose some of its predictive power, and (2) the calibration and testing samples are not completely independent, they are linked by the NFI protocol. The fact that 13 models are being jointly evaluated also helps better apprehend the relative quality of Salem's predictions.
Salem is therefore intended to be used above all over the French territory. Similarly, Salem being calibrated on the past climate, the validity of its predictions in the future remains uncertain. However, the great diversity of ecological and climate conditions found in the French NFI dataset, which spans over four biogeographical regions (mediterranean, alpine, continental and atlantic; Roekaerts, 2002), could make Salem predictions robust over a larger area and in a wide range of climate conditions. In fact, some preliminary results indicate Salem remains reliable at various locations in Europe (Mats Mahnken, unpublished report). In the forthcoming version of Salem under development, the effect of climate fluctuations both on species growth and on the mixture effect (i. e. on species interactions) will be modelled.
○ It would perhaps be advisable to include that "mortality" does not cover stand failure by events, such as storm, drought or barck beetles. boundaries. The quantile of the regression was 0. 95, meaning that the resulting line corresponds to the 5% of the denser stands of the dataset. In Table  1  we specify the data used for the calibration of the self-thinning boundaries and refer the reader to  Toïgo et al. (2018)  for further details on the method. Subsequently, in section 3. 1. 2 we briefly present the calibration method and the calibration results. We would rather not expand further on this subject so as not to make this paper, which is already 29 pages long, any longer. Is the use of the word circumference appropriate? In the equations we find only diameters. We confirm that the word circumference is appropriate wherever it is used.
Models of individual tree volume 3. 7. 1 Data. The models of individual tree volume were fitted to a large dataset that was mainly collected by the French National Institute of Agricultural Research between 1920 and 1983. During that period, a large sample of harvested trees was selected and the volume of each individual tree was measured from the base up to a 7 cm small-end diameter(Deleuze et al. , 2013). This large dataset was later complemented by two field campaigns in 2009 and 2010. Before screening, it included 44,173 volume measurements of individual trees. Trees that did not reach the French commercial limit (dbh = 7. 5 cm ) were discarded.
This article is a synthesis of work carried out for a long time through several conventions and projects. This work was supported by the  French National Forest Office (ONF)  and three projects funded by the  French Agency for Ecological Transition (ADEME) : the  SATAN  project (n°1660C0008, REACCTIF program), the  PROTEST  project (n°1703C0069,  GRAINE program ) and the I- MAESTRO  project (n°1903C0009). Project  I-Maestro  is supported under the umbrella of  ERA-NET Cofund ForestValue  by  ADEME (FR) ,  FNR (DE) ,  MIZS (SI) ,  NCN  (PL). ForestValue is financially supported by the  European Union 's  Horizon 2020 research and innovation programme  under the grant agreement No  773324. The volume models and bark ratio models were carried out under the  EMERGE  project ( ANR 2008-BIOE-003 ).
3. 7 7 Models of individual tree volume 3. 7. 1 Data. The models of individual tree volume were fitted to a large dataset that was mainly collected by the French National Institute of Agricultural Research between 1920 and 1983. During that period, a large sample of harvested trees was selected and the volume of each individual tree was measured from the base up to a 7 cm small-end diameter(Deleuze et al. , 2013). This large dataset was later complemented by two field campaigns in 2009 and 2010. Before screening, it included 44,173 volume measurements of individual trees. Trees that did not reach the French commercial limit (dbh = 7. 5 cm ) were discarded.
Ann For Sci. 2012; 69(2): 195-205. Publisher Full Text Courbaud B, Lafond V, Lagarrigues G, et al. : Applying ecological model evaludation: Lessons learned with the forest dynamics model samsara2. Ecol Modell. 2015; 314: 1-14. Publisher Full Text del Río M, Pretzsch H, Alberdi I, et al. : Characterization • Table A. 3 (Mean diameter at breast heigh (dbh), height and volume of trees in the volume dataset, for species that are not relevant to Salem) •. Forestry. 2014; 87(1): 109-128.
