Method of performing machine learning of small angle x-ray scatterometry data analysis model

Abstract

The invention relates to a computer-implemented method of generating (E1, E2) a training dataset (41, 42) and performing machine learning of a first small angle X-ray scattering SAXS measurement data analysis model (DAM) using (E3, E31, E32) the training dataset, where generating the training dataset comprises the steps of:-calculating (E1) a 1D SAXS intensity distribution,-calculating (E2) the 1D SAXS intensity distribution, and-calculating (E3) the 1D SAXS intensity distribution; each intensity distribution corresponds to a variable parameter of at least one structural model of the sample in the medium; and-estimating (E2) a first experimental 1D SAXS intensity distribution from each of the calculated 1D SAXS intensity distributions based on a first set of SAXS measurement experiment settings comprising a first X-ray beam intensity distribution at the 2D detector. The estimating includes smearing each of the calculated 1D SAXS intensity distributions by a convolution of a point spread function associated with the first X-ray beam intensity distribution.

Description

Technical Field

[0001] The field of the invention is the field of material nanostructure analysis using Small Angle X-ray Scattering (SAXS). The invention more specifically relates to the training and inference of SAXS measurement data analysis models based on machine learning. Background Art

[0002] Small-angle X-ray scattering (SAXS) is a powerful analytical technique for studying the structure of bulk, disordered samples such as nanoparticles and colloids, nanocomposites, polymers in solution, and biomaterials.

[0003] SAXS measures the intensity of X-rays scattered by a sample as a function of the scattering angle. Figure 1 shows how SAXS works. In a typical experiment, a beam 1 of highly collimated monochromatic x-rays is transmitted through a sample 2 of approximately 1 mm thickness. The scattered x-rays are collected on a 2-dimensional area detector 3 with an azimuthal intensity profile that deviates from the scattering angle of the direct transmitted beam. The scattering angle, which is conventionally defined as 2θ, defines the "probe length", which is expressed as D = 2π / q, where q = 4πsin(θ) / λ, where λ is the wavelength of the x-rays (typically 0.154nm for a Cu x-ray source). Measurements are made at very small angles, typically in the range of 0.1 to 10 degrees, and sample parameters can be determined from analysis of the sample scattered intensity profile as a function of angle.

[0004] Materials scientists are accustomed to processing SAXS measurement data by fitting a theoretical scattering model associated with the nanostructure in the medium (in the case of dispersions, the medium is a solvent solution, or in the case of powders it can be air) to the experimental scattering curve. The difficulty in SAXS analysis lies in the fact that a large range of scattering models have been developed to describe various form factors (associated with the shape of the particles) or combinations of form factors, potentially combined with structure factors to describe sample interactions. Furthermore, different models (and / or associated structural parameters) may fit the experimental data equally well. The number of possible models and the fact that SAXS data are poorly characterized curves makes the selection of an appropriate model complicated for the user.

[0005] In this context, machine learning (ML) methods have recently been used to assist users in selecting the best model for analyzing SAXS data. For example, a trained ML classification algorithm can automatically provide the compatibility probability of experimental SAXS measurement data with each model from a large set of theoretical scattering models. Summary of the invention

[0006] The object of the present invention is to provide a SAXS analysis assisted ML method with improved accuracy. To this end, the present invention relates to a computer-implemented method of generating a training data set and using the training data set to perform machine learning of a first small angle X-ray scattering SAXS measurement data analysis model. Generating the training data set comprises the following steps:

[0007] - calculating 1D SAXS intensity profiles, each 1D SAXS intensity profile corresponding to a variation of a parameter of at least one structural model of the sample in the medium; and

[0008] - estimating a first experimental 1D SAXS intensity profile from each of the calculated 1D SAXS intensity profiles based on a first set of SAXS measurement experimental setups comprising a first X-ray beam intensity profile at the 2D detector.

[0009] More specifically, the estimating comprises smearing each of the calculated 1D SAXS intensity distributions by convolution with a point spread function associated with the first X-ray beam intensity distribution.

