dataesr/scientific-paragraphs-categorization huggingface dataset:
Moreover, with respect to the other semantic domains investigated, this one has a much lower instances number; hence, it is much smaller and less representative. An experiment for computing centers of gravity for classes has been carried out for the GHSOM case. The technique is the same we used in  [1]  for the classical SOM architecture. There are, however, some differences that need to be highlighted and further clarified. Given that GHSOM has a hierarchical and dynamically growing structure, its final architecture is composed of many maps with different sizes at different levels of granularity, instead of just one with fixed size, as in SOM case. In particular, the whole GHSOM structure has a high number of maps (for the settings used in our experiments more than fifty), each exploring different portions of the dataset going down the hierarchy.
The implication for this fact is that all the maps in the GHSOM, whose growth is controlled by parameters τ 1 and τ 2 , have very different and smaller sizes compared to the SOM, where the size of the unique map is one of the parameters manually set for each experiment. To make an example, the GHSOM map in the first level (after the zero unit), which is the one receiving in input the whole dataset has a size after training of 3x2 neurons, while for the SOM map analyzed with centers of gravity test the size is 30x30 neurons (because they are all condensed in that unique map). The positions of centers of gravity for the map placed at the first level of the hierarchy, which is a map with 3x2 neurons, are displayed on the grid in Fig. 8. In Table  4 , we report the detailed results obtained for centers of gravity, winning neurons and relative Euclidean distances related to the same map.
Optimizing parameters for controlling maps growth An optimization algorithm has been implemented for a correct definition of proper values of the two parameters τ 1 and τ 2 , responsible for the growth of the GHSOM architecture. The goal of this process is to shove the formation of visual clusters toward a semantics-based interpretation. The task has been accomplished by realizing a genetic algorithm used to fine-tune the parameters. Other optimization algorithms could be used as well; however, evolutionary   properties of genetic algorithms are the most suitable in this context. The sets of experiments on the dataset 34 synsets have proven that a relation exists among visual features and semantics knowledge. Therefore, the idea is to exploit such information to minimize semantics diversity in visual clusters.
Combined approach implementation and evaluation As explained in Sect. 4. 4, the goal of combination is to use a function or operator for merging the results of individual approaches together (see Fig. 3 ). The weights used in the experiments are reported in Table  5. Each combination scheme is identified by a letter. For example, the scheme named A gives equal importance to top-down and bottom-up approaches. Other schemes evaluate the performance for several different configurations of weights. Schemes F and G refers to individual performances of bottom-up and top-down approaches, respectively. The algorithm has been implemented in Python language and tested over a test-set extracted from the dataset, 34-synsets. It receives in input two lists of predicted synsets with corresponding probabilities.
In conclusion, the experiments suggest that the best option is scheme D, which assigns weights of 0. 6 and 0. 4 to bottom-up approach and top-down approach, respectively. In fact, giving slightly more importance to bottom-up approach allows us to exploit goodness of both approaches and it could be helpful considering the advantage in top-5 accuracy of bottom-up approach, resulting into better final overall performance, which was our initial goal for the combination task. Same results, shaped as a chart, are reported in Fig. 11. Such considerations reflect the results obtained from the experiments we carried on the datasets at our disposal. Given their not very big size, further experimentation on wider datasets could help increase the confidence of these insights.
In this study, a new method for identifying and characterizing straight cracks in plate-like structures is presented. The method combines the finite element method (FEM) using the software Abaqus and the success history-based adaptive differential evolution algorithm (SHADE). The objective of the method is to minimize the mean relative error between the measured experimental frequencies of a plate with an unknown crack identity and the numerical frequencies obtained using the Shade-FEM approach. The crack identity is defined by its length, orientation, and centre coordinates.
NUMERICAL EXAMPLES Computing natural frequencies by finite element method he performed simulations using the FEM method are achieved under the Abaqus 6. 14 software, which is a powerful simulation software used in many fields of mechanical engineering. In this section, the investigated plate has a thickness of 1 mm, with 480mm in length and 280mm in width and the four edges of the plate are clamped. The crack has a length of 120 mm and is in the centre of the plate. The Young's Modulus and Poisson's ratio of the material are𝐸=200GPa and 𝜈=0. 33 respectively. The plate is meshed with quadrilateral elements with the size of the element fixed to 4. 0 mm. The Fig. 1  shows the values of natural frequencies in modes 4 and 7 present the opening of the crack in each mode. In this study 10 modes are considered.
