Method for validating prediction of supervised model for multivariate quantitative analysis of spectral data

Abstract

A computer-implemented machine learning method for learning a multi-output prediction model (231) configured to: collectively determine, based on a characteristic spectral data set of a sample: at least one primary prediction (251) of at least one first physical quantity characterizing a given species in the sample; and at least one secondary prediction (252) of at least one second physical quantity characterizing the species, the multi-output prediction model being trained using the annotated spectral data set (210).

Description

Technical Field

[0001] The present invention relates to the field of quantitative analysis (e.g., determining the concentration of chemical species contained in a sample) and supervised qualitative analysis (e.g., classifying a sample based on spectral data (i.e., data with multiple intensity values ​​in various wavelength channels or spectral bands). The data can be both multispectral data or hyperspectral data, where the number of spectral bands varies from tens to hundreds, and data derived from emission or absorption spectra of chemical species containing thousands of wavelength channels. Summary of the invention

[0002] The present invention relates to a new multivariate analysis method for quantitatively analyzing chemical species contained in a sample based on spectral data obtained using spectroscopy techniques. One object of the present invention relates to using a multi-output algorithm to determine a measure of confidence in the prediction of a model used for quantification. More precisely, in the context of the present invention, the model returns both a primary prediction based on the spectrum (e.g., the value of the species content) and a secondary output about a task related to the prediction, so a multi-output system is required. These secondary predictions are then used to measure the confidence of the primary prediction. In other words, unlike conventional quantitative methods that only predict the primary output (e.g., the content of the species of interest), the present invention aims to simultaneously predict quantities that can be directly verified in experimental data (i.e., present in the experimental data both during the learning period and during the inference phase), so that the reliability of the predicted content can be ensured.

[0003] One possible application of the invention relates to the determination of the content of chemical elements and the reliability indicator of the prediction based on spectral data, wherein the spectral data are acquired, for example, with the aid of the LIBS technique, which stands for laser-induced breakdown spectroscopy. The invention is not limited to this particular technique - it can be applied to any type of spectroscopic technique that produces multispectral data or hyperspectral data or spectral data on the emission or absorption of chemical species.

[0004] Specifically, the LIBS technique allows the analysis of materials by focusing a laser beam on the surface of a sample. The emission of the plasma generated by the focusing is collected by a spectrometer. The data acquired by this method are spectral data, which, for each focus on the surface, corresponds to an emission spectrum including atomic and molecular lines, which are characteristics of the basic chemical composition of the sample. The intensity of these lines increases rather than simply increases with the content of the chemical elements present in the sample. Calibration is performed using multiple standards (i.e., samples whose content of species is known in advance) to obtain a model that allows spectral features to be related to the content of the species. Then, the model can be used to predict the unknown content of the species based on the spectrum. Once the model has been defined, there are methods that allow the definition of the measurement of uncertainty (e.g., confidence intervals) in the predictions made by the model. However, the nature of evaluating uncertainty in the inference stage is complex: it may be impossible or very difficult to determine whether the uncertainty is completely related to statistical fluctuations, or whether the standard used to define the quantitative model actually represents the sample to be measured. In addition, in the absence of a specific weighting of the data, the calibration is characterized by a relative uncertainty that increases with the decrease of the species content in the standard (until the detection limit). In fact, a level of 100% relative uncertainty is sometimes used as the definition of the detection limit. In general, the limitations of the LIBS technique are typical for any spectroscopic technique: verification of the reliability of the predictions is always problematic and, by definition, relative uncertainties close to the detection limit are high.

[0005] The present invention aims to overcome these limitations by proposing the use of:

[0006] A multivariate, multi-output quantitative model for obtaining both predictions of species content and values ​​that can be used to determine confidence therein. To this end, the present invention introduces a technique for validating the predictions of the quantitative model and for establishing a measure of confidence in the predictions or for identifying the presence of anomalies (i.e., predictions that do not have a good confidence level).

[0007] • Multivariate analysis models allow to reduce the uncertainty in species content determinations in order to obtain more reliable and accurate measurements in the context of the present invention.

[0008] The present invention aims to solve the problems associated with determining species content based on spectral data, which can be generated by LIBS or other spectroscopic methods (e.g., multispectral or hyperspectral imaging). Typically, this type of data is characterized by spectra specific to the species present in the sample. Quantitative analysis of the spectral features (e.g., using the intensity of the emission or absorption lines of chemical elements) ultimately allows the determination of the species content. In this context, several problems may arise.

