Processing measured raman spectrum with neural networks

Abstract

The invention relates to a method (100) for processing a measured input Raman spectrum (1) which is emitted from molecules of a sample stimulated by monochromatic stimulation light due to inelastic scattering of the stimulation light at these molecules, wherein the input Raman spectrum (1) specifies the light intensity (I) as a function of the frequency or wave number k of the light. The method comprises the following steps: - the input Raman spectrum (1) is converted (110), using a trained encoder network (2), into a representation (3) in a latent space which is reduced in comparison with the input Raman spectrum (1) in terms of dimensionality; - the representation (3) is converted, using a trained decoder network (4), into an output Raman spectrum (5), wherein the arrangement consisting of the encoder network (2) and the decoder network (4) is trained to remove from the output Raman spectrum (5), with respect to the input Raman spectrum (1), the impact of at least one undesired effect (1a) that arises when measuring the input Raman spectrum (1).

Description

[0001] Processing of measured Raman spectra with neural networks

[0002] The invention relates to the evaluation and / or correction of measured Raman spectra resulting from wavelength-dependent inelastic Raman scattering of the monochromatic excitation light irradiated onto a sample.

[0003] State of the art

[0004] When monochromatic excitation light strikes a sample consisting of molecules, some of the incident photons change the rotational and / or vibrational states of the molecules. These states can be excited, transferring energy from the photon to the molecule, or they can be de-excited, transferring energy from the molecule to the photon. The scattered light thus has wavelengths that differ from the wavelength of the monochromatic excitation light. The intensity of the scattered light as a function of wavelength forms the Raman spectrum, which is a "fingerprint" of the sample's chemical composition.

[0005] This Raman scattering occurs only with a low probability, so the scattered light has only a low intensity. This small signal is overlaid by a significantly larger background caused by fluorescence, additive noise, and non-additive unwanted effects. Before evaluation with regard to the composition of the sample, the measured Raman spectrum must therefore first be processed. For example, the Raman spectrum is transformed using Fourier analysis or wavelet analysis into a working space in which the desired signal on the one hand and the unwanted effects on the other can be more easily distinguished. An appropriate correction is applied in the working space, and the result is transformed back into a corrected Raman spectrum.

[0006] As with image denoising, it cannot be avoided that part of the desired signal is lost, thus degrading the spectral resolution of the ultimately obtained corrected Raman spectrum.

[0007] Task and solution

[0008] It is therefore the object of the present invention to provide a method for processing a Raman spectrum which removes undesired effects from the Raman spectrum with the least possible loss of desired information.

[0009] This object is achieved according to the invention by a method according to the main claim. Further advantageous embodiments emerge from the dependent claims.

[0010] Disclosure of the invention

[0011] The invention provides a method for processing a measured input Raman spectrum. The input Raman spectrum is emitted by molecules of a sample excited by monochromatic excitation light due to inelastic scattering of the excitation light by these molecules. It indicates the light intensity as a function of the frequency or wavenumber of the light.

[0012] In this method, the input Raman spectrum is converted into a representation in a latent space using a trained encoder network, which is reduced in dimensionality compared to the input Raman spectrum. This representation is then converted into an output Raman spectrum using a trained decoder network. The arrangement of the encoder network and the decoder network is trained to correct the output Raman spectrum for at least one unwanted effect that occurred during the measurement of the input Raman spectrum.

[0013] It was recognized that in this way, the capabilities of the encoder network, on the one hand, and the decoder network, on the other, complement each other synergistically. The encoder network must force all the information contained in the input Raman spectrum through a "bottleneck" where space is very limited due to the lower dimensionality of the latent representation. It must therefore decide which information in the input Raman spectrum is truly important and must therefore be incorporated into the latent representation. The decoder network, in turn, must reconstruct an output Raman spectrum from sparse information in the latent representation.

[0014] The task is thus divided between the encoder network and the decoder network. This means that both networks are actually active when determining the output Raman spectrum. This significantly increases flexibility, allowing a broader class of interference to be removed with significantly less loss of information regarding the desired signal.