First, an estimate of the natural frequencies of the cracked and the crack-free plate is obtained by means of a hammer test. The plate is impacted by the hammer, and an estimate of the natural frequencies is obtained from the peaks on the frequency spectrum (Tab. 3 ). An average of several readings is taken for each natural frequency. Tab. 4 relates the numerical values of the natural frequencies of the cracked plate, given by a finite element analysis with Abaqus software, and the experimental frequencies.
The proposed approach has been numerically validated in the case of a steel plate with an inclined straight crack identified by its length, orientation and coordinates of the centre. To evaluate the efficiency of the minimization algorithm, the natural frequencies obtained by a modal analysis are used in an inverse search problem to get the identity of the crack and the results have showed good convergences on both objective function and crack's parameters. In a second experimental proof, a hammer test is used to measure the natural frequencies of a cracked steel plate with the same dimensions as in the first example. The frequencies of the plate, with some experimental errors, are used to set the fitness function to be minimized by SHADE algorithm. The results obtained by this experience demonstrate that a certain level of accuracy for the measured data is essential for accurate damage detection.
It remains however to investigate how well these algorithms would adapt to more complex use cases (nonlinear physics, involved unit operations, etc. ), in terms of optimality of the results as well as computation cost, hyperparameter finetuning, etc. Besides, although a popular choice, it has been shown that RL requires careful validation in practice to strengthen the robustness of the results because of the inherent statistical uncertainty of the algorithms  (Agarwal et al. , 2021). Alternatively to reward-driven design, another line of work much used in the literature of molecular design  (Elton et al. , 2019) , consists in training a generative statistical model that learns the underlying distribution of a dataset of process samples, before biasing the distribution towards regions of high fitness values.
Once trained, the model can generate new words by recursively sampling from the conditional distribution P(x[i + 1]|x[1],. , x[i]), starting from the GO token only and until the EOS token is drawn. In practice, the training set D should be large enough to learn a meaningful distribution, with 10 5 -10 6 samples, however no such collection exists for power cycles. To circumvent this issue, the initial dataset is instantiated by a pseudo-random generator, as follows: i) every cycle is initialized as a simple Brayton cycle TACH, formed successively by a turbine, a cooler, a compressor and a heater; ii) a random number of mutations are applied to the layout, where a mutation consists in choosing a random stream and inserting a process unit chosen at random. Training is performed iteratively, starting from a small set D 0 of random layouts, training an LSTM model on it, using the model to generate a set G k of new layouts and adding the thermodynamically valid ones to the training set for the next iteration of training.
1 and in the Supplementary Materials, Section 4. Consequently, layouts with poor thermal efficiency are strongly penalized, as well as those with small heat recuperation ratio, to focus the computational effort on cycles with promising thermal performances. More details about PSO can be found in the Supplementary Materials (Section 1). All computations and models are implemented in Python 3. 8, using the libraries CoolProp  (Bell et al. , 2014)  for the thermodynamic properties, PyTorch 1. 9. 0  (Paszke et al. , 2019)  and Lightning 1. 4. 7  (Falcon, 2019)  for the deep learning models, which are optimized using the Adam solver with a learning rate of 10 -3. Because the discussion of the economic hypotheses leading to the optimal exergoeconomic cost is beyond the scope of this article, all results are presented in terms of specific cost normalized by a reference value.
Other challenges The field of machine learning based process design is still nascent  (Schweidtmann et al. , 2021) , in particular purely datadriven methods. Hence, from a methodological perspective, AIbased process design faces several challenges, in particular: initial dataset constitution, reward design, model architecture and finetuning strategy  (Nabil et al. , 2022). In the sequel, we discuss dataset constitution and search space exploration, based on the experiments carried out in this paper. The discussion of the latter two challenges is postponed to Section 3 of the Supplementary Materials. Initial dataset The models used in this paper are trained to learn the underlying distribution of a dataset. To do so, they require large amount of data -for instance the models trained on the similar problem of molecular design are based on datasets with 10 5 -10 6 samples  (Elton et al.
