Introduction

Vibrational spectroscopy involves specific optical techniques including Fourier-transform infrared (FTIR), Brillouin scattering and Raman spectroscopy1. Classification models for vibrational spectroscopy data can map input objects (spectra) to desired outputs (class assignments)2. While building such a classification tool is a challenging task, it would benefit a wide range of application sectors including semiconductors, pharmaceutical, polymers, forensics, environmental and food sciences, as well as medicine3,4. Also, vibrational spectroscopy data often requires additional and complex pre-processing steps before chemometric measurements5. Several data pre-processing approaches are used to improve the robustness and accuracy of subsequent multivariate analysis and to increase the interpretability of the data by providing adjustments for the challenges associated with spectral data acquisition5. However, pre-processing methods are often proprietary, or they can vary significantly depending on the objective of the study and the technique. These expert guided pre-processing pipelines are brittle and are based on empirical evidence6. As a result, a pre-processing technique suitable for a given model or material system might decrease the performance of another7. The effects of a given pre-processing technique also varies significantly with the data sample, often requiring a trained expert’s intervention. Thus, we believe it is important to remove the non-standard expert guided pre-processing of signals to ensure better generalization.

Recent advances in the development of instruments coupled with more powerful compute resources and tools have brought Raman spectroscopy from a research laboratory-based method to a widely-used method in a diverse set of fields. Portable or handheld systems are currently helping clinicians in the detection of cancerous cells and in the identification of unknown chemical substances8,9,10,11 Raman spectroscopy provides unique fingerprints pertaining to individual molecules and compounds and it requires minimal sample preparation. Similarly, Raman spectroscopy can detect and characterize defect states that significantly affect the material’s properties12,13. For instance, the presence of surface defects in metal-oxides allow anions and cations to assume a variety of charged states contributing to photocatalysis14, corrosion protection15, sensors16, microelectronics17, magnetic recording devices12,15 and micro-porous materials18.

Spectroscopy techniques can be subject to individual interpretations. During manual pre-processing, human bias might be added to the data, which can impact the results or their interpretations7. Thus, there is an urgent requirement to develop more robust computational tools, which would help users rapidly analyse the spectrum patterns in a more uniform and reliable (unbiased) manner. Traditional methods require a highly-skilled expert to correctly identify the compound and/or structural properties from the Raman spectroscopy measurements. Convolutional Neural Networks (CNNs) have been widely used to extract feature patterns in complex high-dimensional data. Thus, they can reduce the need for brittle manual pre-processing by highly-skilled experts19. Automated real-time CNN models enable professionals from a diverse set of fields to use Raman spectroscopy to identify increasingly complex compounds from more affordable (lower-resolution) instruments with minimal preprocessing of data.

In this work, we propose a powerful deep-learning framework to accurately identify compounds from their Raman spectra. Using the proposed model, we achieve a Top-1 accuracy of 99.12% and a Top-5 accuracy of 99.30% on the public RRUFF Dataset. To support our findings, we present experimental validations using our model to accurately identify both Rutile and Anatase in the synthesized samples. Most importantly, we establish that the proposed model does not require any additional expert guided proprietary data pre-processing to achieve accurate identification. This leads to better cost efficiencies and standardisation.

Related works

Several researchers worked on the development of spectral-matching algorithms20,21. These algorithms identify the similarities between a reference spectrum and the samples in an iterative manner20. These techniques can be classified into unsupervised or supervised methods22.

The unsupervised methods tend to reduce the number of dimensions using Principal Component Analysis (PCA), and then use a similarity or distance-based algorithm like K-Nearest Neighbour (KNN) to identify homogeneous clusters in the spectral data23. The distance-based algorithms maximize the similarity within a class and reduce the inter-group similarity24. The reference sample and technique used for dimensionality reduction have a significant impact on the performance of the unsupervised method25. In contrast, the similarity-based methods either compare the maximum peaks or the full spectrum26. Then, a wide selection of distance metrics such as Euclidean distance and least squares can be used to calculate similarity27. These algorithms require feature engineering and a reference database to identify compounds. Several researchers report that the feature engineering approach is not robust28,29. Feature engineering is usually specific to a dataset and it cannot be easily applied across different datasets. Furthermore, it provides a gateway for human bias to be introduced in the model and it still requires a highly-skilled practitioner to analyse the results.