[0009] Conventional calibration methods provide predictions of the abundance of species in a sample. Since the model is defined using known standards, it is not possible to verify that the standards used to define the model represent the samples to be measured, even though this is necessarily an underlying assumption used by the model. In other words, it is not possible to verify that the samples to be measured lie outside the learned distribution, and therefore it is not possible to verify the generalization of the learned model. For example, the experimental conditions of the measurements made using the model may not correspond to the experimental conditions used when training the model, as various uncontrolled external variables related to the instrumentation, environmental conditions, or the samples themselves may alter these experimental conditions.

[0010] However, trained models make predictions based on measurements without verifying that the data used to train the model actually represents real data. Therefore, there is a need for a tool that can verify the reliability of predictions when the conditions under which the model is used differ slightly from those under which it was learned, or conversely, that the conditions under which the model is used have not changed.

[0011] Currently, quantification of chemical species based on spectral data is achieved using various univariate methods (which only partially consider the information contained in the spectrum) or multivariate methods (which utilize all or nearly all of the content of the spectrum). An example of such a method is given in reference [1]. Of all the variables available in the spectrum (wavelength channels or spectral bands), the univariate method uses the information contained in one spectral band or one variable (usually the intensity of an emission line at a given wavelength (or the sum of the intensities of adjacent channels)) associated with the species desired to be analyzed. This information can then be used to obtain a calibration function (e.g., a straight line) that relates the content of the species in question to the signal intensity for each of the standards, for which the content of the species is known. Mathematically, this process defines a relationship between content and spectral intensity. The calibration function can then be used to obtain a prediction of the content of the species in an unknown sample by inverting this relationship and, for example, by means of interpolation (e.g., as described in reference [2]).

[0012] Other multivariate methods have also been investigated, in particular those using algorithms based on principal component analysis and multivariate linear regression (see Ref. [3]). Neural networks have been employed in the context of LIBS (described in [4]), either based on the use of the intensities of specific lines selected in advance (as proposed in [5]), or on coupling principal component analysis and neural networks to achieve multi-output regression (as proposed in [6]), or on the use of the information contained in the time-resolved spectra (as proposed in [7]). The result of the analysis is always a prediction of the content of a species (or species in [6]) that depends on multiple variables (hence the expression "multivariate analysis").

[0013] In recent years, deep learning techniques (given their high ability to extrapolate) have become relevant for sample classification (see, e.g., [8], [9]): these analyses use high-performance algorithms (e.g., convolutional neural networks) to predict the class of chemical species contained in a sample. Although such architectures achieve good classification results, the models do not allow for a direct establishment of the confidence level of the predictions. As emphasized by the authors of references

[10] and

[11] , conventional metrics such as the mean squared error can be very misleading, depending on the content level: the authors therefore suggest using different metrics for each subgroup of the data in order to better assess the performance of the model. Other approaches have been proposed to verify the robustness of the models, e.g., randomization of the model reference values ​​in

[12] : the authors describe a technique that makes it possible to test whether a given prediction of a model was obtained by chance.

[0014] Typically, known analyses focus on predicting a single variable (content) based on input data of different dimensions ([5], [7]). However, some studies have adopted multi-output models, for example, in

[13] the PLS2 technique was used to simultaneously predict the contents of multiple chemical elements. The first example of multi-output regression using neural networks was described in [6]. These multi-output algorithms are used to obtain more information (in particular the contents of multiple elements instead of just one element) simultaneously using the same input data.

[0015] However, the prior art fails to determine an indicator of the reliability of the content predictions provided by the various proposed learning models.

[0016] Unlike prior art solutions, the present invention relates to the validation of predictions, not to the validation of models. The present invention relates to a technique that allows to use information available at any time (even in unknown data) to obtain a measure of confidence in the predictions, and thus compare them directly with the ground truth. In the present invention, this is achieved by using multi-output models, in particular by using deep learning architectures that are able to efficiently process the information contained in the data.

[0017] The present invention relates to a method for validating predictions based on a multi-output model. In other words, the secondary outputs are experimentally measurable in order to allow the assessment of the relevance of the primary outputs that were assumed to be unknown in the inference phase.