Agric For Meteorol. 2018; 263: 258-266. Publisher Full Text Vallet P, Fortin M, de Coligny F, et al. : Salem simulator 2. 0. 2021. http://www. doi. org/10. 5281/zenodo. 5578340 Vospernik S: Basal area increment models accounting for climate and mixture for austrian tree species. For Ecol Manage. 2021; 480: 118725. Publisher Full Text Weiskittel AR, Hann DW, Kershaw JA, et al. : Forest Growth and Yield Modeling. John Wiley & Sons, 2011. Publisher Full Text Wernsdörfer H, Colin A, Bontemps JD, et al. : Large-scale dynamics of a heterogeneous forest resource are driven jointly by geographically varying growth conditions, tree species composition and stand structure. Ann For Sci. 2012; 69(7): 829-844. Publisher Full Text.
Is the rationale for developing the new software tool clearly explained? Partly Is the description of the software tool technically sound? Yes Are sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others? Yes Is sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool? Partly Competing Interests: No competing interests were disclosed. implementation details I confirm that I Reviewer Expertise: Ecosystem modelling, climate change impacts and adaptation, disturbance dynamics and management. I am not a model developer to comment adequately on.
We present FlowPM, a Particle-Mesh (PM) cosmological N-body code implemented in Mesh-TensorFlow for GPU-accelerated, distributed, and differentiable simulations. We implement and validate the accuracy of a novel multi-grid scheme based on multiresolution pyramids to compute large scale forces efficiently on distributed platforms. We explore the scaling of the simulation on large-scale supercomputers and compare it with corresponding python based PM code, finding on an average 10x speed-up in terms of wallclock time. We also demonstrate how this novel tool can be used for efficiently solving large scale cosmological inference problems, in particular reconstruction of cosmological fields in a forward model Bayesian framework with hybrid PM and neural network forward model. We provide skeleton code for these examples and the entire code is publicly available at https://github.
, 2019; Kodi Ramanah et al. , 2020). However these approaches often only learn the mapping between input features (generally initial density field) and final observables and completely replace the correct underlying physical dynamics of the evolution with end-to-end modeling. As a result, the generalization of these models across redshifts (time scales), length scales (cosmological volume, resolution etc. ), cosmologies and observables of interest is limited by the training dataset and needs to be explored exhaustively to account for all failure modes. At the same time, there has been a considerable interest in exploring novel techniques to push simulations to increasingly smaller and non-Gaussian regimes for the purpose of cosmological analyses. Recent work has demonstrated that one of the most promising approaches to do this is with forward modeling frameworks and using techniques like simulations based inference or reconstruction of cosmological fields for analysis  (Seljak et al.
, 2017; Alsing et al. , 2018; Cranmer et al. , 2019). However given the highly non-linear forward dynamics and multimillion dimensionality of the cosmological simulations, such approaches are only tractable if one has access to differentiable forward simulations  (Jasche and Wandelt, 2013; Wang et al. , 2014; Seljak et al. , 2017; Modi et al. , 2018). To address both of these challenges, in this work we present FlowPM, a TensorFlow implementation of an N-Body PM solver. Written entirely in TensorFlow, these simulations are GPU-accelerated and hence faster than CPU-based PM simulations, while also being entirely differentiable end-to-end. At the same time, they encode the exact underlying dynamics for gravitational evolution (within a PM scheme), while still leav-ing room for natural synthesis with machine learning components to develop hybrid simulations.
In Section 5, we build upon these and introduce FlowPM. We compare the scaling and accuracy of FlowPM with the python FastPM code in Section 6. At last, in Section 7, we demonstrate the efficacy of FlowPM with a toy example by combining it with neural network forward models and reconstructing the initial conditions of the Universe. We end with discussion in Section 8. Throughout the paper, we use "grid" to refer to the particlemesh grid and "mesh" to refer to the computational mesh of Mesh-TF. Unless explicitly specified, every FFT referred throughout the paper is a 3D FFT.
• the dimensions of every tensor are also named. Depending on their name, these dimensions are either distributed/split across or replicated on all processors in a mesh. Hence every processor holds a slice of every tensor. The dimensions can thus be seen as 'logical' dimensions which will be split in the same manner for all tensors and operations. • a user specified computational layout to map which tensor dimension is split along which mesh dimension. The unspecified tensor dimensions are replicated on all processes. While the layout does not affect the results, it can affect the performance of the code. The user builds a Mesh-TensorFlow graph of computations in Python and this graph is then lowered to generate the Ten-sorFlow graphs. It is at this stage that the defined tensor dimensions and operations are split amongst different processes on the mesh based on the computational layout.