[0015] The process is somewhat analogous to the task of filtering out the essential information from the impressions of a whole week of vacation. This information fits on a postcard as a "latent representation" and enables the recipient, as a "decoder network," to imagine this week as faithfully and in as much detail as possible. Through training, the encoder network and the decoder network can be specifically adapted to remove unwanted effects whose origins are physically understood and possibly even modelable. Training data can then be generated using a physical forward model for the origin of the unwanted effects. This allows the encoder network and the decoder network to be specifically trained to eliminate the effects of these unwanted effects.When the trained networks are then applied to measured Raman spectra, the unwanted effects are corrected.

[0016] In this way, a major problem can be avoided that often arises when attempting to construct an inverse backward model for a known physical forward model and then apply this to measured data. This is a so-called "ill-posed problem" because Hadamard's requirements for the existence and uniqueness of a solution and the continuous dependence of the solution on the input data are not met. For example, unavoidable deviations of the real measurement process from the physical forward model, and even more so the noise that is omnipresent in measurements, mean that the measured data are not a "true" product of the physical forward model, i.e., they do not lie within the image domain of the physical forward model. Accordingly, the measured data lie outside the domain of the inverse backward model. This does not guarantee that there is an exact solution and that this solution is unique.Rather, systems of equations can arise in which contradictory equations, so that only the least-bad compromise solution can be found, for example, using the least squares method or regularization. A continuous dependence of the solution on the input data is also no longer guaranteed, because even a small, continuous change in the measured data can cause it to fall outside the scope of the physical forward model. As a result, for example, noise in the measured data can be amplified when applying an inverse backward model to such an extent that the intended effect of the inverse backward model is completely or partially negated.

[0017] The method proposed here thus makes it possible to use a known forward physical model for an undesirable effect to correct for this undesirable effect, without having to solve an "ill-posed problem" directly by applying an inverse backward model. Instead, the solution can be obtained indirectly.

[0018] In a particularly advantageous embodiment, the at least one undesirable effect comprises at least one nonlinear effect that changes the transfer function from the intensity of the excitation light to the wavelength-dependent intensity according to the measured input Raman spectrum. The complete Raman apparatus can thus be understood as a single "black box" system that receives excitation light with a specific intensity and wavelength as input and generates Raman light from this, the intensity of which depends on the wavelength. Such effects, which occur in Raman spectroscopy, are physically understood, and there are good physical forward models for their description. However, it is precisely this nonlinearity that leads to inverse backward models behaving in a non-benign manner and, in particular, significantly amplifying noise.It is therefore particularly advantageous that no inverse backward model is required to correct the undesirable effect.

[0019] For the same reasons, the undesired effect can also include any other non-linear effect that changes the intensities of the Raman spectrum through a non-linear function. The undesired effect can, for example, include at least one spatially periodic modulation effect and / or interference effect in the sample, in the detector used for the measurement, and / or in a light guide in the beam path. For example, protective layers or coatings on the detector or other optical elements can lead to the formation of standing waves (“etaloning”). Similar effects can also occur, for example, in the sample or in a container in which this sample is located. For example, liquid or gaseous samples can be measured in a transparent cuvette. Interference effects can also occur in a sample consisting of several layers with different refractive indices.

[0020] The undesirable effect can, for example, also include a wavelength-dependent transmission of at least one element in the equipment used for the measurement. For example, absorption coefficients are wavelength-dependent. Dispersion in optical elements can also change the beam path, and thus the ultimately output intensity, depending on the wavelength.

[0021] The undesired effect can, for example, also include energy transfer between two or more optical modes of the light transported through a fiber optic cable. Such effects occur, for example, in optical fibers used to guide the beam path. During transmission in optical fibers, which depends on multiple total internal reflection between the light-guiding core and a cladding surrounding this core with a different refractive index, the propagation of certain optical modes is always favored or disadvantaged over the propagation of others. The modes each have self-consistent field distributions, and not all of these field distributions can satisfy the boundary conditions specified by the configuration of the optical fiber. The energy transfer between optical modes is very well described by physical forward models and can therefore be simulated very accurately.However, it is much more difficult to find an inverting backward model for such a forward model.

