dataesr/scientific-paragraphs-categorization huggingface dataset:
Further deployments of AMICA in future airborne campaigns are planned. Currently, work is being done to further improve the signal-to-noise ratio, e. g. by filtering the zero offset signal from the PC to the preamplifier. It is also planned to install mirrors with higher reflectivity and possibly an ICL with higher power output for the 3331 cm -1 channel to render it suitable for measuring N 2 O, HCN and C 2 H 2 https://doi. org/10. 5194/amt-14-5271-2021 Atmos. Meas. Tech. , 14, 5271-5297, 2021 at atmospheric concentrations. It is also envisaged to eventually add further channels at different wavenumber regions to AMICA in order to target additional trace gases, depending on the science questions of future missions. Data availability. AMICA data from the two StratoClim Geophysica campaigns in 2016 and 2017 will be accessible via the HALO database at https://halo-db.
pa. op. dlr. de/mission/101 (last access: 22 July 2021, DLR, 2021b). Data from the 2019 South-TRAC campaign will be accessible via the HALO database at https://halo-db. pa. op. dlr. de/mission/116 (last access: 22 July 2021, DLR, 2021a). As long as database access is still restricted, AMICA data will be provided by the corresponding author upon request. Supplement. The supplement related to this article is available online at: https://doi. org/10. 5194/amt-14-5271-2021-supplement. Author contributions. CK and MvH coordinated the AMICA instrument development, carried out laboratory tests, operated AM-ICA during airborne campaigns and prepared the article with contributions from all co-authors. VT, JBL, GLM, AG, XD, TK, JS, HS and SS made major contributions to the AMICA conceptual design, development and construction.
We also thank Rolf Maser, Dieter Schell and Jana Stahl from Enviscope GmbH for their support of the AMICA integration on HALO, as well as Nicole Spelten for helping with AMICA operations in Oberpfaffenhofen. We thank Harald Franke from Enviscope GmbH for his work on design and installation of the trace gas inlet on the M55 Geophysica dome. We are grateful to Jörn Ungermann and Reimar Bauer for their valuable support with the imple-mentation of the AMICA instrument control and spectral analysis software in Python and to Raffaele Sury from Meerstetter Engineering for his support and guidance when setting up the LTC-1141 for laser control and data acquisition. We thank Frans Harren and an anonymous referee for their constructive peer review that helped increase the quality and readability of this paper.
Financial support. This research has been supported by the European Commission, Seventh Framework Programme (STRA-TOCLIM (grant no. 603557)), the Bundesministerium für Bildung und Forschung (BMBF-FKZ; grant no. 01LG1205) and the graduate school HITEC of Forschungszentrum Jülich. The article processing charges for this open-access publication were covered by the Forschungszentrum Jülich. Review statement. This paper was edited by Mingjin Tang and reviewed by two anonymous referees.
Possible solution procedures (verifyeig) are included in the MATLAB toolbox INTLAB  [40]. Assume that the system under investigation contains ñ mutually disjoint conjugatecomplex eigenvalue pairs with n * = n -2 ñ ≥ 0 as the number of remaining real eigen- values. To simplify the notation, assume further that all eigenvalues are sorted so that all complex pairs are listed first, cf. [28]. Now, an equivalent system representation in block diagonal structure with Ã = blkdiag Ã1 ,. , Ã ñ+n * (23) can be obtained, where pairs of conjugate-complex eigenvalues with ω i = -ω i+1 , i ∈ {1, 3,. , 2 ñ -1} , (24) lead to the blocks Ãj ∈ [σ j ] [ω j ] -[ω j ] [σ j ] (25) with j ∈ {1, 2,. , ñ}, while an uncertain real eigenvalue is reflected by Ãj ∈ [σ i ] , j = i -ñ , i ∈ {2 ñ + 1, 2 ñ + 2,. , n}. ( 26 ) The respective transformation between the original system matrix A(p) and the representation in (  23 ) is given by the column-wise partitioned matrix T ∈ T = T1 ,.