In contrast, supervised methods minimize the error between the predicted label and the ground truth label during training30. As such, they require a labeled corpus of data for the training. The algorithm extracts the features from the input spectrum. It then makes a prediction of the compound class based on these features. Subsequently, it quantifies the difference between the ground truth and the predicted value using a measure for similarity. This loss can then be optimized using different optimisation algorithms. Several researchers have applied traditional machine-learning (ML) techniques to classify Raman spectra31,32. Support vector machines (SVMs) were used with limited success33,34. Unfortunately, the performance of the SVMs deteriorates rapidly as the number of classes increases35.

Fully-connected dense network were recently applied to Raman spectra analysis36. However, dense networks are unable to extract features from the spectrum and have a large number of parameters leading to data overfit37. Researchers also explored the use of 1D CNNs to analyze Raman spectra35,38,39. Their results suggest that convolutional networks can accurately classify the spectra with minimal pre-processing treatment. An accuracy of 93.3% was reported on the pre-processed samples of the RRUFF dataset35,40. Building on these promising results, a two-step model was trained for identifying each compound from their spectra and then performing the identification of compounds from a mixture with a classification accuracy of 98.8%41. However, this approach is not scalable to a mixture of many compounds.

More recent transfer learning and data augmentation techniques are now widely used to reduce overfitting and improve the performance of the models42. Augmented spectral datasets were generated by adding various offsets, slopes and multiplications on the vertical axis43. Meanwhile, transfer learning was also performed by training the network on a spectral database and using the model to predict the observations from a different database44. This approach yields an accuracy of 88.4% for the unprocessed data and 94% for the processed data.

Raman spectrum analysis usually requires baseline correction prior to spectral matching. There is a wide range of methods for baseline correction, such as a least-squares polynomial curve fitting for the subtraction of the baseline45. The literature provides a comprehensive survey of baseline and correction methods46, and a comprehensive overview of the applications of convolutional neural networks to vibrational spectroscopy measurements46.

In this work, we implement a deep-learning convolutional model to identify compounds from their Raman spectra. Using this approach, we perform an experimental verification of the model using anatase and rutile TiO2 polymorphs.

The proposed model is an end-to-end framework, which does not require any additional proprietary pre-processing. To the best of our knowledge, this is the first model using a combination of Long Short Term Memory networks (LSTM)47 and convolutional neural networks (CNNs) for Raman spectra analysis. Most importantly, the ablation study indicates that LSTM incorporation leads to a significant improvement in classification accuracy. In time, we firmly believe such real-time machine learning-assisted compound identification and analysis will help rapidly and more accurately identify the mineral and chemical compounds.

Materials and methods

This section gives a brief overview of the various models used in the paper. The Fig. 1 presents a high-level overview of the methodology. The proposed model is trained using the Raman spectra from the database. The trained model takes a Raman spectrum as an input and identifies the mineral. We compare the model prediction against real world data to validate the model outcome. The section presents a detailed overview of the training and experimental methodology.

Figure 1
figure 1

Schematic overview of the process flow.

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Proposed model architecture

The input to the CNN in application to Raman spectrum classification is one dimensional and it contains the entire spectrum. Hence, we trained one dimensional convolutional kernel in our CNN. We use a ReLU activation for the convolutional layers:

$$f\left(x\right)\left\{\begin{array}{ll}x & \quad x\ge 0\\ 0 & \quad otherwise\end{array}\right.$$
(1)

The “Ablation studies” section will compare results using other activation functions. A convolutional layer can be expressed as follows:

$${y}^{j}=F\left({b}^{j}+\sigma {k}^{ij}*{x}^{j}\right)$$
(2)

where xi and yj are the ith input and jth output map, respectively. Kij is a convolutional kernel between the maps i and j, * denotes the convolution operator and bj is the bias parameter of the jth map. The convolutional layer is followed by a max-pooling layer, in which each neuron in the output map yi pools over an SXS non-overlapping region in the input map xi.