[0022] In another particularly advantageous embodiment, the undesired effect comprises an electronic reaction of the sample and / or a material of the apparatus used to measure the input Raman spectrum to the excitation light and / or to the emitted light. These effects are typically highly nonlinear and also highly wavelength-dependent, because transitions between electronic energy levels can only be excited by photons with the appropriate energy.

[0023] However, the at least one undesirable effect may also include, for example, an additive disturbance contained in the input Raman spectrum and / or a background contained in the input Raman spectrum. Even if proven methods exist for eliminating these disturbances, it may be advantageous to also use the encoder network and the decoder network for this purpose. This is especially true if the previous method focused more on the symptoms visible in the measurement data than on the physical mechanism causing the disturbance.

[0024] The dimensionality of the representation of the input spectrum in the latent space can, for example, be between 1 / 16 and 1 / 100 of the dimensionality of the input Raman spectrum. Experiments have shown that dimensionalities in this range represent a particularly advantageous compromise between suppressing unwanted effects on the one hand and preserving details in the output Raman spectrum on the other. The value of the dimensionality thus determines the degree to which unwanted effects are suppressed. This underscores that, despite the similar network architecture of encoder and decoder used, removing unwanted effects from input Raman spectra is qualitatively different from mere denoising, for example, of images, with so-called "denoising autoencoders." With "denoising autoencoders," the representation of the input data in the latent space can even have a higher dimensionality than the input data itself.An input Raman spectrum typically has several thousand values.

[0025] As explained above, the method shows its strengths particularly in connection with undesirable effects for which a physical forward model is known.

[0026] Therefore, the invention provides yet another method for training an arrangement of an encoder network and a decoder network for use in the method described above.

[0027] This procedure provides target Raman spectra that are realistic as the output of a Raman measurement apparatus free from unwanted effects.

[0028] The target Raman spectra can, for example, be synthetically generated spectra. For this purpose, generators trained in Generative Adversarial Networks (GANs) can be used. In a GAN, the generator to be trained is trained together with a discriminator. The discriminator is presented with Raman spectra randomly drawn from a pool containing a mixture of real Raman spectra and Raman spectra generated with the generator. The generator is trained with the goal of reducing the accuracy with which the discriminator distinguishes real spectra from those generated with the generator. The discriminator is trained with the goal of improving this accuracy.

[0029] The target Raman spectra can also be measured and subsequently processed to a high quality. For example, one or more modifications can be created from a target Raman spectra using standard data augmentation methods, which can then also serve as target Raman spectra. Measured target Raman spectra can also be used, for example, to further improve the physical forward model for the undesired effect.

[0030] At least one forward physical model is provided that describes the effect of at least one undesired effect on a Raman spectrum. This at least one forward physical model is applied to the target Raman spectra. This creates training examples.

[0031] The training examples are converted into representations using the encoder network to be trained. The resulting representations are then converted into reconstructions as output Raman spectra using the decoder network to be trained.

[0032] Deviations of the reconstructions from the target Raman spectra from which they were derived are evaluated using a predefined cost function (also called a "loss function"). Parameters characterizing the behavior of the encoder network and the decoder network to be trained are optimized with the goal of improving the evaluation by the cost function with continued processing of training examples.

[0033] As previously explained, the combination of the encoder network and the decoder network is thereby enabled to specifically correct the unwanted effect(s) imposed on the training examples from measured Raman spectra. Two things are trained here: firstly, the removal of the unwanted effects and, secondly, the reconstruction of the true Raman spectrum. Regarding the advantages of using a physical forward model in this way and the types of unwanted effects for which these advantages are particularly pronounced, what was said in connection with the previously described method applies. All disclosures relating to the previously described method also apply to the training method, and vice versa.