[0010] Certain preferred but non-limiting aspects of this method are as follows:

[0011] - the first set of SAXS measurement experimental settings also includes a signal-to-noise ratio setting, the signal-to-noise ratio setting including a size of the 2D detector and a beam position on the 2D detector, and the estimating further includes adding noise to each of the calculated SAXS intensity distributions based on the signal-to-noise ratio setting;

[0012] - it also comprises determining experimental 1D SAXS intensity profiles of the blank solution based on the first set of SAXS measurement experimental setups and based on theoretical 1D SAXS intensity profiles of the blank solution, and subtracting the experimental 1D SAXS intensity profiles of the blank solution from each of the experimental 1D SAXS intensity profiles;

[0013] - calculating the 1DSAXS intensity distribution corresponding to a parameter of a variation of at least one structural model of the sample in the medium is performed for a plurality of structural models, and the first SAXS measurement data analysis model is a structural model classifier trained to predict compatibility of the experimental SAXS measurement data with each of the plurality of structural models;

[0014] - calculating the 1DSAXS intensity distribution corresponding to the varying parameters of at least one structural model of the sample in the medium is performed for a single structural model, and the first SAXS measurement data analysis model is a regression model trained to predict the value of at least one of the varying parameters based on experimental SAXS measurement data;

[0015] - generating the training data set also includes the steps of normalizing, transforming to a logarithmic scale and standardizing the determined experimental SAXS intensity distribution;

[0016] - The first set of SAXS measurement experimental settings also includes the detector pixel size and the sample-to-detector distance;

[0017] - The first set of SAXS measurement experimental settings also includes the measurement time;

[0018] - it also includes determining a second experimental 1D SAXS intensity distribution for each of the calculated 1D SAXS intensity distributions based on a second set of SAXS measurement experimental settings, the second set of SAXS measurement experimental settings including a second X-ray beam intensity distribution at the 2D detector, and the first experimental 1D SAXS intensity distribution is used to perform machine learning of a first SAXS measurement data analysis model, and the second experimental 1D SAXS intensity distribution is used to perform machine learning of a second SAXS measurement data analysis model associated with the second set of SAXS measurement experimental settings.

[0019] The present invention also relates to a method for SAXS measurement data analysis, comprising the following steps:

[0020] - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument; and

[0021] - Processing the acquired SAXS data using the first SAXS measurement data analysis model learned according to the present invention.

[0022] The present invention also relates to a method for SAXS measurement data analysis, comprising the following steps:

[0023] - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument;

[0024] - Processing the acquired SAXS data using a structural model classifier trained according to the invention;

[0025] - Select the structural model with the highest compatibility with the experimental SAXS measurement data; and

[0026] - Processing the obtained SAXS data using a regression model trained according to the invention using the selected structural model as the single structural model to determine the value of at least one of the varied parameters.

[0027] It may also include determining parameters of the sample model by fitting the acquired SAXS data to the sample model, the determining being initiated based on the determined values ​​and the selected structural model.

[0028] The present invention also relates to a method for SAXS measurement data analysis, comprising the following steps:

[0029] - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument with a given experimental setup;

[0030] - based on a given experimental setup, selecting the first SAXS measurement data analysis model or the second SAXS measurement data analysis model learned according to the present invention; and

[0031] - Processing the acquired SAXS data using a selected one of a first SAXS measurement data analysis or a second SAXS measurement data analysis.

[0032] The present invention also relates to a method for SAXS measurement data analysis, comprising the following steps:

[0033] - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument with an experimental setup;

[0034] - performing machine learning of a first SAXS measurement data analysis model according to the present invention using the experimental setup; and

[0035] - Processing the acquired SAXS data using the learned first SAXS measurement data analysis model. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Other aspects, objects, advantages and features of the present invention will better emerge on reading the following detailed description of a preferred embodiment thereof, which is provided as a non-limiting example and is made with reference to the accompanying drawings, in which:

[0037] - Already discussed above Figure 1 is a diagram illustrating the principle of SAXS measurement;

[0038] - Figure 2 is a diagram illustrating a possible embodiment of a method of generating a training data set and performing machine learning of a SAXS measurement data analysis model using the training data set according to the present invention;

[0039] - Figure 3is a diagram illustrating possible uses of a trained SAXS measurement data analysis model according to the present invention;

[0040] - Figure 4 is a diagram illustrating a possible in-situ training of a SAXS measurement data analysis model according to the present invention;

[0041] - Figure 5 Theoretical SAXS intensity distribution estimated according to the present invention and the corresponding experimental SAXS intensity distribution are shown. DETAILED DESCRIPTION

[0042] The invention relates to a computer-implemented method of generating a training data set and using the training data set to perform machine learning of a SAXS measurement data analysis model associated with one or several sets of SAXS measurement experimental setups.

[0043] In one embodiment, the SAXS measurement data analysis model is a classification model that is trained to predict compatibility of experimental SAXS measurement data with each of a plurality of structural models.

[0044] In another embodiment, the SAXS measurement data analysis model is a regression model trained to predict the value of at least one parameter of the structural model based on experimental SAXS measurement data.