[0018] The proposed invention includes additional steps with respect to prior art methods. A multi-output algorithm is used to predict secondary outputs that are verifiable in experimental data so that a certain degree of confidence in the prediction can be ensured. This is not possible when only predicting the content (or multiple contents) of a chemical species.

[0019] The present invention provides the use of an algorithm that is not only trained to predict the content of a species based on spectral data, but is also trained to provide secondary outputs that predict additional quantities, such as the emission or absorption intensity of one or more spectral lines or spectral bands characteristic of the analyzed species. These additional data must be experimentally measurable and verifiable during inference. In addition, the prediction of these values ​​must be sufficiently complex for the model compared to the main prediction. In other words, the prediction must take into account a non-simple task (whose complexity is comparable to that of the main prediction) and be based on the input data to avoid imbalances during the learning process. For example, the intensity of a spectral line or spectral band integrated over adjacent wavelength channels can be used. In contrast, it is not recommended to use only the intensity of a line in the spectrum, as this is a simple task to be solved (it is a single component of the input data). This type of information makes it possible to obtain additional information that may be related to the real data during the inference phase (hence the use of a multi-output algorithm).

[0020] The invention makes it possible to provide an indicator of the reliability of the prediction for any content prediction, thereby allowing, for example, to discard certain measurements which are affected by uncontrolled variables, making the prediction provided by the model based on these measurements unreliable.

[0021] A subject of the present invention is a computer-implemented machine learning method for learning a multi-output prediction model, which is configured to jointly determine the following based on a characteristic spectral dataset of the sample: at least one primary prediction of at least one first physical quantity characterizing a given species in the sample; and at least one secondary prediction of at least one second physical quantity characterizing the species, the multi-output prediction model being trained using an annotated spectral dataset.

[0022] According to a specific aspect of the invention, the multi-output prediction model is a multi-task neural network and is implemented with the aid of a first common learning engine configured to extract a common representation of various tasks to be solved from a spectral data set received as input, and a plurality of learning engines specific to each task to be solved, wherein each of the plurality of learning engines receives the common representation as input and provides a prediction corresponding to the task to be solved as output.

[0023] According to a particular aspect of the invention, the common learning engine is a convolutional neural network, and the specific neural network is a convolutional neural network supplemented by a fully connected neural layer.

[0024] According to a particular aspect of the invention, the species is a chemical species, the primary prediction is a value of the content of the chemical species, and the secondary prediction is an intensity value of a spectral line for at least one given wavelength or at least one wavelength band with a given width.

[0025] Another subject of the invention is a computer-implemented prediction model obtained using the machine learning method according to the invention.

[0026] The present invention also relates to a computer-implemented quantitative analysis method for quantitatively analyzing spectral data, comprising: implementing a prediction model according to the present invention to determine the following based on a spectrum measured on a sample: at least one primary prediction of at least one first physical quantity characterizing a given species in the sample; and at least one secondary prediction of at least one second physical quantity characterizing the species, the method also comprising: a step of calculating a reliability index of at least one primary prediction based on an index of the difference between at least one secondary prediction and the value of the corresponding second physical quantity measured on the spectrum.

[0027] According to one particular aspect of the invention, the reliability indicator is equal to the relative error between the intensity values ​​predicted via implementation of the prediction model and the corresponding intensity values ​​measured on the spectrum.

[0028] According to one particular aspect of the invention, the reliability indicator is equal to the absolute value of the difference between the intensity value predicted via implementation of the prediction model and the corresponding intensity value measured on the spectrum divided by the standard deviation of this difference.

[0029] In a variation of the embodiment, the quantitative analysis method according to the present invention further includes: implementing a classification model configured to classify predictions about the content of chemical species into two categories corresponding to normal values ​​and abnormalities based on predictions of spectral line intensity values ​​or based on reliability indicators.

[0030] According to a particular aspect of the invention, the measured spectrum is acquired by means of the LIBS method, LIBS standing for Laser Induced Breakdown Spectroscopy.

[0031] The present invention also relates to a computer program, comprising instructions, which, when executed by a processor, are used to execute the method according to the present invention, and the present invention also relates to a processor-readable recording medium having a program recorded thereon, the program comprising instructions, which, when executed by a processor, are used to execute the method according to the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Other features and advantages of the present invention will become more apparent from the following description read in conjunction with the following drawings.