Formally, the max-pooling operation is described as:

$${y}_{j}^{i}= {\underset{0<m<s}{\mathrm{max}}}x_{j \cdot s+m}^{i}$$
(3)

The output of the max-pooling layer is fed to a Long Short-Term Memory (LSTM) layer to process the one-dimensional sequence. The LSTM network has a cell state, which can be used to remember the previous timestamp. The output of the LSTM is flattened and processed using fully-connected dense layers.

We use ReLU as the non-linear activation for the fully connected layers. The model has four 1D Convolutional layers with a kernel size of 2 and same padding. The max pooling layers have a pool size of 2 and a stride of 2. The SoftMax operates as a squashing function that re-normalises the K dimensional input vector z of real values to real values in the range [0,1] that sum to 1 specifically,

$$\sigma {\left(z\right)}_{j }= \frac{{e}_{j}^{z}}{\sigma {e}_{k}^{z}}$$
(4)

To avoid overfitting, we apply a dropout after the first and second fully-connected layer48. The block diagram in Fig. 2 shows the structure of the proposed network. A detailed description of the model and the hyperparameters is provided in the supplementary information in the section “Model Diagram”.

Figure 2
figure 2

Proposed Model Architecture. Dark coloured boxes indicate a ReLU activation function at the end of a convolution "conv" layer. The max-pooling operation is represented by the nomenclature "mp" and the fully connected dense layers are denoted by “fc”.

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Model training

The training of the model is performed using RMSProp algorithm49, which is a variant of the stochastic gradient descent using 100 epochs with learning rate of 1e -3 and β = 0.9. The layers are first initialised from a Gaussian distribution with a zero mean and variance equal to 0.05. The framework is implemented using the Tensorflow library version50. We use a Tesla T4 graphics processing unit (GPU) to run all experiments.

RRUFF dataset

The project uses the public RRUFF dataset40. The RRUFF project provides access to X-ray diffraction patterns, Raman spectroscopy, Fourier-transform infrared (FTIR) spectroscopy, references, photographs and characterization data of different minerals. The database is constantly reviewed and updated to ensure the quality and durability of data. The database contains the spectral information of 3527 (over 70%) of the 4985 known minerals. Public access is provided with reviewed and validated characterizations of 2128 of those minerals.

The dataset contains the Raw and baseline-corrected Raman spectra of mineral polymorphs. The Raman spectra of the minerals in the project are acquired using several spectrometers. Some of the spectrometers are: Downs spectrometer with 514 nm laser, Thermo Almega XR with 532 and 785 nm lasers, Kaiser Optical Systems HoloProbe 785 and a Renshaw microRaman system for work at 514.5 and 780 nm. Based on the quality of sample collection, the samples are divided into excellent, fair, poor and unrated. These are further divided by the orientation and the processing. A detailed description of the different splits has been provided in the supplementary information in the section “Analysis of RRUFF Dataset”.

Evaluation metrics

Classification models use true positives and false positives for precision and recall assessment:

$$Precision =\frac{True \; Positives}{True \; Positives+False \; Positives }$$
(5)
$$Recall = \frac{True \; Positives }{True \; Positives+False \; Negatives }$$
(6)

The Precision value indicates the model's positive predictive value or the ability to avoid false positives (here, this would mean predicting it is a given mineral when it is not). Meanwhile, the Recall value indicates the model's true positive rate or sensitivity or the ability to avoid false negatives (here, this would mean predicting it is not a given mineral when it is). Balancing the Precision and Recall in the context of a specific application is one of the main challenges facing any machine-learning developer51.

Methodology

We have used a training methodology to train the model and experimental evaluation to predict the TiO2 polymorphs from synthetized samples.