[0045] The structural model is an analytical shape factor describing a scattering sample (scatterers) with varying parameters in a medium or buffer (typically a solvent in the case of a dispersion, or air in the case of a powder). The varying parameters may include variable geometric parameters describing the size of the structural objects (and possibly also the associated polydispersity). The varying parameters may also include electronic parameters. As is known from the prior art, the structural model may be the product of a shape factor and a structure factor, wherein the structure factor describes the interactions between the scatterers.

[0046] As an example, six structural models may be considered to be each associated with one of the following shape factors: sphere, cylinder, ellipsoid, core-shell sphere, core-shell cylinder, and core-shell ellipsoid. Geometric parameters may include radius, length, shell thickness and polydispersity depending on the object. For example, in the case of core-shell, electronic parameters may include the scattering length density of the sample in solution (obtained as the difference between the scattering length density of the scatterer and the buffer), the scattering length density of the core, and the scattering length density of the shell. The scattering length density defines the scattering power of the sample and can be estimated based on the sample and buffer composition and mass density.

[0047] Reference Figure 2In order to generate a training data set, the method according to the invention comprises a step E1 of calculating 1D SAXS intensity distributions, each 1D SAXS intensity distribution corresponding to a parameter of a change of at least one structural model of the sample in the medium. When training a classification model, this step is performed with a plurality of structural models. When training a regression model, this step is typically performed with a single structural model. The calculated 1D SAXS intensity distributions can be stored in a database 4.

[0048] Each calculated 1D SAXS intensity profile is a theoretical 1D scattering curve associated with a shape factor and associated geometrical and electronic parameters. The calculated 1D SAXS intensity profiles each correspond to a varying parameter of the same structural model, thus forming a set of theoretical 1D scattering curves associated with the same shape factor but with different values ​​of the associated geometrical and electronic parameters. When calculating such theoretical 1D scattering curves associated with the same shape factor, at least one of the associated geometrical and electronic parameters may be affected by random sampling.

[0049] In an exemplary embodiment, 10,000 curves I(q) are calculated for each shape factor, resulting in a total of 60,000 simulated curves. The curves are simulated over a range of q defined by a lower boundary qmin, an upper boundary qmax, and a number of q points. As an example, in the case of a core-shell cylinder, for each simulated curve radius value may be to The length value can be randomly varied between 1 and 30 times the radius, and the shell thickness can be randomly varied between to The size polydispersity (which is expressed as a percentage of the half-maximum width of a Gaussian function centered on the mean) can vary randomly between 0% and 30%. The electronic parameters can be fixed parameters, such as the scattering length density of the solution, the scattering length density of the core, and the scattering length density of the shell, respectively. and

[0050] Still refer to Figure 2 , the method according to the invention further comprises a step E2 of estimating an experimental 1D SAXS intensity distribution from each of the calculated 1D SAXS intensity distributions based on a set of SAXS measurement experimental settings. This step E2 estimates the 1D experimental curves to be obtained using a SAXS laboratory instrument having the settings of this set of SAXS measurement experimental settings. In other words, it simulates the influence of these settings on the SAXS measurement by transforming the 1D theoretical curves into 1D experimental curves. As discussed below, this transformation can model the influence of a given sample property, the influence of an instrument resolution parameter, and the influence of an instrument signal-to-noise ratio parameter.

[0051] According to the present invention, each set of SAXS measurement experimental setups comprises an instrument resolution setting including an X-ray beam intensity distribution at the 2D detector, and estimating the experimental SAXS intensity distribution from each of the calculated SAXS intensity distributions comprises: smearing each of the calculated SAXS intensity distributions by convolution with a point spread function associated with the X-ray beam intensity distribution. In this regard, Figure 5 The calculated SAXS intensity distribution It and its corresponding experimental intensity distribution Ie for smearing according to the present invention are shown.

[0052] In one embodiment, the beam size and distribution are given values ​​based on calculations that take into account the divergence of the direct beam and the size of the collimating slits. In another embodiment, the true direct beam size distribution is used.

[0053] The point spread function can be defined by a smearing parameter describing the beam size distribution at the detector. This parameter can be the FWHM (full width at half maximum) of the intensity beam distribution at the detector estimated from the measurement configuration (estimated from the optical design of the X-ray scattering beamline) or obtained by experimental characterization and Gaussian fitting of the beam distribution at the detector used to determine this smearing parameter (e.g. FWHM). The experimental SAXS intensity distribution is then obtained by applying a finite size convolution kernel (FWHM) to the theoretical intensity distribution obtained by step E1.