Application Scenario: Step-Down Converter The algorithms for a transformation of dynamic system models into a cooperative statespace representation are now compared by means of numerical simulations for the state equations of a linear step-down converter circuit. All interval evaluations are performed in INTLAB V. 12  [40]. For the numerical simulation of point-valued bounding systems, the floating-point solver ode23 with standard tolerance setting and the maximum step size 10 -5 was used. This solver is sufficiently accurate and more effective than, for example, ode45 for the moderately stiff system model under consideration. For this application, the resulting approximation errors are also several orders of magnitude smaller than the absolute values of the corresponding states. This was checked by a computation of the corresponding solutions with the help of symbolic formula manipulation in MATLAB.
The new solution approach (without counting the offline parameter splitting) is faster by a factor of at least 100 than the alternative solver despite the use of multiple parameter intervals in the simulation if both are executed on the same computer using MATLAB 2019B. Remark 3. Due to the linearity of the point-valued bounding systems produced by the new Algorithms 1-4, it is even possible (in the case when the dimension n is sufficiently small) to compute the worst-case state enclosures efficiently in closed form by using techniques for symbolic formula manipulation. The existence of such symbolic expressions can be exploited in future work to design fast model-predictive control strategies for uncertain dynamic systems. Remark 4. Due to cooperativity of the transformed system models-which are obtained with the approach presented in this paper-they are less affected by overestimation resulting from the wrapping effect, even if simulations were carried out for the corresponding interval boxes of the uncertain parameter and not for the decoupled bounding systems as suggested.
BPMN supports the design of intra-organization workflows and inter-organization collaborations. This rich notation includes elements to deal with models where time is central. However, the expressiveness of the BPMN time-related constructs hampers the definition of a formal semantics including them, and the provision of formal analysis means for timed process models. We propose here a first-order logic semantics for a subset of BPMN that includes its time-related constructs. With reference to related work, we support the specification of datetimes, durations, and cycles, using ISO-8601 formats as specified in the standard. Our approach is tool-supported by a model transformation into the Alloy formal language and its bounded counter-example generator. Our tool and model database are open source and freely available.
In a previous work  (Houhou et al. , 2019) , we have defined a formal semantics for a sub- set of BPMN (Fig. 1 , but for time-related events), with a focus on BPMN communication constructs and different communication models. We also had defined a tool, fbpmn, to support the formal analysis of processes, and generate and animate counter examples. In the paper at hand, we extend this work by supporting the expressive time-related features of BPMN, including the use of the ISO-8601 standard, and show how we can support the Process Time Patterns. The proposed semantics is directly defined in terms of First-Order Logic (FOL), rather than through a mapping to some formal language. This choice makes it possible for researchers to map the FOL semantics to verification frameworks of their choice like (Alloy with SAT solvers) as we did here; TLA+ with the TLC model-checker (as we did before), SMT, or others).
Alloy Alloy is a declarative modelling language based on FOL and relational calculus for expressing complex structural and behavioral constraints  (Jackson, 2012 ). Alloy's logic is quite generic and does not commit to a particular specification style  (Cunha, 2014). We believe that this is more natural and allows preserving the expressiveness of the input modelling language, BPMN in our case. Alloy comes with a tool, Alloy Analyser, a constraint solver that provides automatic simulation and verification based on a model-finding approach using a SAT solver. Alloy has been used for the verification of UML Activity Diagrams  (Laurent et al. , 2014) , in the Model-Driven Engineering domain  (Kleppe et al. , 2003) , for the modelling and analysis of distributed system protocols  (Taghdiri and Jackson, 2003) , networks  (Georg et al.
CONCLUSION We have proposed a formal semantics for the timerelated constructs of BPMN. This semantics supports different combinations of events, time information categories (date-times, durations, cycles) and the corresponding ISO-8601 descriptions as prescribed by the BPMN standard. It can be then used to give a semantics to BPMN models using Process Time Patterns  (Lanz et al. , 2010; Lanz et al. , 2014; Lanz et al. , 2016). Our proposal is based on a direct formalization in First Order Logic which we have then implemented in the Alloy input language, together with an extension of our fbpmn tool  (Houhou et al. , 2019)  to transform BPMN models into Alloy modules. The Alloy implementation of our semantics is direct. Yet, one still has to find a better representation of time steps in it in order to make automated verification amenable.