, 2019). Such large datasets do not exist for process design, which limits their applicability. Observe on the other hand that the reward-driven process design literature discussed in Section 2. 3, in particular reinforcement learning algorithms, does not need an initial training set since they are optimization procedures in the topological space of process layouts. As such, these methods are more straightforward to implement. In this work, we used a random generator to initialize the procedure and obtained good performances despite the smaller training size. Vogel et al. (2022)  also built a synthetic generator, a Markov-chain process based on process design heuristics, training their data-driven flowsheet completion model on about 8,000 synthetic data. Besides, the generative model is only as diverse as its training set is.
We refer to  Alaa et al. (2022)  for a recent contribution on the topic. Finally, we can draw a connection with  Palowitch et al. (2022) , who recently introduced GraphWorld, a generator of arbitrarily large populations of synthetic graphs, and showed that it could efficiently explore regions of the search space uncovered by standard benchmark data. This indicates that insights and successful results can be obtained starting from synthetic data only. Another promising track explores the opposite direction:  Balhorn et al. (2022)  suggest to scan the process design literature in order to build a digital process flowsheet dataset, not available as of writing time.
2 spectrometry (CA-ID-TIMS) U-Pb zircon crystallization ages and in-situ zircon trace-element 25 geochemistry for a suite of caldera-related, coeval plutonic and volcanic units of the Permian 26 Sesia Magmatic System (northern Italy). This dataset documents the protracted growth and 27 evolution (~1 Myr) of a voluminous (>1000 km 3 ), upper crustal (3. 5-2. 0 kbar) silicic magma 28 reservoir. Systematic changes in zircon composition with time reveal episodic intrusions of new 29 magma into a single, progressively differentiating reservoir which was dominantly kept at high 30 crystallinity conditions (>60 vol. %). The volcanic and plutonic units both show dispersed and 31 heterogeneous CA-ID-TIMS age distributions. A stochastic, thermodynamics-based zircon 32 saturation model accounting for fractional crystallization, recharge and thermal rejuvenation 33 effects on zircon growth and stability in a rhyolitic magma body reproduces the observed 34 distributions of zircon U-Pb ages.
Materials and methods 141 Informed by recent, detailed mapping and petrologic investigation  (Tavazzani et al. , 142 2017 (Tavazzani et al. , 142 , 2020)) , we selected six samples for high-precision CA-ID-TIMS U-Pb zircon dating (Fig. 143  1b) that cover the full extent of textural and geochemical variability of the upper-crustal intrusive 144 and eruptive products of the SMS. We compile 39 new dates with recently published zircon ages 145 of  Karakas et al. (2019)  into a dataset of 96 single CA-ID-TIMS zircon U-Pb dates for upper-146 crustal lithologies of the SMS. 147.
U and Pb were separated using 169 a single-column HCl-based ion exchange chemistry  (Krogh, 1973). The U-Pb fractions were 170 loaded on outgassed Re filaments with ~1 μl of Si-gel emitter (modified from  Gerstenberger and 171 Haase, 1997). U and Pb isotopes were measured using a Thermo TRITON Plus thermal ionization 172 mass spectrometer at the Institute of Geochemistry and Petrology of ETH Zurich  (Wotzlaw et al. , 173 2017). Data reduction, age calculation and uncertainty propagation were performed using the 174 Tripoli and ET_redux software package  (Bowring et al. , 2011; McLean et al. , 2011). Detailed 175 analytical procedures are reported in Supplementary Text. 176.
2d ; Fig. 6d ), with zircon crystallizing from progressively cooler residual 408 melt. These predictions are backed by evidence from silicic intrusions characterized by 409 comprehensive high-precision U-Pb zircon datasets, which display decreasing mass of 410 crystallized zircon with time and linear decrease in temperature (e. g. Samperton et al. , 2017; 411 Large et al. , 2021) 412  In intrusive and volcanic units of the SMS, the relative distribution of zircon 413 crystallization ages (i. e. increase in relative number of crystallized zircons with time; Fig. 3b  and 414 3c) is incompatible with zircon growth from a monotonically cooled, isolated magma batch (Fig. 415  6). Additionally, the SMS zircon geochemical record shows non-linear variations in temperature-416 modulated Ti contents (Fig.