[0034] In a particularly advantageous embodiment, the entire set of training examples represents Raman spectra measured on several different devices and / or under different operating parameters of one or more devices. This allows the training to be better generalized to applications on unseen Raman devices or under unseen parameters.

[0035] In another particularly advantageous embodiment, the encoder network and / or the decoder network are further trained, retaining some of the parameters, using a set of fine-tuning examples, each labeled with the target Raman spectra to be reconstructed. These fine-tuning examples can, in particular, contain Raman spectra measured on a specific device. The fine-tuning can then serve, among other things, to adapt networks pre-trained generically and / or based on training examples with respect to another device to a specific new device.

[0036] In another particularly advantageous embodiment, an encoder network and a decoder network are selected that are pre-trained so that the encoder network converts Raman spectra into representations, and the decoder network reconstructs these Raman spectra identically. For this pre-training, only arbitrary training examples for Raman spectra are required, without any undesired effects having to be imposed on them. In particular, for example, one and the same generically pre-trained combination of an encoder network and a decoder network can be used as a starting point to start the training with respect to different devices and the undesired effects that may occur therein.

[0037] In another particularly advantageous embodiment, the dimensionality of the representations formed by the encoder network is optimized as a hyperparameter with the goal that, after training is completed, the arrangement of the trained encoder network and the trained decoder network reconstructs these target Raman spectra as accurately as possible from validation examples unseen during training, each of which is labeled with the target Raman spectra to be reconstructed. As previously explained, the dimensionality of the representations is the key to the compromise between suppressing unwanted effects on the one hand and faithfully reproducing the true details of the Raman spectra on the other. The optimal value for this dimensionality can depend, for example, on the type and strength of the unwanted effects that a specific device imposes on the Raman spectra measured with it.

[0038] The validation examples may or may not contain the unwanted effects to be corrected. In particular, a mixture of validation examples with and without unwanted effects can be used. This makes it possible, for example, to check whether the networks trained to suppress unwanted effects "overshoot" in the absence of these effects and introduce artifacts into the output Raman spectrum.

[0039] The methods can in particular be fully or partially computer-implemented. Therefore, the invention also relates to a computer program with machine-readable instructions which, when executed on one or more computers and / or compute instances, cause the computer(s) and / or compute instances to execute one of the described methods. In this sense, control units for embedded systems for technical devices which are also capable of executing machine-readable instructions are also to be regarded as computers. Technical devices with embedded systems can in particular be, for example, measuring devices or measuring apparatus. Compute instances can be, for example, virtual machines, containers, or serverless execution environments, which can in particular be provided in a cloud.

[0040] The invention also relates to a machine-readable data carrier and / or a downloadable product containing the computer program. A downloadable product is a digital product that can be transmitted over a data network, i.e., downloaded by a user of the data network, and which can be offered for immediate download, for example, in an online shop.

[0041] Furthermore, one or more computers and / or compute instances may be equipped with the computer program, the machine-readable data carrier or the download product.

[0042] Special description section

[0043] The subject matter of the invention is explained below with reference to figures, without limiting the subject matter of the invention. It is shown:

[0044] Figure 1: Embodiment of the method 100 for processing a measured Raman spectrum 1;

[0045] Figure 2: Embodiment of method 200 for training an arrangement comprising an encoder network and a decoder network for use in method 100. Figure 1 is a schematic flow diagram of an embodiment of method 100 for processing a measured input Raman spectrum 1. The measured input Raman spectrum 1 was generated by molecules of a sample excited by monochromatic excitation light due to inelastic scattering of the excitation light by these molecules. It indicates the light intensity I as a function of the wavenumber k of the light. The input Raman spectrum 1 is subject to at least one undesirable effect 1a.

[0046] In step 110, the input Raman spectrum 1 is converted into a representation 3 in a latent space using a trained encoder network 2. This representation 3 is sketched as a vector in Figure 1. The dimensionality of the representation 3 is significantly reduced compared to the dimensionality of the input Raman spectrum 1.