Training methodology

We first randomly divide the whole dataset into training (80%), validation (10%) and test (10%) sets. The stochastic gradient descent (SGD) optimizer is used for most of the experiments. Additional experiments were performed using the Adam and AdamW optimizers49. However, we find that a variant of SGD consistently produces the best results. The same behavior was previously reported in the literature52. The hyperparameters are fine-tuned for each model and the detailed list of hyperparameters associated with each model is provided in the supplementary section. We trained our model using various Convolutional network architectures and activation functions for comparison.

Experimental evaluation

TiO2 polymorphs play an essential role in diverse applications ranging from photo-catalysis to energy-harvesting53,54. Furthermore, researchers have shown that it is possible to have an enhanced room temperature photo conversion by utilising a defect-rich synthesis of TiO255. Rapid characterization of TiO2 polymorphs is crucial for several applications such as additive manufacturing56. To test our model using real data from our laboratory, we synthesized standard white anatase, defect rich anatase and rutile TiO2, by sol gel chemistry using a protocol described in the literature57. In this context, we can evaluate the performance of our model at predicting and identifying crystalline TiO2 phases in a real empirical scenario. We focus on the Top-5 model predictions for each experimental evaluation in the bar charts presented below. The high Top-5 accuracy of our model indicates that for most instances the correct mineral lies within the top 5 predictions of the model. The model outputs for all experiments are presented in detail in the Supplementary Information.

Processed dataset

In the real world, a Raman spectrum might be corrupted by a poor focus (when performed through a microscope), a fluorescence background (from the sample), CCD background noise (from the detector), Gaussian noise, stray-light cosmic noise (from the spectrometer)7. All these phenomena can distort the Raman spectrum. Whenever possible, it is essential to remove these undesirable artefacts in order to extract the best information. In addition to these corrections, it is sometimes necessary to correct for varying sampling geometries and highly redundant variables7. The RRUFF database provides both raw and processed data.

First, we train our model using the processed data for benchmark comparisons. This is consistent with the state-of-the-art, where researchers usually compare their model performances using the processed RRUFF data to evaluate their models. The processed RRUFF dataset has 5681 samples.

Raw dataset

Pre-processing the Raman spectrum is an essential part of the analysis process. The use of specialised software to pre-process the samples significantly increases the cost. Moreover, samples can be pre-processed separately by different experts leading to significant costs, delays and discrepancies from one expert to another. Also, this pre-processing is not versatile, prone to human errors and cannot be easily adapted to different environments. During pre-processing, information can be incorporated into or removed from the data, preventing generalization and hampering its performance. On the other hand, deep neural networks are data hungry and training the network on a larger dataset is often necessary to allow better generalization of the model58.

We added a processing step in our framework to treat the raw data before passing it into the neural network. We first use the Savitzky Golay filter59 to remove the noise from the sample and subsequently, use penalized least square method for subtracting the background noise60. This enables the use of raw oriented samples available in the RRUFF dataset for additional training. Thus, we can directly identify the compounds from the raw spectra without using any additional expert guided proprietary data pre-processing. Figure 3 shows a typical example of pre-processing the raw data using Savitzky Golay filter and background subtraction using penalized least squares. The processed data does not suffer from the effects of the noise and fluorescence.

Figure 3
figure 3

The effect of processing the raw data using Savitzky Golay filter and background subtraction using penalized least squares. The processed data does not suffer from the effects of the noise and fluorescence.

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Synthesis of experimental samples

For the experimental evaluation, first we synthesize the mineral samples as per the methodology described below. Subsequently, we obtain our own Raman spectroscopy results from the synthesized samples using the WITec Alpha 300 confocal Raman microscope using a 532 nm laser excitation through a 10× microscope objective. The software provides a series of correction features. We first remove the cosmic ray noise and then the harmonic peaks. Subsequently, we perform background (baseline) subtraction. We repeat the same processing for each of the individual samples.