Multi-CPU/GPU meshes are implemented with PlacementMeshImpl, i. e. a separate TensorFlow operations is placed on the different devices, all in one big TensorFlow graph. In this case, the TensorFlow graph will grow with the number of processes. On the other hand, TPU meshes are implemented in with SimdMeshImpl wherein TensorFlow operations (and communication collectives) are emitted from the perspective of one core, and this same program runs on every core, relying on the fact that each core actually performs the same operations. Due to Placement Mesh Implementation, time for lowering also increases as the number of processes are increased. Thus currently, it is not infeasible to extend Mesh-TensorFlow code to a very large number of GPUs for very large computations. We expect such bottlenecks to be overcome in the near future.
Returning to Mesh-TF computations, lastly, the tensors to be evaluated are exported to TF tensors in which case they are gathered on the single process. Figure  4  shows an example code to illustrate these operations which form the starting elements of any Mesh-TensorFlow. The code also sets up context for FlowPM, naming the three directions of the PM simulation grid and explicitly specifying which direction is split along which mesh-dimension. Note that for a batch of simulations, computationally the most efficient splitting will almost always maximize the splits along the batch dimension. While FlowPM supports that splitting, we will hence-import mesh_tensorflow as mtf import tensorflow. compat. v1 as tf # Setup graph and associated mesh graph = mtf. Graph() mesh = mtf. Mesh(graph, "my_mesh") # Define named dimensions for defining a 3D volume x_dim, y_dim, z_dim = (mtf.
Scaling and Numerical Accuracy In this section, we will discuss the numerical accuracy and scaling of these simulations. Since the novel aspects of FlowPM are a differentiable Mesh-Tensorflow implementation and multigrid PM scheme, our discussion will center around comparison with the corresponding differentiable python implementation of FastPM which shares the same underlying PM scheme. We do not discuss the accuracy with respect to high resolution N-Body simulations with correct dynamics, and refer the reader to  Feng et al. (2016)  for details on such a comparison. Our tests are performed primarily on GPU nodes on Cori supercomputer at NERSC, with each node hosting 8 NVIDIA V100 ('Volta') GPUs each with with 16 GB HBM2 memory and connected with NVLink interconnect. We compare our results and scaling with the differentiable python code run on Cori-Haswell nodes.
This consists of FastPM code for forward Algorithm 3 Force computation in Muti-grid pyramid method procedure ForceGrids(G, mode) Estimate the component force grids with 3D FFT G ⇐ FFT3D(G, mode) for i ∈ x, y, x do F i ⇐ iFFT3D(∇ i ∇ -2 G, mode) end for return [F x , F y , F z ] end procedure procedure Force(H, f = 2, n = 6, S = 2) Pyramid scheme to estimate force meshes D ⇐ REDUCE(H, f, n, S ) F L ⇐ ForceGrids(D, mode = distributed) F S ⇐ ForceGrids(H, mode = local) for i ∈ x, y, x do F i,L ⇐ EXPAND(F i,L , f, n, S ) F i,l ⇐ REDUCE(F i,S , f, n, S ) F i,l ⇐ EXPAND(F i,l , f, n, S ) F i,S ⇐ F i,S -F i,l F i ⇐ F i,L + F i,S end for return [F x , F y , F z ] end procedure modeling, vmad 6  for automated differentiation and abopt 7  for optimization.
Scaling on Cori GPU We perform the scaling tests on the Cori GPUs for varying grid and mesh sizes, and compare it against the scaling of the python implementation of FastPM. As mentioned previously, though the accuracy of the simulation is independent of the mesh layout, the performance can be dependent on it. Thus for the FlowPM implementation, we will look at the timing for different layouts of our mesh. Different symbols indicate different layout for computational mesh, with legends indicating the number of splits along x-direction. For a given number of processors, we use divergent color-scheme with more splits along x-axis than y-axis shown in red and blue otherwise. We use the same gradient for identical overall configuration. Since 3D FFTs are typically the most computationally expensive part of a PM simulation, we begin with their time-scaling.