[0033] [ Figure 1 ] shows an example of spectral data characterizing a sample containing various chemical species,

[0034] [ Figure 2 ] shows a schematic diagram illustrating the learning and use of a multi-output prediction model according to the present invention,

[0035] [ Figure 3 ] shows a schematic diagram of an example of implementing a prediction model according to the present invention by means of one or more convolutional neural networks,

[0036] [ Figure 4 ] shows an example of a table of results of learning and analysis of secondary outputs. DETAILED DESCRIPTION

[0037] In the following, a description of the invention is given in the context of using the LIBS technique, but the invention is not limited to this technique and is more generally applicable to any type of spectral data, whether multispectral or hyperspectral.

[0038] The LIBS technique allows the analysis of materials by laser ablation and spectroscopy. The data acquired by this technique are spectral data which, for each point in the area, correspond to an emission spectrum consisting of atomic and molecular lines that are characteristic of the basic chemical composition of the sample.

[0039] LIBS spectral data is obtained by focusing a laser beam on a point on the surface to be analyzed. The emission of the plasma generated by this focusing is collected and processed by spectroscopy to obtain the emission spectrum of atomic lines (or molecular bands). This process is iterated for each point in the area to be analyzed.

[0040] Figure 1 An example of a spectrum of atomic lines 101 obtained for a sample having a specific chemical composition is shown by way of illustration. Figure 1 In , the spectral signatures of specific chemical elements (Ca, Al) corresponding to atomic lines in a given wavelength channel have been identified.

[0041] One object of the present invention is to determine a prediction model that can be based on e.g. Figure 1 Automatic analysis of the spectra to estimate the content of chemical elements and also to provide an indication of the reliability of the provided estimate.

[0042] Figure 2 A method for learning and using a prediction model according to the present invention is shown schematically.

[0043] The method consists in determining, in a learning phase, a prediction model 231 configured to determine, based on a spectrum measured on a given sample, on the one hand, the content of one or more chemical species and, on the other hand, to determine a prediction of the intensity of one or more atomic lines (or molecular bands) in the spectrum.

[0044] The method then consists in using the trained model in a use phase to determine these predictions for newly measured spectral data.A secondary output of the model is used to determine a reliability indicator for the predictions.

[0045] More precisely, in the learning phase, the method uses as input spectral input data 210 in the form of sets of spectra obtained by LIBS to characterize a given sample. The spectral data 210 are labeled, i.e., in the case of quantitative analysis, for example, the content of the various chemical elements to be quantified in the sample is known.

[0046] In other words, the input data 210 is a set of pairs, each pair relating a spectrum to the content of one or more chemical elements in a sample of a given type. The sample is characterized, for example, by the type of material and the content of a particular chemical element in the material.

[0047] The input data 210 is divided into a first training data subset 221 and a second evaluation data subset 222. The model 231 is trained using the training data 221 and then optimized on the evaluation data 222 in an optimization cycle 232 to determine the best hyperparameters for the model 231.

[0048] To maximize the architecture learning capability, the choice of the percentage of realizations used for learning 221 may depend on the computational medium and the data type. For example, for a data set containing 100,000 realizations, typically 80% may be used for learning, but for data sets with millions of realizations, the percentage may be increased unless the computational medium does not allow. The training data 221 is used to directly compute the model parameters, while the evaluation data 222 is used to evaluate the predictions and optimize the model 231.

[0049] The prediction model 231 is a multivariate multi-output statistical model that receives the entire spectrum as input via input data and is trained to predict, on the one hand, a first set of primary outputs 251 corresponding to one or more predictions of the content of one or more chemical species, and, on the other hand, a second set of secondary outputs 252 corresponding to one or more predictions of the intensity values ​​of atomic lines within a specific wavelength range.

[0050] Once the model 231 has been trained, it can be applied to a new spectral data set 240. A first set of predictions 251 is used to determine the content of chemical species in the sample on which the input spectrum 240 was measured. A second set of predictions 252 is processed to determine a measure of confidence in the first predictions 251.

[0051] The confidence measure is based on an interpretation in terms of the probability (e.g., the probability distribution using a given estimator, as shown below) or relative error of the predictions of the secondary outputs 252 of the model 231. These outputs must predict quantities present in the unknown real data 240 that are relevant to the prediction of species content, such that a comparison between the true and predicted values ​​allows the reliability of learning and prediction to be quantified. Since the secondary outputs 252 are trained using the same representation of the input data 210, the secondary predictions 252 are related to the predictions 251 of species content and share at least a subset of the model's weights (so-called hard parameter sharing). Therefore, it can be assumed that reliable secondary output results can lead to equally reliable content predictions, i.e., the generalization ability of the model to the primary and secondary outputs is comparable.