The necessity of coding in a dedicated programming language (e. g. CUDA) has probably hindered the use of GPUs. However, the emergence of user-friendly Python libraries such as TensorFlow and PyTorch, which allow running relatively simple code on GPUs, will certainly contribute to popularize it in the coming years. Compared to physic-based numerical models (referred here as instructor models), statistical emulators (or surrogate models), which mimic the behavior of the simulator as closely as possible, are computationally cheap to evaluate. Surrogate models are solely constructed from intelligently chosen input-output data of the instructor model without any knowledge of its inner working. The arrival of machine learning has led to the development of deep learning-based surrogate models  [Reichstein and others, 2019]  to accelerate computational fluid dynamics (CFD) codes [e.
g. Ladický and others, 2015 , Tompson and others, 2019 , Kim and others, 2019 , Obiols-Sales and others, 2020]. The main idea is to take advantage of the large amount of modelling results (data) that a CFD solver can produce to train a neural network emulator delivering high fidelity solutions at much lower computational cost. The fidelity of the emulated solution, relative to the instructor model, is directly dictated by the emulator complexity and the quality of the training dataset, which must be representative of all dynamical states. This approach can therefore be seen as a way to compress a large number of model realizations  [Kim and others, 2019] , and to take benefit of this information for new model runs that are fairly close to the runs already performed in generating the training dataset.
This paper intends to explore the potential of constructing ice flow model emulators. In the machine learning paradigm, artificial neural networks have been increasingly used in recent years to deal with various kinds of problems such as image classification  [Simonyan and Zisserman, 2015] , segmentation  [Ronneberger and others, 2015]  and domain transfer  [Isola and others, 2017] , whenever a large scale training dataset is available  [LeCun and others, 2015]. Classical examples of classifiers are email filtering to identify spam  [Dada and others, 2019] , handwriting recognition  [Cireşan and others, 2010] , or image segmentation for biomedical applications  [Yang and others, 2017]. In the case of image analysis, a breakthrough occurred in the early 2010s  [LeCun and others, 2015]  thanks to successful Convolutional Neural Networks (CNN) that are today widely used in image recognition or classification.
Recently, Brinkerhoff and others [2021] used a neural network to emulate an expensive coupled ice flow / subglacial hydrology model, and infer the optimal parameters that best reproduce the observed surface velocities using a Bayesian approach. In this paper, we apply deep learning to ice flow modelling. Our approach consists of setting up a CNN that predicts ice flow from given topographic variables and basal sliding parametrization in a generic manner. By contrast,  Brinkerhoff and others [2021]  emulated a coupled ice flow-hydrology model for a specific glacier from a small-size ensemble of relevant parameters. Our neural network em-ulator is trained from a large dataset, which is generated from ice flow simulations obtained from two state-of-the-art models -the Parallel Ice Sheet Model [PISM,  Khroulev and the PISM Authors, 2020]  and CfsFlow  [Jouvet and others, 2008, 2009]  -equipped with two different mechanics (hybrid SIA+SSA and Stokes) and at two different spatial resolutions (2 km and 100 m).
We integrate mass balance and mass conservation with our ice flow emulator to obtain a time evolution model, the "Instructed Glacier Model" (IGM) written in Python, which permits highly efficient, and mechanically state-of-the-art ice flow simulations. In the following, we first describe the IGM model with its neural network-based emulator and the generation of the training dataset. Then, we present our results in terms of fidelity and computational performance of the emulated ice flow model with respect to the instructor model, and of embedding the ice flow emulator into a time evolution model. Last, we compare and discuss the IGM results with state-of-the-art ice flow model results.
Ice flow emulator Our ice flow emulator predicts vertically averaged horizontal velocity from ice thickness, surface slope, and basal sliding coefficient c, which is defined later in Eq. (  6 ): M : {h, ∂s ∂x , ∂s ∂y , c} -→ {ū, v} (3) R N X ×N Y ×4 -→ R N X ×N Y ×2 where input and output are two-dimensional fields, which are defined over the discretized computational domain (or subparts) of size N X × N Y. We approximate M by means of an Artificial Neural Network (ANN) M p (see Appendix E for a digest on  ANN and LeCun and others [2015]  for an in-depth review). ANNs map input to output variables using a sequence of network layers connected by trainable linear and non-linear operations with weights p = [p 1 ,. , p N ], which are adjusted (or trained) to a dataset (realizations of an instructor model in the present case).