[0047] In step 120, the representation 3 is converted into an output Raman spectrum 5 using a trained decoder network 4. This output Raman spectrum 5 is corrected for the unwanted effect la compared to the input Raman spectrum 1a. Comparison with the original input Raman spectrum 1 shows that the peaks of the output Raman spectrum 5 are significantly more pronounced and sharper. Thus, the chemical composition of the sample under investigation, which is sought with the Raman measurement, can be evaluated much more reliably and accurately from the output Raman spectrum 5 than from the input Raman spectrum 1.

[0048] Figure 2 is a schematic flow diagram of an embodiment of the method 200 for training an arrangement comprising an encoder network 2 and a decoder network 4 for use in the previously described method 100. The method 200 can optionally start according to block 205 from a state in which the encoder network 2 and the decoder network 4 are already pre-trained such that the encoder network 2 converts Raman spectra into representations 3 and the decoder network 4 reconstructs these Raman spectra identically.

[0049] In step 210, target Raman spectra 6 are provided that are realistic as the output of a Raman measurement apparatus free of unwanted effects. These target Raman spectra 6 can, in particular, be synthetically generated, for example, according to block 211. As previously explained, measured target Raman spectra 6 can also be used. The target Raman spectra 6 indicate the light intensity I as a function of the wavenumber k. The target Raman spectrum 6 shown in Figure 2 has many high, sharply defined peaks.

[0050] In step 220, at least one physical forward model 7 is provided that describes the effect of at least one undesired effect 1a on a Raman spectrum. As previously explained, such forward models 7 are available for many undesired effects 1a. Inverse backward models that invert the effect of the respective undesired effect 1a on the Raman spectrum, however, may be difficult or even impossible to obtain, and / or their application to Raman spectra may be an "ill-posed problem" and, for example, greatly amplify noise.

[0051] In step 230, the at least one physical forward model 7 is applied to the target Raman spectra 6, resulting in training examples 8. These training examples 8 are also Raman spectra that specify the light intensity I as a function of the wavenumber k. In the example shown in Figure 2, the application of the physical forward model 7 has the effect that the many sharp peaks essentially blur into two very broad maxima, which no longer allow a clear conclusion about the desired chemical composition of an examined sample.

[0052] In step 240, the training examples 8 are converted into representations 3 using the encoder network 2 to be trained.

[0053] In step 250, the representations 3 are converted into reconstructions as output Raman spectra 5 using the decoder network 4 to be trained.

[0054] In step 260, deviations of these reconstructions 5 from the target Raman spectra 6 from which they were derived are evaluated using a predefined cost function L. In particular, the cost function L can, for example, weight different types of deviations against each other. For example, deviations that favor a misclassification of the sample's composition based on the reconstruction 5 can be penalized more severely than deviations that merely degrade the quality of the reconstructions 5 in generic and / or summary form.

[0055] In step 270, parameters 2a, 4a, which characterize the behavior of the encoder network 2 and the decoder network 4 to be trained, are optimized to the goal of improving the evaluation by the cost function L as training examples 8 continue to be processed. The optimization can continue until an arbitrary termination condition is reached. For example, a predetermined number of epochs and / or training iterations can be specified. Training can also be terminated, for example, when parameters 2a, 4a no longer change significantly. The fully optimized state of parameters 2a, 4a is denoted by reference symbols 2a*, 4a*. In step 280, the encoder network 2 and / or the decoder network 4 can be further trained while retaining a portion of the parameters 2a, 4a with a set of fine-tuning examples 10, each labeled with target Raman spectra 6 to be reconstructed.The parameters 2a, 4a further optimized in this way are designated by the reference symbols 2a**, 4a**. The fine-tuning examples 10 can, for example, be Raman spectra measured with a specific apparatus. However, they can also be created from predefined target Raman spectra 6, for example, using a physical forward model that describes the effect of this apparatus.