There is, however, still a communication overhead as we move from GPUs on a single node to multi-nodes (see for grid size of 128). Secondly, as expected, given the increase in number of operations for the pyramid scheme as compared to single-mesh implementation the single-mesh implementation is more efficient for small grids. However its scaling is poorer than the pyramid scheme which is ∼ 20% faster for grid size of N = 1024. In Figure  11 , we compare this implementation with the python implementation. We find that FlowPM is alteast 10x faster than FastPM for the same number of processes, across all sizes (except the combination of smallest grid and largest mesh size). Moreover, since the both FlowPM and FastPM benefit with increasing the number of processes, we expect that it will be hard to beat the performance of FlowPM with simply increasing the number of processes in FastPM.
To reconstruct the initial conditions, we need to minimize the negative log-posterior Eq. 12. The snippet of Mesh-TensorFlow code for such a reconstruction using TF Estimator API  (Cheng et al. , 2017)  is outlined in Listing 7. 1. In the interest of brevity, we have skipped variable names and dimension declarations, data I/O and other setup code and included only the logic directly relevant to reconstruction. Using Estimators allows us to naturally reuse the entire machinery of Ten-sorFlow including but not limited to monitoring optimization, choosing from various inbuilt optimization algorithms, restarting optimization from checkpoints and others. As with other Estimator APIs, the reconstruction code can be split into three components with minimal functions as -  • recon model : this generates the graph for the forward model using FlowPM from variable linear field (initial con-ditions) and metrics to optimize for reconstruction • model fn : this creates the train and predict specs for the TF Estimator API, with the train function performing the gradient based updates • main : this calls the estimator to perform and evaluate reconstruction We show the results of this reconstruction in Figure  13  and 14.
Here, the forward model is a 5-step PM simulation in a 400 Mpc/h box on 128 3 grid with force resolution of 1. In addition to gradient based optimization outlined in Listing 7. 1, we implement adiabatic methods as described in  Feng et al. (2018) ;  Modi et al. (2018 Modi et al. ( , 2019b) )  to assist reconstruction of large scales. We skip those details here in the code for the sake of simplicity, but they are included straightforwardly in this API as a part of recon model and training spec. We compare our results with the previous reconstruction code in python based on FastPM, vmad and abopt (hence-forth referred to as FastPM reconstruction). Both the reconstructions follow the same adiabatic optimization schedule to promote converge on large scales as described in  Modi et al. (2018); Feng et al.
The code snippet in Listing 7. 2 modifies the code in 7. 1 by including these pre-trained neural networks NNp and NNm in the forward model to supplement FlowPM. It also demonstrates how to include associated variables like M 0 in the recon model function that can be updated with ease over iterations to modify the model and optimization. We again compare the results for FastPM and FlowPM reconstruction with the same configuration as before in Figure  16  and 17. Here, the data is halo mass field with number density n = 10 -3 (Mpc/h) -3 on a 128 3 grid for a 400 Mpc/h box. At this resolution and number density, only 17. 5% of grid points are non-zero, indicating the sparsity of our data. The forward model is a 5 step FastPM simulation followed by two layer fully connected networks with total 5000 and 600 weights respectively (see  Modi et al.
(2018)  for details). The position network takes in non-local features as a flattened array that can also be implemented as a convolution kernel of size 3 in TensorFlow. Both the codes reconstruct the initial conditions equally well at the level of cross-correlation. However the transfer functions for both the reconstruction is quite different. In addition to the ease of implementing reconstruction in FlowPM, the most significant gain of FlowPM is in terms of the speed of iteration. The time taken for 1 FlowPM iteration is ∼ 1. 7 second while the time taken for 1 iteration in FastPM reconstruction in ∼ 15 seconds. The huge increase in time for FastPM iterations as compared to FlowPM is due to the python implementation of single convolution kernel and its gradients as required by the neural network bias model, which is very efficiently implemented in TensorFlow.
Conclusion In this work, we present FlowPM -a cosmological N-body code implemented in Mesh-TensorFlow for GPU-accelerated, distributed, and differentiable simulations to tackle the unprecedented modeling and analytic challenges posed by the next generation of cosmological surveys. FlowPM implements FastPM scheme as the underlying particle-mesh gravity solver, with gravitational force estimated with 3D Fourier transforms. For distributed computation, we use Mesh-TensorFlow as our model parallelism framework which gives us full flexibility in determining the computational layout and distribution of our simulation. To overcome the bottleneck of large scale distributed 3D FFTs, we propose and implement a novel multi-grid force computation scheme based on image pyramids. We demonstrate that without any fine tuning, this method is able to achieve sub-percent accuracy while reducing the communication data-volume by a factor of 64x.