While there are several possible choices of loss (e. g. , the mean squared error L 2 , the mean absolute error L 1 , or more general L p errors), we opted for the error L 1 loss function by simply imitating existing neural networks [Thuerey and others, 2020, Kim and others, 2019] designed for emulating CFD solutions: ūP -ūR L 1 = 1 |Ω| |ū P -ūR | 1 dΩ. (4) The loss function is minimized on GPU using a minibatch gradient descent method, namely the Adam optimizer  [Kingma and Ba, 2015]  with a learning rate of 0. 0001, and a batch size of 64. Let us note that we use a norm clipping to protect against gradient vanishing or exploding behaviour. To reach a satisfying level of convergence, we usually iterate between 100 to 200 epochs, which means that the optimization algorithm passes 100 to 200 times over the entire dataset (Appendix D).
Data generation for training and validation To train our ice flow emulator and assess its accuracy and performance, we perform an ensemble of simulations to generate large datasets using two ice flow models of variable complexity: the Parallel Ice Sheet Model [PISM, Khroulev and the PISM Authors, 2020], and CfsFlow  [Jouvet and others, 2008]. The goal is to construct diverse states to obtain a heterogeneous dataset that a large variety of possible glaciers (large/narrow, thin/thick, flat/steep, long/small, fast/slow, straight/curved glaciers,. ) that can be met in future modelling. For simplicity, we assume the ice to be always at the pressure melting point to focus on the dynamics in this study. PISM and CfsFlow simulate the evolution of the ice thickness combining ice flow and mass balance models for given basal topography, initial conditions, and climate forcing as depicted in Figure  1.
6  and Section "Data selection") among the 41 glaciers, we carry the same simulation varying parameter c in {0, 6, 12, 25, 70} km MPa -3 a -1 to explore different basal sliding conditions. We additionally carry out two further simulations of existing glaciers -Aletsch and Rhone glaciers (Switzerland) -for 250 and 200 years, respectively, that we use for assessing the method accuracy. Further modelling details are given in Appendix C. In all simulations, the fields of ice thickness, ice surface, sliding coefficient, and depth-average velocity, covering various domains are recorded on a structured grid at different times. The transformation of raw modelling data to be usable for training our neural network emulator (Eq. (  3 )) consists of the following three steps (the two last are illustrated in Figure  7 ): First, the data are normalized to fit the interval [-1,1] by dividing by a typical value over the entire dataset for each variable independently.
Such a normalization is widespread in deep learning to deal with different ranges of data and homogenize their values prior learning  [Raschka and Mirjalili, 2017]. Second, patches of dimension N X × N Y are randomly extracted from all slices of the dataset. The motivation to work patch-wise instead of the entire domain is that i) ice flow at a given location is only determined by predictors within a certain neighbourhood, it is therefore unnecessary to carry irrelevant distant information for model prediction, ii) it gives higher flexibility to exclude ice-free patches, which do not carry any relevant information for training, iii) to apply data augmentation (see next item). Here we found that a N X × N Y = 32 × 32 patch size was suitable for all applications, and we therefore always used this value.
Last, data augmentation  [Raschka and Mirjalili, 2017]  is applied after patching. For that purpose, we randomly apply 90 • , 180 • , 270 • rotations, as well as vertical and horizontal flipping to the patches shortly after being picked in the dataset. This augmentation increases the amount of data and permits to regularize the underlying optimizing problem, and is supported by the fact that the process we wish to capture -the ice flow -is invariant to these transformations.
Implementation IGM is implemented in Python with the Tensorflow  [Abadi and others, 2015]  library to evaluate the neural network emulator, solve the mass balance and the mass conservation equation (  1 ) in parallel on CPU  or GPU. The training of the neural network emulator was performed separately on GPU using the Keras library  [Chollet and others, 2015]  with a Tensorflow backend. The Python code as well as some ice flow emulators are publicly available at https: //github. com/jouvetg/igm.