[0056] According to block 290, the dimensionality of the representations 3 formed by the encoder network 2 can be optimized as hyperparameters. This optimization is aimed at ensuring that, after training is completed, the arrangement of the trained encoder network 2 and the trained decoder network 4 reconstructs these target Raman spectra 6 as accurately as possible from validation examples 11 unseen during training, each labeled with target Raman spectra 6 to be reconstructed. The validation examples 11 can, for example, be Raman spectra measured with a specific apparatus. The corresponding target Raman spectra 6 can, for example, be obtained by any desired processing of these measured Raman spectra or by calculation based on a known composition of the sample under investigation.

[0057] To optimize dimensionality as a hyperparameter, the encoder network 2 and the decoder network 4 are set up with different values ​​of this hyperparameter and then trained. The accuracy of the trained configuration of the encoder network 2 and the decoder network 4 when evaluating input Raman spectra is then determined using validation examples 11. The respective accuracy can serve as feedback for any optimization algorithm that determines the next value of the hyperparameter. Such an optimization algorithm can, for example, be aimed at getting as close as possible to the optimum dimensionality with as few steps as possible, since a complete training of the encoder network 2 and the decoder network 4 is necessary for each attempt.

[0058] List of reference symbols

[0059] 1 Input Raman spectrum la unwanted effect in input Raman spectrum 1

[0060] 2 Encoder network

[0061] 2a Parameters characterizing the behavior of the encoder network 2

[0062] 2a* fully trained state of parameters 2a

[0063] 2a** further trained state of parameters 2a

[0064] 3 Representation generated from input Raman spectrum 1

[0065] 4 Decoder network

[0066] 4a Parameters characterizing the behavior of the encoder network 4

[0067] 4a* fully trained state of parameters 4a

[0068] 4a** further trained state of parameters 4a

[0069] 5 Output Raman spectrum, corrected for unwanted effect la

[0070] 6 Target Raman spectra

[0071] 7 physical forward model for undesired effect la

[0072] 8 training examples, generated with forward model 7

[0073] 10 fine-tuning examples

[0074] 11 validation examples

[0075] 100 Methods for preparing the input Raman spectrum 1

[0076] 110 Converting the input Raman spectrum 1 into representation 3

[0077] 120 Converting representation 3 into output Raman spectrum 5

[0078] 200 Procedure for training the encoder network 2, decoder network 4

[0079] 210 Providing the target Raman spectra 6

[0080] 211 synthetic generation of the target Raman spectra 6

[0081] 220 Providing the physical forward model 7

[0082] 230 Applying the forward model to target Raman spectra 6

[0083] 240 Creating representations 3 from training examples 8

[0084] 250 Generating output Raman spectra 5 from representations 3 260 Evaluating deviations with cost function L

[0085] 270 Optimizing parameters 2a, 4a

[0086] 280 Continue training while maintaining some of the parameters 2a , 4a

[0087] 290 Optimization of the dimensionality of representations 3 I Light intensity

[0088] L cost function

[0089] Wavenumber

Claims

Patent claims 1. A method (100) for processing a measured input Raman spectrum (1) emitted by molecules of a sample excited by monochromatic excitation light due to inelastic scattering of the excitation light by these molecules, wherein the input Raman spectrum (1) indicates the light intensity I as a function of the frequency or wavenumber k of the light, comprising the steps: • the input Raman spectrum (1) is converted (110) into a representation (3) in a latent space using a trained encoder network (2), which representation is reduced in its dimensionality compared to the input Raman spectrum (1); • the representation (3) is converted into an output Raman spectrum (5) using a trained decoder network (4), wherein the arrangement of the encoder network (2) and the decoder network (4) is trained to correct the output Raman spectrum (5) compared to the input Raman spectrum (1) by the effect of at least one undesirable effect (1a) that occurred during the measurement of the input Raman spectrum (1).