Synthesis of standard white anatase

To prepare the standard white anatase, we mix 28.8532 g of ethanol (Sigma-Aldrich 493511) with 10.8604 g of titanium (IV) butoxide (Sigma-Aldrich 244112). This solution is stirred for 40 min. Then, the hydrolysis reaction is triggered by adding 0.84 mL of deionized water. The precipitation of the amorphous white TiO2 occurs within the first few seconds after the reaction is triggered. This mixture is aged for 72 h and then the solvent is evaporated at ambient temperature. The amorphous TiO2 powder is annealed at 550 °C for two hours to yield standard white anatase. In the same way, rutile crystalline phase is obtained by annealing the amorphous TiO2 at 1100 °C for 2 h.

Synthesis of defect-rich black anatase

To prepare the defect-rich black anatase, 28.9024 g of ethanol (Sigma-Aldrich 493511) are mixed with 1.4748 g of acetylacetone (Sigma-Aldrich 10916). This solution is stirred for 20 min. Then, 10.8512 g of titanium (IV) butoxide (Sigma-Aldrich 244112) are added and stirred for 40 min more. The hydrolysis reaction is triggered by adding dropwise 0.84 mL of deionized water. This solution is covered with parafilm to restrict the income of air and avoid contamination. Finally, the resulting mixture is stirred for 120 min and then aged for 8 months. During the aging time, the ethanol evaporates to precipitate a defect-rich TiO2 amorphous powder.

These defect-rich TiO2 amorphous powders are annealed at 450 °C for 2 h to obtain defect-rich black anatase. In the same way, modified rutile crystalline phase is obtained by annealing at 1100 °C for 2 h.

Commercial Degussa TiO2 powder

Degussa TiO2 (Sigma-Aldrich 634662) was purchased and used as received. The crystalline composition of Degussa is typically around 78% anatase, 14% rutile and around 8% of amorphous TiO261.

Results and discussions

The results in the Table 1 show that our method can accurately identify pure compounds from the Raman spectra. The cited metrics reported in the Table are based on the processed spectra in the “excellent oriented” and “excellent unoriented” subsets of the RRUFF database. Furthermore, the cited authors have split the dataset based on the number of samples in the same category. When deploying the model in a real-world scenario, it is likely to expect that the dataset will contain a mix of different data qualities. Thus, we have reported the results on a mix of excellent, fair, poor and unrated oriented processed spectra without any segmentation. Most importantly, our model is able to achieve a similar accuracy on the un-processed data. Compared with the state-of-the-art, our proposed model achieves an increase in accuracy of 2% in Top-1 accuracy. Indeed, the model achieves a Top-1 accuracy of 99.12% and a Top-5 accuracy of 99.30%.

Table 1 The table benchmarks our model against the state-of-the-art models from the literature.
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The Top-5 accuracy metric indicates that the correct mineral is 99.30% of the time in the five (5) most likely candidates identified by the model. The Top-1 accuracy metric indicates that the correct mineral is 99.12% the most probable candidate identified by the model. In this case, the Top-1 accuracy is obviously equal to the recall value, while the precision value is slightly higher at 99.30%. As should be expected, the raw unprocessed data yield a similar Top-5 accuracy of 99.31% but a slightly lower Top-1 accuracy of 98.61%.

The results clearly show that our model is able to identify the compounds from their Raman spectra. The training dataset includes multiple spectra to characterize the same mineral. These spectra have been acquired by different operators at different institutes, using different instruments, environments and sample preparation conditions. This makes the model resilient to minor changes in the pattern and makes the model generalize to the test data.

Misclassification

There are a few cases where the model is not able to accurately identify a compound. In this section, we will investigate these rare instances in further details to better understand the mechanisms involved. These misclassifications almost exclusively occur when the model associates a low probability with all the predictions. This suggests that the model is confused as it shows a low level of confidence in its prediction. To mitigate these cases, we suggest that the users conduct an expert evaluation when the model yields a low probability.