[0054] In a preferred embodiment of the invention, the full 1D intensity beam profile at the detector (e.g., with Q values ​​exceeding 9 orders of magnitude) is used to convolve the theoretical intensity profile. In practice, since the beam is not completely Gaussian, approximating it as a Gaussian function may result in poor accuracy of the model. Since the direct beam profile can be determined experimentally, it can be used directly for beam smearing. This has been shown to improve accuracy on real data.

[0055] Instrument resolution settings may also include detector pixel size and / or sample-to-detector distance.

[0056] The set of SAXS measurement experimental settings may also include sample property settings characterizing the scattering ability of the sample, for example selected from the chemical composition of the sample or its scattering length density, the chemical composition of the buffer solution or its scattering length density, the sample thickness and the volume fraction of the sample relative to the solution.

[0057] The set of SAXS measurement experiment settings may also include measurement condition settings such as measurement time.

[0058] The set of SAXS measurement experimental settings may also include a signal-to-noise ratio setting selected, for example, from beam intensity, detector area, and beam position on the detector. In such cases, estimating the experimental curve from the theoretical curve may further include adding noise to each of the calculated SAXS intensity distributions based on the signal-to-noise ratio setting. For example, Poisson statistics may be added to take into account real data in terms of signal-to-noise ratio.

[0059] Unlike other approaches that have been used to train AI (artificial intelligence) models for SAXS applications, the present invention here simulates the scattering data with realistic statistics for a given set of models (form factors) and a given experimental setup, taking into account in particular the effect of the beam profile at the detector on data smearing. While this may have limited impact for synchrotron applications, the applicants have found this to be particularly important for laboratory SAXS applications.

[0060] Furthermore, the influence of the measurement and detection geometry on the signal-to-noise ratio can also be taken into account. Some models apply only simple Poisson statistics based on the sample scattering ability (an intrinsic property due to the electronic contrast of the material with its buffer or air in the case of powders), the beam intensity and the measurement time. Here, in addition to the beam intensity and measurement time and the sample scattering properties, the measurement and detection scheme can also be considered. For example, the detecting surface of the detector affects the number of pixels that collect the signal and are used to azimuthally average the 2D data pattern into a 1D scattering curve. This therefore affects the signal-to-noise ratio of the 1D scattering curve, especially near the edges (Qmax) of the 1D scattering curve.

[0061] In a preferred embodiment, step E2 may also include simulating the scattering distribution of a buffer solution (e.g., a solution in which the material to be characterized (e.g., nanoparticles) is dispersed). Such estimates are based on taking into account the experimental configuration (i.e., the set of experimental settings), e.g., in terms of signal-to-noise ratio and resolution.

[0062] In this embodiment, the method includes estimating an experimental SAXS intensity distribution of a blank solution based on a first set of SAXS measurement experimental settings and based on a theoretical SAXS intensity distribution of a blank solution (i.e., a buffer without the material to be characterized). The experimental SAXS intensity distribution of the blank solution is then subtracted from each of the estimated experimental curves (intensity distribution of the sample dispersed in the solution).

[0063] In a possible embodiment, the impact of the simulated experimental setup takes as input a shape factor model describing the sample (i.e., ideal, theoretical intensity) and the buffer, respectively. At output, it predicts the expected measured intensity and signal-to-noise ratio at each q-value achievable in the experiment. The number of photons scattered by the sample and collected by each pixel of the detector is estimated for both (a) the sample in the buffer and (b) the buffer alone. Pixel-independent noise based on the signal-to-noise ratio setting can be added to each pixel in the (a) and (b) scenes, for example based on a Poisson distribution. The 2D data matrix (pixel values ​​at the detector) is simplified to a 1D vector by averaging equivalent azimuth angles and fully accounting for geometric distortion effects. The results can be normalized with respect to the number of photons scattered in (a) and (b), respectively. The signal of the sample alone can then be obtained by subtracting the previously obtained 1D vector.

[0064] The estimated experimental SAXS intensity distribution forms a training data set. This training data set can be split into a learning data set 41 (with, for example, 80% of the experimental distribution) and a test data set 42 (with, for example, 20% of the experimental distribution). The method then comprises a step E3 of performing machine learning of the SAXS measurement data analysis model DAM using the training data set. This step E3 is divided into a first step E31 of obtaining a model using an AI algorithm and the learning data set 41 and a second step E32 of evaluating the obtained model using the test data set 42 for testing the accuracy of its predictions.

[0065] In step E31, the experimental distribution may be preprocessed before passing it to the AI ​​algorithm. Such preprocessing may include normalization, transformation to logarithmic scale and standardization of the experimental distribution.