2. The method (100) of claim 1, wherein the at least one undesired effect (1a) comprises at least one non-linear effect that changes the transfer function from the intensity of the excitation light to the wavelength-dependent intensity according to the measured input Raman spectrum (1).

3. Method (100) according to one of claims 1 to 2, wherein the at least one undesirable effect (1a) • at least one non-linear effect that changes the intensities of the input Raman spectrum (1) by a non-linear function, and / or • at least one spatially periodic modulation effect and / or interference effect in the sample, in the detector used for the measurement, and / or in a light guide in the beam path, and / or • at least one wavelength-dependent transmission of at least one element in the apparatus used for the measurement, and / or • involves an energy transfer between two or more optical modes of light transported through a light guide.

4. The method (100) according to any one of claims 1 to 3, wherein the at least one undesirable effect (1a) includes an electronic reaction of the sample, and / or a material of the apparatus used to measure the input Raman spectrum (1), to the excitation light, and / or to the emitted light.

5. The method (100) according to any one of claims 1 to 4, wherein the at least one undesired effect (1a) comprises an additive disturbance contained in the input Raman spectrum (1) and / or a background contained in the input Raman spectrum (1).

6. The method (100) according to any one of claims 1 to 5, wherein the dimensionality of the representation (3) is between 1 / 16 and 1 / 100 of the dimensionality of the input Raman spectrum (1).

7. A method (200) for training an arrangement comprising an encoder network (2) and a decoder network (4) for use in the method (100) according to any one of claims 1 to 6, comprising the steps of: providing (210) target Raman spectra (6) which are realistic as the output of a Raman measuring apparatus free from undesired effects; • at least one physical forward model (7) is provided (220) which describes the effect of at least one undesired effect on a Raman spectrum; • the at least one physical forward model (7) is applied (230) to the target Raman spectra (6) so that training examples (8) are created; • the training examples (8) are converted (240) into representations (3) using the encoder network (2) to be trained; • the representations (3) are run over (250) with the decoder network (4) to be trained in reconstructions as output Raman spectra (5); • Deviations of the reconstructions (5) from the target Raman spectra (6) from which they originate are evaluated with a given cost function (L) (260); and • Parameters (2a, 4a) that characterize the behavior of the encoder network (2) and the decoder network (4) to be trained are optimized (270) to the goal that with continued processing of training examples (8) the evaluation by the cost function (L) is improved.

8. The method (200) according to claim 7, wherein the target Raman spectra (6) are generated synthetically (211).

9. The method (200) according to any one of claims 7 to 8, wherein the totality of the training examples (6) represents Raman spectra measured on several different apparatuses and / or under different operating parameters of one or more apparatuses.

10. Method (200) according to one of claims 7 to 9, wherein the encoder network (2) and / or the decoder network (4) are / is configured to retain a part of the Parameters (2a, 4a) are further trained with a set of fine-tuning examples (10), each labeled with the target Raman spectra (6) to be reconstructed (280).

11. The method (200) according to any one of claims 7 to 10, wherein an encoder network (2) and a decoder network (4) are selected (205) which are pre-trained such that the encoder network (2) converts Raman spectra into representations (3) and the decoder network (4) reconstructs these Raman spectra identically.

12. The method (200) according to any one of claims 7 to 11, wherein the dimensionality of the representations (3) formed by the encoder network (2) is optimized (290) as hyperparameters to the goal that, after completion of the training, the arrangement of the trained encoder network (2) and the trained decoder network (4) reconstructs these target Raman spectra (6) as accurately as possible from validation examples (11) unseen during training, which are each labeled with target Raman spectra (6) to be reconstructed.

13. A computer program comprising machine-readable instructions which, when executed on one or more computers and / or compute instances, cause the computer(s) and / or compute instances to perform a method according to any one of claims 1 to 12.

14. Machine-readable data carrier and / or download product with the computer program according to claim 13.

15. One or more computers and / or compute instances with the computer program according to claim 13, and / or with the machine-readable data carrier and / or download product according to claim 14.

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