We also believe that increasing the training data by including a wider variety of minerals will mitigate this type of misclassification. This may be also caused by a spectrum which was not acquired using optimal parameters. Often in such cases, the correct prediction is amongst the list of prediction albeit with a low probability. This is consistent with measuring a Top-5 accuracy (99.30%) slightly higher than the Top-1 accuracy (99.12%).

However, there are some very rare instances where our model associated a high probability (suggesting a high level of confidence) to an incorrect prediction. This usually indicates a generalization problem, where the distribution of the test samples is very similar to the distribution of another sample in the training data65. In layman’s terms, this occurs when the distribution of a given test spectra is very similar to a different mineral from a training spectrum. For example, this can occur if we have a single low-quality Raman spectrum (very noisy or where the crystal structure is not clearly defined) present in the dataset. Impurities in the sample may also lead to shifts in the peak or changes in distribution, thus affecting the model. We have provided a specific example of such a misclassification error in the supplementary information, which is consistent with this interpretation.

Ablation studies

The following section presents ablation studies performed on the different constituents of the model. An ablation consists in removing and/or modifying certain components of the model and observing the effect on the model performances.

LSTM module

LSTMs are widely used in the literature to analyse time-series data66. It helps the model extract features from sequential datasets. In our model, LSTM works in the latent space across feature maps. We observe a significant drop of 2.29% in Top-1 accuracy if we remove the LSTM module altogether (CNN1D). Therefore, the LSTM module is crucial for improving the model performance. However, we observe that using a Bidirectional LSTM (CNN-BiLSTM) leads to a major deterioration in performances. This can be intuitively expected because the ordering and distribution of the peaks defines the Raman spectrum. We also stacked multiple LSTM layers (CNN-2LSTM), which also leads to a significant reduction in performances. The addition of layers adds levels of abstraction of input observations over time, which may lead to grouping similar observations over time67. This can confuse the model between similar spectra and is detrimental to the performance of the model. The Table 2 compares the results using different LSTM architectures or no LSTM at all (CNN1D).

Table 2 The table compares the performance using different or no LSTM architectures.
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Activation function

We also compare the performances of the model using different activation functions. We change the activation function for the convolutional layer and dense layers. We observe that using a ReLU activation function gives the highest accuracy. As per our observations, the Tanh, LeakyRelu, Selu, Swish and GeLU activation functions all show lower performances compared to the ReLU activation. Very interestingly, we get a significant performance degradation using the sigmoid activation function. Since the derivative of the sigmoid function is always less than one, we believe multiplying the gradient across layers may diminish the signal and create a vanishing gradient problem68. The Table 3 compares the model performance using different activation functions.

Table 3 The table compares the performance of different activation functions.
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Experimental outcomes

The Fig. 4a,b shows the predictions from the model. Our model correctly identifies both anatase (Fig. 4a) and rutile (Fig. 4b) from our pure samples with a high degree of confidence. It yields a 80.24% percent confidence for the rutile TiO2 sample, compared with 99.99% for the anatase TiO2 sample.

Figure 4
figure 4

(a) The figure shows the response of the model to our synthesized anatase TiO2 sample. The model can identify the presence of anatase with utmost certainty. (b) The figure shows the response of the model to our rutile TiO2 sample. The model correctly identifies Rutile with a high degree of confidence. The Raman spectrum of the mineral and the image of the sample are presented to provide adequate context. The bar chart shows the Top-5 predictions and the other predictions are combined as others.

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The presence of surface defects on the crystalline lattice of black anatase shifts the Raman spectrum56. This presents an interesting challenge for the model. We find that the model is able to identify Anatase in the modified Spectrum. Moreover, it assigns a lower probability to the presence of Anatase which may indicate the presence of defects in the crystalline structure. It is pertinent to point out that even though the model was not exposed to the modified spectrum of black anatase during training, the model is able to recognise it as Anatase. This demonstrates an ability of the model to generalise. The Fig. 5a–e shows the prediction of the model given the spectrum of black anatase and presents a comparative view of the Raman spectra.