[0052] The input data 210 for training the model represents a sample of standards for defining the model: multiple spectra can represent the same standard. These data can be preprocessed to reduce experimental fluctuations in spectral intensity values. For example, in one embodiment of the present invention, each spectrum can be normalized by the intensity of a given line or band, or preprocessed using the SNV method (SNV stands for standard normal variate) or any other preprocessing method. In another embodiment, for each standard, the average spectral intensity value of the spectrum at a given wavelength can be used to determine the outlier. For example, before defining the model, spectra whose intensity values ​​are outside any interval (e.g., outside the fifth percentile and the ninety-fifth percentile, or outside the first percentile and the ninety-ninth percentile) at a given wavelength can be rejected. The interval depends on the measurement conditions and the number of realizations of each standard: if the number is high, a larger interval (e.g., the first percentile and the ninety-ninth percentile) can be selected. In another embodiment, these two types of preprocessing can be combined. The real data 240 used during the use phase of the model absolutely must be preprocessed in the same way as the input data, but outliers can be kept in the unknown real data 240. In particular, if the trained model is able to generalize to a high degree, outliers will be correctly handled during the inference phase. The goal is to learn to perform the prediction task based on a reliable representation of the standard: a good model must be able to extrapolate the necessary information to the case where the sample contains defects.

[0053] Evaluation of the model using evaluation data 222 can be accomplished directly using each spectrum as input data. The predicted average can then be calculated and the differences can be correlated to the predictions in order to better assess the performance of the algorithm (and to train the algorithm in more complex situations where noise may produce significant differences between spectra (even those obtained from the same standard)).

[0054] In one embodiment of the present invention, in order to reduce the influence of noise during the inference phase, the average spectrum of the real data 240 may be pre-calculated and used as input data to represent the sample.

[0055] In one embodiment of the invention, the primary output 251 consists of the content of the chemical species analyzed. The secondary output 252 of the model contains the intensity of the emission (or absorption) line (or molecular band) associated with the same chemical species in the case of spectral data, or the intensity measured in the spectral band in the case of multispectral or hyperspectral data. In the context of univariate models, the intensity of the spectral line or spectral band is used for the prediction of the content. Therefore, the decision to include these two elements in the secondary output of the model makes it possible to obtain a secondary prediction corresponding to a physical quantity related to the content of the chemical species.

[0056] In one embodiment of the present invention, the quantitative analysis method includes the step of calculating a reliability index of the primary output of the model based on the secondary output of the model. For example, the reliability index corresponds to a measure of the difference between the predicted intensity output from the model and the true intensity directly measured on the input data 240. For example, the formula t=|I predicted -I real | / σ to calculate the Student's t value of the difference between two values, where I predicted is the average intensity 252 of the sample predicted by the model 231, I real is the true mean intensity measured on the input data 240, and σ is the standard deviation of the difference (i.e., the square root of the sum of the squares of the differences between the predicted and true intensities). Finally, a normal confidence level (e.g., 95% or 99%) can be chosen in the statistical analysis to define the threshold t depending on the number of realizations per sample (degrees of freedom). limit If the prediction I predicted Leading to the value t>t limit , it can be inferred from this that the prediction 251 of the content is biased, which allows the prediction to be rejected on the basis of an interpretation in terms of probability (i.e., the hypothesis that the difference between the prediction and the actual value is only due to statistical fluctuations is rejected). predicted Leading to the value t≤t limit , then the available evidence does not allow prediction 251 to be rejected, so the content prediction associated with the intensity prediction can be determined by t limit The quantitative confidence level was accepted.

[0057] Alternatively, the relative error between the true value of the intensity and its predicted value can be expressed as r = |I predicted -I real | / I realA simple threshold is used: there is no need to reject values ​​below the chosen value, since their distance to the true value is mainly due to statistical fluctuations. This estimator is independent of the standard deviation of the emission intensities and can be used as a first statistical test, applied directly to the intensity values: if the prediction does not pass this test, it can be rejected without risk, because the error is too large. The (Student's) t-test can then be used as an improvement of the procedure, since it also depends on the variance of the data.