[0066] Normalization may include performing a normalization of the intensity I at the first q points, or a normalization of the invariant - dividing the curve by its area multiplied by q raised to the power of 2.

[0067] Transforming to a logarithmic scale may include applying a threshold to negative points, which is set to 10. -12 or included in 10 -6 and 10 -15 A random value between .

[0068] Normalization can be performed using a standard scaler, whereby the mean of the experimental distribution at a given q-value is subtracted from the experimental distribution and the result of this subtraction is divided by the standard deviation of the experimental distribution at the given q-value.

[0069] When the model to be trained is a regression model for predicting particle size (e.g., radius when the shape factor is that of a sphere) and polydispersity, the training features are all I(q) values ​​for each of the q points associated with each experimental distribution, and the targets are two scalars: size and polydispersity. Several AI regression algorithms for predicting size and polydispersity can be considered. However, the best performance was shown on the test dataset using classical machine learning random forests and 1D convolutional neural networks. Once trained, the model takes only the I(q) curve as input, applies the required preprocessing, and outputs predictions for 2 values ​​of size and polydispersity. Using a regression model trained based on the random forest algorithm, the prediction given by the model can be the average of the predictions given by the N estimators (trees) that make up the forest. The model can also provide a standard deviation parameter associated with the predictions of the N estimators.

[0070] Different types of laboratory SAXS instruments can be found on the market. Instruments with either rather fixed experimental setups or with setups with very large variability are available. In both cases, at least some of the instrument and signal-to-noise configurations are based on settings defined by the user, such as beam size and the corresponding intensity. This requires creating different models for a given classifier or creating different models for a given regression algorithm (such as different analysis modules corresponding to a set of selected experimental parameters for a given algorithm trained for, e.g., sphere size determination or ellipsoid size determination). For example, three models are to be trained, corresponding to three different beam size settings and associated intensities. As an example of typical values ​​for such setups and applications, in order to apply the models to samples with scatterer sizes (or diameters) ranging from about 1 nm to 200 nm, one may consider building three types of models based on beam size settings and associated intensities, corresponding to and The point spread function and the corresponding 1x10 6 ph / s, 1x10 7 ph / s and 6x10 7 Beam strength in ph / s.

[0071] Therefore, the present invention may include:

[0072] - determining a first experimental SAXS intensity profile for each of the calculated SAXS intensity profiles based on a first set of SAXS measurement experimental setups including a first X-ray beam intensity profile at the 2D detector;

[0073] - determining a second experimental SAXS intensity profile for each of the calculated SAXS intensity profiles based on a second set of SAXS measurement experimental setups comprising a second X-ray beam intensity profile at the 2D detector;

[0074] - the first experimental SAXS intensity distribution is used to perform machine learning of a first SAXS measurement data analysis model associated with the first set of SAXS measurement experimental setup settings; and

[0075] - The second experimental SAXS intensity distribution is used to perform machine learning of a second SAXS measurement data analysis model associated with a second set of SAXS measurement experimental setup settings.

[0076] Of course, more than two SAXS measurement data analysis models can be learned according to the previous procedure.

[0077] The first SAXS measurement data analysis model and / or the second SAXS measurement data analysis model may be labeled with the first set or the second set of associated SAXS measurement experimental settings. Such labeling may include associating a minimum scattered wave vector from the experimental SAXS intensity distribution.

[0078] The present invention also relates to using a trained SAXS measurement data analysis model to perform SAXS measurement data analysis. Figure 2 , such use typically comprises, at step E4 , obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument and processing the obtained SAXS data using the trained SAXS measurement data analysis model DAM to obtain the predicted PRED.

[0079] In a possible embodiment, several SAXS measurement data analysis models have been trained, each SAXS measurement data analysis model being associated with a given set of experimental settings. These SAXS measurement data analysis models may contain or include the first SAXS measurement data analysis model and the second SAXS measurement data analysis model listed above. In this case, the method for SAXS measurement data analysis may include the following steps: obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument with a given experimental setting; selecting one of the trained SAXS measurement data analysis models based on the given experimental setting; and processing the obtained SAXS data using the selected one of the trained SAXS measurement data analysis models.

[0080] In a possible embodiment, once the first SAXS measurement data analysis model is trained using the first set of SAXS measurement experimental setups, the method may further include determining a usage boundary of the first SAXS measurement data analysis model. As exemplified below, determining the usage boundary may include evaluating a prediction error of the first SAXS measurement data analysis model when processing SAXS data corresponding to experimental measurements performed by a SAXS instrument having a test experimental setup that is different from the first set of SAXS measurement experimental setups. If the prediction error remains below a threshold, then the test experimental setup may be included in the usage boundary of the first SAXS measurement data analysis model.