Figure 5
figure 5

(a) The figure shows the response of the model to defect-rich black Anatase. (b–e) shows a detailed comparative view of the four main peaks in the Raman spectra of defect rich black Anatase and Standard white Anatase. The model correctly identifies Anatase in the modified spectra with a slightly lower level of confidence. The ability of the model to correctly characterise the modified spectrum shows the generalisation power of the model. The Raman spectrum of the mineral and the image of the sample are presented to provide adequate context. The bar chart shows the Top-5 predictions and the other predictions are combined as others.

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We also wanted to evaluate our model’s ability to recognize the differences in crystalline structure for TiO2 in an intermediate phase between anatase and rutile. To do so, a sample was prepared by annealing at 800 °C. The TiO2 fully converts from anatase to rutile at 1100 °C. At 800 °C, the crystalline structure resembles rutile, but the conversion is not complete69. The Fig. 6a shows the measurements for rutile TiO2 annealed below the full-conversion temperature. Here, the model still predicts rutile but with a lower confidence level since the Raman spectrum is significantly different from the fully-converted rutile. As such, we believe that the probability value could potentially be also be used as an indicator for impurities and defects in the crystal structure. However, this would require more extensive studies well beyond the scope of this work.

Figure 6
figure 6

(a) The figure shows the response of the model to TiO2 at 800 °C, below the 1100 °C temperature allowing full-conversion to rutile. The model still identifies rutile with a confidence of 49.59% suggesting an intermediate state with incomplete conversion. (b) The figure shows the response of the model to Degussa, P25. Degussa contains more than 70% anatase and around 20% rutile and amorphous compounds. The model can identify anatase with a lower confidence (86.71%). The Raman spectrum of the mineral and the image of the sample are presented to provide adequate context. The bar chart shows the top 5 predictions and the other predictions are combined as others.

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Finally, commercial Degussa (Evonik) P25, Aeroxide TiO2 is a titania photocatalyst that is widely used because of its relatively high levels of activity in many photocatalytic reactions systems70. The literature shows that this P25 contains more than 70% anatase TiO2, with significantly lower amounts of rutile and amorphous TiO2 powders61. Figure 6b indicates a dominant anatase Raman structure, with some contributions of the rutile TiO2 with peaks around 445 cm−1 and 611 cm−1. Accordingly, our model successfully detects the dominant anatase TiO2 in the commercial P25 powder. However, the small features at 200 cm−1 and 450 cm−1 are consistent with the presence of much smaller concentrations of rutile TiO2 powder. As a result, the model detects anatase with a lower confidence (86.71%). However, our model is unable to detect the presence of rutile in the spectrum. Once again, we believe that future studies could exploit this lower probability and use it as a good indicator to detect the presence of contaminants or defects in the pure compound.

Neophytes sometime describe neural networks as black-box models. However, we believe that it is important to look under the hood to achieve a deeper understanding and visualize the patterns recognized by the neural network. Feature maps have been previously used to visualize the representations learned by the neural network71. We plot the feature maps learned by our model at each layer to show the progression of features learned by the model while analysing the spectrum of our pure white anatase powder sample. Figure 7 shows that initially the model faintly recognizes the high intensity peak at 150 cm−1. However, as we go deeper, the model learns to recognize the other peaks. This enables the model to correctly identify the compound with a higher confidence. The feature maps for all the layers of the proposed model are provided in the supplementary information.

Figure 7
figure 7

The figures shows the feature maps learned by the model while analysing the Raman spectrum of white anatase powder annealed at 500 °C. The initial layers recognise a faint representation of the high intensity peak at 150 cm−1. However, deeper layers help clearly recognize the other peaks.

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To further investigate the effect of noise and integration time on the model's performance, we conduct a sensitivity analysis as described in the following section.