For 511 large-n samples (e. g. LA-ICP-MS datasets) a prior distribution generated by bootstrapping the 512 data may be the most appropriate; however, in cases where few zircon dates are available to 513 estimate eruption/deposition age (e. g. CA-ID-TIMS datasets), significant biases may be 514 introduced via bootstrapping, or by choosing an inappropriate prior. Our forward modelling (Fig. 515  6) and data compilation (Fig. 7, 8 ) suggest that in absence of other information, the best choice to 516 estimate eruption age of large volcanic explosive events might be approximating the time 517 evolution of mass of zircon crystallized with a truncated normal distribution  (Keller et al. , 2018) , 518 as this distribution reproduces the late peak of zircon crystallization characteristic of long-lived, 519 interconnected magmatic reservoirs (Fig.
Acknowledgments 574 We thank  Stefano Peres  and  Maria Paula Castellanos Melendez  for support during field work 575 and data acquisition. We also thank  Calvin Miller ,  Robert Ernst ,  Brenhin Keller ,  Oleg Melnik ,  576 Adam Kent ,  Simon Large  and  Kyle Samperton  for providing stimulating and insightful 577 comments on the current and previous versions of this manuscript. This work was partially 578 supported by  2018 Geological Society of America Research Grant  (to Tavazzani) and  RES-RC 579   Università di Trieste  (to Demarchi). 580.
ACKNOWLEDGMENTS The authors acknowledge  Florian Fröwis  for discussions and technical support at an early stage of this project. All authors acknowledge support from the  Swiss National Foundation  through the  NCCR QSIT  and the following projects and Grants Project  2000021_192244/1  and Project No. 172590  for KTK and MA; a  Doc. Mobility grant  (project  P1GEP2_199676 ) for TK, SNFS grant 197168 for MA and a starting grant  PRIMA PR00P2_179748  for GH. J. E. also acknowledges the  National Research Agency (ANR)  through the project  WAQUAM  ( ANR-21-CE47-0001-01 ).
The Affnet method The Affnet  [42]  method was conceived to predict normalizing ellipse shapes for single patches based on a 3-variable parametrization. Figure  4  depicts the passage from Affnet affine maps to the affine map transforming query into target (i. e. A). The connection provided by two Affnet-normalizing affine maps for the query and target patches is richer than each normalizing transformation. Indeed, for different choices of A 1 = T 1 R 1 and A 2 = T 2 R 2 one would need the four parameters (zoom, camera    1 (namely zoom λ, camera rotation ψ, tilt t, tilt direction φ, and translation x, y), for the locate method, the Affnet method  [42]  and the identity map method. The  [62]  dataset is used; it contains 3352 patch pairs with corresponding ground truth. The sub-index GT means ground truth, conversely, no sub-index stands for estimated parameters.
Precision In order to measure the precision in a realistic environment of these three methods (Naive, Affnet and locate) we used the viewpoint dataset presented in  [62] , consisting of five pairs of images with their ground truth homographies and 3352 true matches. Notice that Equations 3-4 allow us to compute ground truth local affine maps around each match. Figure  5  shows the accuracy of Naive (Identity), Affnet  [42]  and locate, represented by error density functions with respect to the affine decomposition appearing in Equation  1. Ideally, we expect a Dirac delta function centered at 0 for a perfect method. This is approximately true for the locate method. Note in Figure  5  that translations from the Affnet  [42]  method do not quite match those from the Identity method; this difference can be explained by the connecting mapping itself (see Equation  7 ) which is different from A 2 A -1 1 x.
Experiments In order to quantify the benefits of the local affine approximations for the homography estimation problem, we will compare RANSAC 2pts and RANSAC affine to RANSAC base. The three variants of RANSAC presented in this work are based on the original RANSAC algorithm and do not include recent modifications proposed in the literature (e. g. RANSAC USAC  [55] , etc). Even if they are not entirely comparable to ORSA  [43]  nor RANSAC USAC  [55] , a line on each experiment will be added for ORSA or USAC as benchmark to compare against the state-of-the-art. The reader should keep in mind that most improvements proposed in RANSAC USAC  [55]  can also be applied to RANSAC 2pts and RANSAC affine. All experiments in this section were conducted on four well known datasets for homography estimation.