[0058] Thus, the present invention provides a method based on a multi-output machine learning algorithm that allows the use of information that is explicitly contained in the experimental data (the intensities of the emission lines of the spectrum) (and is therefore verifiable (by direct measurement of the spectrum)) to obtain an interpretation of the content predictions in terms of probability. Thus, the present invention provides a method for quantitatively characterizing the confidence of these predictions based on errors in secondary outputs. In particular, these predictions absolutely must have elements in common with verifiable elements in the real data 240 in order to allow comparison. Statistical tests can then be used to reject (or not reject) the results.

[0059] In one embodiment of the invention, since the characterization of the confidence of the prediction is quantitative, the results of the secondary prediction or statistical test can be combined with a classification algorithm to determine anomalies in the sample being analyzed. In other words, the difference between the predicted and actual values ​​of the secondary output can be used as input data for a classification algorithm that is trained to identify normal values ​​and anomalies in manufacturing, composition, or measurement. In another embodiment, an arbitrary threshold value based on the t-value or relative error calculated based on the prediction can be used directly to determine whether an anomaly is present.

[0060] In one embodiment of the present invention, the prediction model 231 can be, for example, a multilinear model (e.g., the PLS2 model described in reference

[13] ) or a decision tree (or its ensemble learning variants, such as random forests or gradient boosting) or a support vector machine. The basis of the model is the ability to use a common representation of the input data to simultaneously obtain multiple output predictions using the same set of parameters that define the model, i.e., the function The composition of is approximated, where and N is the dimensionality of the spectra, L is the dimensionality of the common representation, and M is the number of predictions output from the model, such that M ≥ 2. In this way, the model first computes a new representation of the input data (spectra), which can then be used to generate predictions.

[0061] Typically, in order to train a model 231, a learning function (or loss function) needs to be defined for the output i of the model ( and are the true and predicted values ​​of output i): This makes it possible to define the goal of training and measure the difference between the predicted and true values ​​(in supervised learning, the true values ​​are known during learning). Therefore, there are loss functions that are typically dedicated to regression learning, which are different from the loss functions typically used for classification tasks. In various embodiments of the present invention, a mean squared error function or a mean absolute error function can be used. In another embodiment of the present invention, these functions can be combined into a so-called Huber loss function, as described in reference

[14] and defined as follows:

[0062]

[0063] where δ forms part of the hyperparameters to be optimized in the optimization loop 232 of the model, and Θ is the Heaviside step function which takes the value 1 for all strictly positive real numbers and 0 for strictly negative real numbers. This function allows outliers in the data set to be directly accounted for.

[0064] Once a loss function has been chosen for the model's output i The overall loss function of the model is then defined as a linear combination of the loss functions specific to each output: Where N is the number of outputs of the model, is the set of true values ​​specific to each output, is the set of predictions of the model's output, and is the coefficient set of the linear combination of the loss function. i are the hyperparameters of model 231.

[0065] In another embodiment of the present invention, the model 231 is implemented with the aid of one or more neural networks. An example of the architecture of the model 231 has been described in Figure 3 Shown in.

[0066] In one embodiment, the constituent neural networks of the model 231 are convolutional neural networks. The convolutional neural network is implemented by a set of convolutions performed with vectors extending in the direction of the wavelength channels of the spectrum. The input data is scanned using multiple convolution filters to obtain both the primary prediction 251 and the secondary prediction 252 from the multi-output model.

[0067] These neural networks can be deep, with multiple hidden layers, and connect convolution and activation operations with their trainable weights. The contribution of this type of algorithm is the direct use of the information contained in the spectrum: by using convolution operations, the relationship between adjacent wavelength channels can be maintained and the physical information contained in the profile of the spectral line (or spectral band), such as emission or absorption intensity and profile width, can be used. More generally, other types of neural network architectures can also be used, such as fully connected neural networks (based on multilayer perceptrons as described in

[16] for example) or graph neural networks as described in

[17] for example: a sufficient condition for the invention is the ability to form multi-output architectures, so there is no specific restriction on the type of neural network.

[0068] exist Figure 3 In the example of , multi-task networks have been shown (as described in Ref.