[0081] Such bounds can be determined by assessing the robustness of the model to sample and experimental setting variability (e.g., as defined by the error in predictions) and identifying those settings that result in outlier errors larger than a threshold.

[0082] As an example, sample-related settings and experimental settings may include chemical composition, volume fraction, acquisition time, beam smearing, and intensity. The chemical composition associated with the scattering power of the measured sample may vary from Au in water, SiO2 in water to polystyrene in toluene. The reference training values ​​of 0.005 vol / vol volume fraction and 30 minutes exposure time are derived from experimental measurements of dilute solutions of SiO2 nanoparticles in water under known conditions. The robustness of the model to sample variability and experimental conditions is evaluated using a test data set obtained with variable parameters (i.e., acquisition time from a few seconds to 1 or 2 hours, and volume fraction 3 or 4 orders of magnitude smaller than the reference volume fraction). For example, outliers can be defined by analyzing the evolution of the prediction error. A 2-fold increase in the root mean square error can be considered as an exclusion condition for outliers. Using this approach, the model established using the above test conditions (0.005 vol / vol, 30 minutes exposure time) can be used for X-ray scattering data of the same type of sample with a measurement time greater than 10 minutes and a volume fraction greater than 0.0005 vol / vol.

[0083] Then, SAXS data corresponding to the experimental measurements performed by the SAXS instrument are obtained, and the following may be to measure the minimum wave vector Qmin of the obtained SAXS data exp a step for checking the compatibility of the experimental setup with the use boundary of the first SAXS measurement data analysis model or the second SAXS measurement data analysis model, and a control step for checking the measured Qmin exp Is it higher than or equal to the simulated Qmin? exp (i.e. the minimum scattering wave vector determined from the experimental SAXS intensity profile). In practice, what is important for the ML algorithm is Qmin expQmin used to create the first SAXS measurement data analysis model or the second SAXS measurement data analysis model sim As close as possible. If Qmin exp is higher than Qmin used to create one of the first SAXS measurement data analysis model or the second SAXS measurement data analysis model exp , then the corresponding model will not be used for inference of the input SAXS data. exp It is typically determined by performing a subtraction between the solution sample and the buffer background scattering signal to extract the signal from the scatterers. A good criterion for a good Qmin with low error is to consider the scattering intensity in absolute value ("absolute intensity") as when the subtracted scattering is just over the buffer background scattering signal. Thus, determining Qmin can be performed during the experiment using previous measurements of the buffer or using a data standard reference on the same buffer for the same experimental setup. exp .

[0084] Importantly, the control step includes checking whether the beam resolution parameter is compatible with the value used to create the first SAXS measurement data analysis model or the second SAXS measurement data analysis model (i.e., it is within the usage boundaries). Obtaining the beam resolution parameter during the experiment can be performed by extracting this value from a measurement without a sample or with a buffer sample just before the experiment. The beam resolution parameter (which can be the FWHM calculated from the Gaussian fit or the complete beam profile) can then be compared with the beam resolution parameter used in step E2.

[0085] In a possible embodiment, the selection of an appropriate SAXS measurement data analysis model (i.e. a model trained with an appropriate experimental setup) can be performed automatically using a preselection tool that is configured to extract the experimental setup from a configuration file updated during the measurement process or from a data header populated at the end of the measurement process. The preselection tool can also be configured to collect the experimental setup from user-entered data (such as chemical formulas and concentrations).

[0086] As discussed above, in the case where a large number of experimental settings can be user defined and have a wide range of values, this means creating a large number of analytical models. Applicants have found that some instrument settings have a greater impact than other instrument settings for which variations compared to the precise measurement position are tolerable. In a possible embodiment of the present invention, tolerances can be applied to certain resolution, signal-to-noise ratio, or sample characteristic parameters so that the experimental settings used for inferring measurements can be distinguished from the experimental settings used for training models (i.e., they are included in the usage boundaries). For example, with respect to the sample-to-detector distance and pixel size, a tolerance of a few percent to ten percent can be applied between the experimental settings used for measurement and the settings used for training models. In that case, preliminary data processing can be performed to resample the experimental data in the same Q grid (a well-known binning process, or splitting process, can be applied).

[0087] In another possible embodiment, the SAXS measurement data analysis model is trained using given sample properties (such as scattering power and concentration) and measurement settings (such as measurement time). The trained model can also be applied to experimental data acquired for samples with different properties and using different measurement settings. Such experimental data can be included in the usage boundary.