Sensitivity analysis

Performing high-quality Raman micro-spectroscopy analysis on our WITec instrument requires a relatively-high level of expertise to optimize the different instrument and software parameters. This high-end equipment allows the expert to adjust the spectrum by controlling a wide range of parameters. For our sensitivity analysis, we fixed the accumulations at 100 scans and varied the integration time and intensity. The integration time defines how long the spectrometer's detector collects light. The longer the integration time, the stronger the signal. However, an excessively long integration time may cause the detector to saturate, which can result in clipping of the peak and spectrum distortion. The same goes for the stray light entering the spectrometer.

We acquired the Raman spectrum for both the pure anatase and rutile samples at three integration times, namely 1 s, 5 s and 10 s. As expected, we observe that the signal-to-noise ratio (SNR) in the spectrum decreases as we reduce the integration time. Even for the 10 s integration time, we did not observe any saturation at the detector.

The intensity of the laser can also be varied by varying the built-in variable attenuator. For the analysis, we experimented with different intensities and found that fixing the attenuator to a lower excitation power setting results in a noisy spectrum. If we gradually increase the excitation power, we can observe a much cleaner spectrum with a higher signal-to-noise (SNR). The Fig. 8 shows the effect of varying the integration time and excitation power density on the Raman spectrum of our pure white anatase sample. The detailed results of the sensitivity analysis are provided in the supplementary information.

Figure 8
figure 8

The figure shows the anatase spectrum at different excitation power densities and different integration times. Increasing integration time and the incident excitation power improves the SNR, which improves the spectrum’s quality.

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There, we observe that the model is far less robust to high noise levels. We observe that reducing the SNR by significantly reducing the excitation power density or the integration time directly leads to lower confidence or even incorrect predictions. We believe that excessive noise reduces the uniqueness of the spectrum, thus increasing the level of confusion for the model. We have presented a study of the misclassification of the noisy Raman Spectrum of the Anatase polymorph in the supplementary information. Several researchers have studied the use of machine learning models for improving the signal-to-noise ratio of the Raman spectrum72,73. We believe that the use of these models in conjunction with our proposed model will address the above-mentioned challenge.

In contrast, we also observe that increasing the SNR significantly helps the model correctly identify the sample. Thus, users of our model are recommended to ensure that the acquisition of the sample is done at optimal excitation power densities and integration times. Most experienced material scientists, chemists and chemical engineers regularly use complementary material characterization tools such as FTIR or XRD to correctly identify compounds. In the near future, we believe that the proposed deep-learning approach could potentially be augmented by adding information from FTIR or XRD for identifying the compounds with even better accuracy using fully-automated multi-modal analysis.

Conclusion

This paper presents a deep-learning framework to accurately identify the mineral compounds from their Raman spectra. Our proposed framework can accurately identify both raw and pre-processed Raman data. The model is lightweight and can achieve a Top-1 accuracy reaching 99.12% on the test samples. Experimental evaluation was also performed using TiO2 powders. For the experimental validation in the laboratory, we synthesized white anatase and rutile using standard procedures from the literature. The model was able to accurately identify both polymorphs from the Raman spectrum.

Furthermore, we evaluated the model for more complex TiO2 samples such as intermediate phases obtained with a lower annealing temperature (so-called mixed-phase TiO2). The TiO2 powder in an intermediate (mixed) phase was correctly identified as rutile with a lower confidence (probability). With more extensive work, we believe that the lower probability can be potentially used as a quantitative indicator to evaluate the presence of surface defects or impurities in more complex samples.

We also carried out extensive ablation studies by modifying/removing components of the model. We observe that the proposed architecture with the LSTM module and ReLU activation function clearly provides the best performances. We also evaluated the performances of the model using noisy data, obtained by varying the integration time and excitation power density during acquisition of the Raman spectra. We find that our model performs best with low-noise samples. Therefore, optimizing the excitation power and the integration time significantly helps the model correctly identify the compounds from the Raman data. While we believe it provides a major breakthrough in the analysis of complex materials and compounds, we believe that leveraging information from other characterization techniques (multimodal analysis) could further increase the model’s performance and remove most misclassification issues.