[20] ). The difference between multi-task networks and multi-output networks is related to the processing of the representation of the data in the hidden layers: multi-output networks use a common representation without subsequent transformation, but multi-task networks make it possible to use a common representation and then use branches dedicated to specific tasks. In this sense, multi-task networks are multi-output networks, but not vice versa. The use of multi-task architectures makes it possible to solve many problems related to overfitting of the training data and to limit the influence of outliers on the predictions (for example, as described in Ref.

[18] ).

[0069] The algorithm used can be based on a multi-task deep convolutional neural network. This enables the model to directly analyze the spectra by formulating a new common representation of the data and predict with high accuracy the content of the species of interest or, for example, the intensity of the spectral emissions associated with the species. These predictions can then be explained by a probabilistic model by examining the differences between the predicted and true values.

[0070] The input data 310 of the model has been described: it is a spectrum acquired using a spectroscopic technique and optionally preprocessed. The first block 320 of the model has been represented by a neural network comprising a one-dimensional convolutional layer. This first block has the task of learning a common representation of the spectra using the same set of weights and parameters (so-called hard parameter sharing). Several examples of embodiments of multi-task neural networks are given in reference

[19] . The purpose of this first block is to transform the input data into a representation that can provide predictions for all tasks simultaneously.

[0071] The output / task of the model 341-343, which consists of the content of the species analyzed and the value used to determine the confidence level, is calculated using other specific convolutional networks 331-333: each network makes it possible to calculate subsequent transformations based on a common representation and obtain a specific result. For example, the model calculates a secondary output (the intensity of the lines present in the spectrum) starting from this common representation and then processes it in a specific branch. Therefore, the model does not simply "read" the intensity in the spectrum, but must first find an appropriate representation of the input data and then process this information. This type of network is a non-negligible improvement over conventional networks.

[0072] The convolutional neural networks 331-333 take as input the vector of common features extracted from the input data via the first neural network 320 and produce as output a prediction in scalar form. To this end, each convolutional neural network 331-333 includes a final layer that is fully connected to the output.

[0073] Figure 3 An example of a possible architecture for a multi-task model is defined as follows:

[0074] A first neural network 320 formed by three convolutional layers, respectively having:

[0075] i.64, 40 and 16 filters,

[0076] ii. Kernel size: 5, 3, and 2 wavelength channels,

[0077] iii. Spacing: 3, 2 and 1 wavelength channels,

[0078] - Neural networks 331-333 for solving specific tasks, having the same hyperparameters as the first neural network 320 and supplemented by two fully connected layers of 16 neurons and 1 neuron respectively (each network 331-333 predicts a real number).

[0079] The activation function after each hidden layer is, for example, of the LeakyReLU type (with a slope of 0.03). For example, the learning rate is set to 10 -3 .

[0080] Figure 4A table is shown which collates the calibration results of the iron (Fe) content in a nickel (Ni) matrix and a zirconium (Zr) matrix. 25 laser shots were recorded for each sample, and each spectrum was formed from 68,000 wavelength channels. The secondary output is the intensity value of the Fe emission line at 373.49nm, 358.12nm, 373.71nm, 374.56nm, 382.04nm, 385.99nm, 404.58nm and 438.35nm. Only the spectrum of the Ni standard (the result obtained in an independent set of tests) is studied. As shown in the table, a multivariate architecture (MVA) based on multi-task learning can provide more accurate predictions than the classical univariate method (UVA) on a matrix having the same properties as the matrix used for learning purposes. The multi-task architecture can also be used to measure the confidence level of the intensity predicted for the emission line (in this case, t limit =t α,v =2.485, where the confidence level is α=0.99 and the degrees of freedom are ν=25) to provide a measure of the reliability of the predictions obtained for the Ni matrix. The table also shows the ability to generalize to a Zr matrix, which has different properties from the training samples: the neural network is able to significantly reduce the error in the extrapolation mechanism. However, the multi-task architecture allows measuring the reliability of the predictions: the relative errors in the intensity (and value t) of the emission lines in the Zr sample are indeed very high. In this case, the Zr matrix is ​​identified as an anomaly relative to the training distribution.

[0081] The present invention makes it possible to quantify the confidence of the predicted content using a set of predicted probability models based on a multi-output model. The model is able to predict species content and other quantities (e.g., the intensity of emission lines of chemical species). This makes it possible to determine unknown quantities (e.g., species content) and secondary quantities that can be directly verified in the spectrum and used to determine the confidence level in quantitative analysis.