[0088] exist Figure 3 In the possible embodiment shown, the invention relates to a method for SAXS measurement data analysis, comprising a step F1 of obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument and a step F2 of processing the obtained SAXS data using a classification model trained according to the invention. Step F2 predicts the compatibility of the obtained SAXS data with each of a plurality of structural models (in Figure 3 denoted as shape factor and prediction in ). The method then comprises a step F3 of processing the SAXS data obtained using a regression model trained according to the invention and associated with the structural model predicted by the classification model at step F2 with the highest compatibility with the SAXS data obtained. Step F3 allows the value of at least one of the parameters of variation (unknown structural parameters such as size and polydispersity and their standard deviation in the case of a random forest regression model) to be determined from the SAXS data obtained. The method may be followed by a step F4 of determining the parameters of the sample model by fitting the SAXS data obtained to the model, said determination being initiated based on the determined values ​​and the structural model selected.

[0089] In another embodiment, for example where the number of user defined parameter values ​​is too high and the performance of the ML algorithm is too sensitive to such values, the training of the ML can be done in real time. For this purpose, a pre-selection tool can be used to extract the real measurement conditions associated with the experimental setup. The ML algorithm is then trained by creating training and test data sets associated with the experimental setup. According to this embodiment, the SAXS measurement data analysis comprises the following steps:

[0090] - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument with an experimental setup;

[0091] - performing machine learning of a first SAXS measurement data analysis model using the experimental setup as a setup of a first set of SAXS measurement experimental setups; and

[0092] - Processing the acquired SAXS data using the learned first SAXS measurement data analysis model.

[0093] In About Figure 4 In a further embodiment shown, the invention relates to a method for SAXS measurement data analysis, the method comprising a step G1 of obtaining SAXS data corresponding to an experimental measurement performed by a SAXS instrument using a given set of experimental settings. In a step G2, the compatibility of this experimental measurement (in terms of sample and experimental settings, i.e. sample scattering power, resolution, sample detector distance, acquisition time) with a previously trained model is checked. The compatibility check may include verifying whether the experimental measurement is within the usage boundaries of the previously trained model. In the case of such compatibility, a step G3 is then performed in which one of the previously trained models is selected based on the given set of experimental settings, followed by a step G4 of analyzing the measured SAXS data using the selected model. In the absence of such compatibility, step G2 is followed by a step G4 of training a model based on the given set of experimental settings (real-time training as described above) and followed by a step G6 of analyzing the measured SAXS data using the trained model.

[0094] The present invention is not limited to the above methods, but also relates to: a computer program product comprising instructions, which, when executed by a computer, cause the computer to perform any of the above methods; a data processing unit comprising a processor, the processor being configured to perform any of the above methods; and a small-angle X-ray scattering instrument comprising such a data processing unit. Although the present invention has been shown and described with reference to its preferred embodiments, those skilled in the art will recognize that various changes in form and details may be made without departing from the spirit and scope of the invention as defined by the appended claims. In particular, those skilled in the art will recognize that the data analysis model (DAM) training and learning data sets can be associated with several sets of SAXS measurement experimental setups, each set of experimental setups being associated with given and different X-ray beam intensity distributions at the 2D detector used in step E2 to estimate the experimental SAXS intensity distribution.

Claims

1. A computer-implemented method of generating (E1, E2) a training data set (41, 42) and using (E3, E31, E32) said training data set to perform machine learning of a first small angle X-ray scattering (SAXS) measurement data analysis model (DAM), wherein: Generating the training data set comprises the following steps: - calculating (E1) 1D SAXS intensity profiles, each of said 1D SAXS intensity profiles corresponding to a variation of a parameter of at least one structural model of the sample in the medium; and - estimating (E2) a first experimental 1D SAXS intensity profile from each of the calculated 1D SAXS intensity profiles based on a first set of SAXS measurement experimental setups comprising a first X-ray beam intensity profile at the 2D detector, Therein, the estimating (E2) comprises smearing each of the calculated 1D SAXS intensity distributions by convolution with a point spread function associated with the first X-ray beam intensity distribution. 2 . The computer-implemented method of claim 1 , further comprising determining a usage boundary for the first SAXS measurement data analysis model.

3. The computer-implemented method of claim 2, wherein: Determining the usage boundary includes evaluating a prediction error of the first SAXS measurement data analysis model when processing SAXS data corresponding to experimental measurements performed by a SAXS instrument having a test experimental setup different from the first set of SAXS measurement experimental setups.