Ice flow field We conducted several experiments with various network parameters to seek for the optimal parameters in terms of model accuracy versus model evaluation costs. For that purpose, we split our dataset in two parts: one for training and one for validation. Appendix D shows the evolution of training and validation losses with respect to epochs. Unless specified differently, we always reserved Icefield A (resp. Aletsch and Rhone glacier with c = 12) for validation and take the others for training for icefield (resp. glacier) simulations. Note that the validation loss is always lower than the training loss demonstrating that our choice of validation data remains safely within the hull of the training dataset (Appendix D).
Last, increasing the kernel size N ker from 3 (the most common value, see Fig. 4 ) does not improve the solution in all cases. Opting for large N lay , N ker and N feat numbers increases the number of network parameters, and thus the computational cost. Therefore, we selected two optimal parameter sets (one for each kind of dataset) that lead to fidelity levels above 90% while keeping low evaluation costs: i) the parameter set (N feat , N ker , N lay ) = (32, 3, 8) for PISM icefield data leads to a neural network that has about 65 k trainable parameters (it stores into a 880 KB file), and ii) the parameter set (N feat , N ker , N lay ) = (32, 3, 16) for CfsFlow glacier data leads to a neural network that has about 140 k trainable parameters (it stores into a 2 MB file). Figures 9 and 10 compare the flow speeds of Icefield A and Aletsch glacier at the maximum ice extent to the reference simulations with the respective selected models.
3 GHz cores) and CPU (Intel(R) Core(TM) i7-8850H CPU with 6 2. 6 GHz cores). A closer look at the emulated ice flow field of Aletsch glacier (Fig. 10 ) shows that the ice flow is well reproduced for the three accumulation basins, however, larger discrepancies occur on the tongue and at Konkordiaplatz where the three tributary basins merge into a single tongue. While the training dataset generated by CfsFlow contains many examples of sin-gle channelized flow (Fig. 6 ), merging ice flows of similar sizes such as at Konkordiaplatz as well as thick ice (up to 800 m) is much less common in the training dataset, explaining why the flow in this region is less well reproduced than anywhere else. By contrast, single-branch and thinner valley glaciers such as Rhone Glacier are much more common and better  The L 1 error (or loss) between a predicted and a reference ice flow has two components, a "network" component that measures the performance of the network to compress and recover solutions and a "data" component that measures the error related to the abundance/lack of relevant training data.
Icefields Here we found that this error component is ∼ 7% in both cases, which is ∼ 1-2% less than the L 1 original validation loss (∼ 8-9%). We therefore attribute the 7% to network errors and the remainder (∼ 1-2%) to a lack of representative data. The reference solution, and the predicted solutions with or without the reference in the training are displayed in Figures  9  and 10. In the case of Aletsch glacier, the spatial error patterns show that including the reference solution in the training locally resolves the discrepancy at the convergence area (Konkordiaplatz) of the three ice flow branches (Fig. 10 ), confirming that this particular source of error mostly lies on the data side (i. e. the absence of analogues in the training dataset) unlike the remaining errors on the main glacier trunk.
While GPU and CPU have close performance for models with few trainable parameters and small domains, the GPU is especially advantageous for complex models (with many weights) and for large size domains. While a key advantage of neural networks is their low evaluation cost, their training necessarily comes with substantial upstream computation costs, which must be invested for each set of ice flow settings. Table 3 lists these upstream costs for generating the data from traditional models and training the model itself. As a result, the generation of the full dataset was the most computationally expensive task: about 7 to 26 days for icefield simulations with PISM and glacier simulations with CfsFlow on CPU, respectively, while the training of the optimal models took 8 to 24 hours on GPU.
By contrast, the error related to the richness of the dataset to include a large diversity of relevant dynamical states is fairly small (< 2%). This therefore demonstrates the ability to learn the relationship between topographic and ice flow variables in a generic manner, i. e. , to translate the knowledge acquired on some glaciers to others. Most importantly, a model as complex as the 3D Stokes equations can be learnt and emulated very efficiently by a neural network, which maps 2D fields. Because using standard network parameters already results in a high fidelity emulator, we have not explored further parameter choices, thus leaving room for future improvements. For instance, we used the L 1 norm as our loss function, which is a common choice in deep learning accelerating CFD [Thuerey and others, 2020, Kim and others, 2019], future studies could explore other loss/misfit functions such as L 2 , L p ,.