[0082] The invention makes it possible to reduce uncertainties by using a high-performance algorithm capable of directly and fully automatically processing the spectral signatures of the species contained in the entire spectrum.

[0083] The steps of the present invention can be implemented by a computer program including instructions for executing the computer program. The computer program can be recorded on a processor-readable recording medium.

[0084] References to computer programs that implement any of the above functions when executed are not limited to applications running on a single host computer. Instead, the terms computer program and software are used here in a general sense to refer to any type of computer code (e.g., application software, firmware, microcode, or any other form of computer instructions) that can be used to program one or more processors to implement aspects of the technology described herein. Computing devices or resources can be distributed (cloud computing) in particular, possibly via peer-to-peer technology. Software code can be executed on any suitable processor (e.g., microprocessor) or processor core or processor set, whether it is provided in a single computing device or distributed between multiple computing devices (e.g., potentially accessible in the environment of the device). The executable code of each program that allows a programmable device to implement a process according to the present invention can be stored in, for example, a hard disk or a read-only memory. Typically, one or more programs can be loaded into one of the storage devices of the device before being executed. The central processing unit is capable of controlling and directing the execution of instructions or software code segments of one or more programs according to the present invention, which are stored in a hard disk or a read-only memory or other storage elements described above.

[0085] References

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Claims

1. A computer-implemented machine learning method for learning a multi-output prediction model (231), the multi-output prediction model (231) being configured to: jointly determine the following based on a characteristic spectral dataset of a sample: at least one primary prediction (251) of at least one first physical quantity characterizing a given species in the sample; and at least one secondary prediction (252) of at least one second physical quantity characterizing the species, the multi-output prediction model being trained using an annotated spectral dataset (210).

2. The machine learning method according to claim 1, wherein: The multi-output prediction model is a multi-task neural network and is implemented with the aid of a first common learning engine (320) and multiple learning engines (331, 332, 333), wherein the first common learning engine (320) is configured to extract a common representation of various tasks to be solved from a spectral data set received as input, and the multiple learning engines (331, 332, 333) are specific to each task to be solved, wherein each of the multiple learning engines (331, 332, 333) receives the common representation as input and provides a prediction (341, 342, 343) corresponding to the task to be solved as output.

3. The machine learning method according to claim 2, wherein: The common learning engine (320) is a convolutional neural network, and the specific neural networks (331, 332, 333) are convolutional neural networks supplemented by fully connected neural layers.

4. A machine learning method according to any one of the preceding claims, wherein: The species is a chemical species, the primary prediction is a value of the content of the chemical species, and the secondary prediction is an intensity value of a spectral line for at least one given wavelength or at least one wavelength band with a given width.

5. A computer-implemented quantitative analysis method for quantitatively analyzing spectral data, comprising: Implementing a prediction model (231) trained by means of a machine learning method as claimed in any of the preceding claims to determine, based on a spectrum (240) measured on a sample: at least one principal prediction (251) of at least one first physical quantity characterizing a given species in said sample; and at least one secondary prediction (252) of at least one second physical quantity characterizing the species, the method further comprising: a step of calculating a reliability indicator of the at least one primary prediction based on an indicator of the difference between the at least one secondary prediction and the value of the corresponding second physical quantity measured on the spectrum.

6. The quantitative analysis method according to claim 5, wherein: The reliability indicator is equal to the relative error between the intensity values ​​predicted via implementation of the prediction model and the corresponding intensity values ​​measured on the spectrum.

7. The quantitative analysis method according to claim 5, wherein: The reliability indicator is equal to the absolute value of the difference between the intensity values ​​predicted via implementation of the prediction model and the corresponding intensity values ​​measured on the spectrum divided by the standard deviation of this difference.

8. The quantitative analysis method according to any one of claims 5 to 7, further comprising: A classification model is implemented, the classification model being configured to classify predictions about the content of chemical species into two categories corresponding to normal values ​​and abnormalities based on the predictions of the spectral line intensity values ​​or based on a reliability indicator.

9. The quantitative analysis method according to any one of claims 5 to 8, wherein: The measured spectra were acquired with the aid of the LIBS method, which stands for Laser Induced Breakdown Spectroscopy.

10. A computer program comprising instructions for performing a method according to any one of the preceding claims when the program is executed by a processor.

11. A processor-readable recording medium having a program recorded thereon, the program comprising instructions for executing the method according to any one of claims 1 to 9 when the program is executed by a processor.

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