4. The computer-implemented method according to any one of claims 1 to 3, wherein: The first set of SAXS measurement experimental settings also includes a signal-to-noise ratio setting, wherein the signal-to-noise ratio setting includes the size of the 2D detector and the beam position on the 2D detector, and wherein the estimating also includes adding noise to each of the calculated SAXS intensity distributions based on the signal-to-noise ratio setting.

5. The computer-implemented method according to any one of claims 1 to 4, further comprising determining an experimental 1D SAXS intensity distribution of the blank solution based on the first set of SAXS measurement experimental settings and based on a theoretical 1D SAXS intensity distribution of a blank solution, and subtracting the experimental 1D SAXS intensity distribution of the blank solution from each of the experimental 1D SAXS intensity distributions.

6. The computer-implemented method according to any one of claims 1 to 5, wherein: Calculation of a 1D SAXS intensity distribution corresponding to a variation of parameters of at least one structural model of a sample in a medium is performed for a plurality of structural models, and wherein the first SAXS measurement data analysis model is a structural model classifier trained to predict compatibility of experimental SAXS measurement data with each of the plurality of structural models.

7. The computer-implemented method according to any one of claims 1 to 5, wherein: Calculation of a 1D SAXS intensity distribution corresponding to a varying parameter of at least one structural model of a sample in a medium is performed for a single structural model, and wherein the first SAXS measurement data analysis model is a regression model trained to predict the value of at least one of the varying parameters based on experimental SAXS measurement data.

8. The computer-implemented method according to any one of claims 1 to 7, wherein: Generating the training data set also includes the steps of normalizing, transforming to a logarithmic scale and standardizing the determined experimental 1D SAXS intensity profiles.

9. The computer-implemented method according to any one of claims 1 to 8, wherein: The first set of SAXS measurement experimental settings also includes detector pixel size and sample-to-detector distance.

10. The computer-implemented method according to any one of claims 1 to 9, wherein: The first set of SAXS measurement experimental settings also includes measurement time.

11. The computer-implemented method of any one of claims 1 to 10, further comprising determining a second experimental 1D SAXS intensity profile for each of the calculated 1D SAXS intensity profiles based on a second set of SAXS measurement experimental setups, the second set of SAXS measurement experimental setups comprising a second X-ray beam intensity profile at the 2D detector, and wherein, The first experimental 1D SAXS intensity distribution is used to perform machine learning of the first SAXS measurement data analysis model, and the second experimental 1D SAXS intensity distribution is used to perform machine learning of a second SAXS measurement data analysis model associated with a second set of the SAXS measurement experimental setup.

12. A method for analyzing SAXS measurement data, comprising the following steps: - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument; and - Processing the acquired SAXS data using the first SAXS measurement data analysis model learned by the method according to claim 1 .

13. A method for analyzing SAXS measurement data, comprising the following steps: - obtaining (F1) SAXS data corresponding to experimental measurements performed by a SAXS instrument; - processing (F2) the SAXS data obtained using the structural model classifier trained by the method according to claim 6; - selecting the structural model having the highest compatibility with the experimental SAXS measurement data; and - Processing (F3) the obtained SAXS data using a regression model learned by the method according to claim 7 using the selected structural model as a single structural model to determine the value of at least one of the varied parameters.

14. The computer-implemented method of claim 13, further comprising determining (F4) parameters of the sample model by fitting the acquired SAXS data to the sample model, the determining being initiated based on the determined values ​​and the selected structural model.

15. A method for analyzing SAXS measurement data, comprising the following steps: - obtaining SAXS data corresponding to experimental measurements performed by a SAXS instrument with a given experimental setup; - based on the given experimental setup, selecting the first SAXS measurement data analysis model or the second SAXS measurement data analysis model learned by the method according to claim 12; and - Processing the acquired SAXS data using a selected one of said first SAXS measurement data analysis model or said second SAXS measurement data analysis.

16. A method for analyzing SAXS measurement data, comprising the following steps: - obtaining (G1) SAXS data corresponding to experimental measurements performed by a SAXS instrument having an experimental setup; -Implementation (G5) The method according to claim 1 to perform machine learning of the first SAXS measurement data analysis model using an experimental setup that is a setup of a first set of SAXS measurement experimental setups; as well as - Processing (G6) the acquired SAXS data using the learned first SAXS measurement data analysis model.

17. A data processing unit comprising a processor configured to perform the method according to any one of claims 1 to 16.

18. A small angle X-ray scattering instrument comprising the data processing unit according to claim 17.

19. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to any one of claims 1 to 14.

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