Those datasets are: EF  [82] , EVD  [41] , OxAff  [39]  and SymB  [26]. The EF dataset presents challenging non-linear lighting variations and occlusions. Both EVD and OxAff datasets present several pairs incurring in strong viewpoint differences. In particular, viewpoint differences between pairs in the EVD dataset are extreme and most matching methods will struggle to find correct matches. Lastly, the SymB dataset consists of painting-to-photo pairs, which will be challenging for detectors, descriptors and local geometry estimators that where not intended to be used under this circumstances. All datasets include ground truth homographies that were used to verify the accuracy. Four combinations of state-of-the-art detectors and descriptors were used as starting point for all RANSACs. These choices are: SIFT  [32]  + AID  [62] ; SIFT  [32]  + HardNet  [40] ; HessianAffine  [38]  + AID  [62] ; HessianAffine  [38]  + HardNet  [40].
Detector + Descriptor EF dataset  [82]  EVD dataset  [41]  OxAff dataset  [39]  SymB dataset  [26]  Affine  A-contrario homography estimation performances for ORSA  [43] , RANSAC base , RANSAC 2pts and RANSAC affine. Four combinations of detectors and descriptors are used: SIFT  [32]  + AID  [62] ; SIFT  [32]  + HardNet  [40] ; HessianAffine  [38]  + AID  [62] ; HessianAffine  [38]  + Hard-Net  [40]. Affine approximations are provided by the locate method presented in Section 3. 1; 'None' states that no affine information is provided. Each RANSAC runs for 1000 internal iterations, except for ORSA that runs for 10000 iterations. To measure probability of success, all RANSACs were run 20 times on resulting matches from each pair of images. Legend: S -the number of successes (bounded by 20× number ); the number of correctly matched image pairs; inl.
Detector + Descriptor EF dataset  [82]  EVD dataset  [41]  OxAff dataset  [39]  SymB dataset  [26]  Affine In Section 4 we have introduced, for the proposed RANSACs, a procedure allowing to order and validate estimations with respect to a measure of statistical significance, the NFA. However, the typical thresholding for determining inliers is less costly and might be a preferred option depending on the application. With this in mind, experiments are separated in two (Subsection 5. 1 and Subsection 5. 2) and are presented in form of tables. Each table should be analyzed by blocks. Each block consists of a fixed matching method and dataset. The reader should pay special attention to the first two columns: total number of successes and total number of image pairs identified at least once. The best method should have these two indicators as high as possible, for most choices of matching method and dataset (i.
Fixed thresholds for inlier discrimination Table  1  shows a comparison of homography estimation methods using fixed thresholds for inlier/outlier discrimination. The performance of each RANSAC (combined with the affine approxi-mations of Section 3. 1) is tested on the four aforementioned datasets for the four choices of detectors and descriptors presented above. The RANSAC USAC  [55]  method is added to Table  1  in order to compare the proposed RANSACs against a well established state-of-the-art method. The USAC  [55]  method shows better performances than RANSAC base when equipped with the HardNet  [40]  descriptor. This situation is inverted for the AID  [62]  descriptor. A plausible explanation is the higher rate of false positive matches for the AID  [62]  descriptor with respect to the HardNet  [40]  descriptor, which might be harming the performance of some steps (like the T d,d and Bail-Out tests, among others) present in USAC  [55].
The reader will also note the performance drop of the locate method in estimating affine approximations between image pairs in the case of the SymB  [26]  dataset. Indeed, locate misreads the information when analyzing the painting-to-photo patch pairs, an invariance for which locate was not trained. The Affnet  [42]  method is less affected by these painting-to-photo image pairs as it analyzes separately each patch, so it is the structure that provides the invariance. However, the Affnet and Naive methods show similar performances under the SymB  [26]  dataset. Incorporating the affine information to the homography fitting step allowed to boost the total number of successes in retrieving ground truth homographies for almost any configuration of detector and descriptor. Indeed, having decreased the sample size (from 4 to 2) has increased the probability that at least one of the 1000 random samples that were drawn while iterating is free from outliers.