Silicate Mineralogy from Vis–NIR Reflectance Spectra

The asteroid composition is the key to understanding the origin and evolution of the solar system. The composition is imprinted at specific wavelengths of the asteroid reflectance spectra. We wish to find the optimal wavelength range and step of reflectance spectra that contain sufficient information about S-complex asteroids while keeping the data volume as low as possible. We especially aim for the ASPECT instrument on board the Milani/Hera CubeSat that will observe the S-complex binary asteroid (65803) Didymos–Dimorphos. We use labeled reflectance spectra of the most common silicate found in meteorites, namely olivine, orthopyroxene, clinopyroxene, and their mixtures. The spectra are interpolated to various wavelength grids. We use convolutional neural networks and train them with the labeled interpolated reflectance spectra. The reliability of the network outputs is evaluated using standard regression metrics. We do not find any significant dependence between the error of the model predictions and normalization position, fineness of coverage within the 1 μm band, and wavelength step up to 50 nm. High-precision predictions of the olivine and orthopyroxene modal abundances are obtained using spectra that cover wavelengths from 750 to 1050 nm and from 750 to 1250 nm, respectively. For high-precision predictions of the olivine chemical composition, the spectra should cover wavelengths from 750 to 1550 nm. The orthopyroxene chemical composition can be estimated from spectra that cover wavelengths from 750 to 1350 nm. We design a simple web interface through which everybody can use the pretrained models.


Introduction
Asteroids are old remnant debris from the formation of the solar system.Except for a few meteorites linked to specific asteroids, we have only a few samples from asteroid surfaces, namely from (25143) Itokawa (Nakamura et al. 2011), (162173) Ryugu (Morota et al. 2020), and (101955) Bennu (Lauretta et al. 2017).Therefore, the composition of asteroids is typically estimated using remote sensing that includes reflectance spectroscopy.In this study, we focus on dry-silicate asteroids with the diagnostic absorption bands of olivine and pyroxene in their visible to near-infrared (Vis-NIR) reflectance spectrum forming the S-complex in the Buss-DeMeo taxonomy system (DeMeo et al. 2009).Olivine exhibits three major absorption bands around 1 μm (Burns 1970), while pyroxene exhibits two major absorption bands around 1 and 2 μm and one minor band around 1.2 μm (Adams 1974).The positions and integrated band areas of these characteristic absorptions correlate with both the olivine-to-pyroxene ratio and the olivine Fe-Mg and pyroxene Fe-Mg-Ca compositions (e.g., Cloutis et al. 1986;Gaffey et al. 2002;Burbine et al. 2003;Reddy et al. 2015).Spectrum unmixing is a highly nonlinear difficult task.Therefore, the widely used methods to derive silicate material compositions are based on empirical correlations with the above-mentioned spectral parameters and are typically only optimized for a narrow composition range.
More general empirical relations can be searched using deep learning.Artificial neural networks (ANN; Goodfellow et al. 2016) are purely mathematical empirical models without physical constraints.They consist of layers of neurons where each neuron performs a linear transformation of its inputs, followed by a simple nonlinear transformation.The coefficients of the linear transformation are set to approximate a dependence between the input data and output results.Therefore, the neural networks are adapted to specific input data without any constraints on them.This makes the neural networks very flexible in searching for complex dependences, such as between reflectance values and mineralogy (Korda et al. 2023a(Korda et al. , 2023b) ) or taxonomy classes (Klimczak et al. 2022;Penttilä et al. 2022).
In this work, we test how variations in the spectral grid affect the ANN reliability to identify mineral composition.For this purpose, we created multiple spectral grids that vary in their spectral range, step, and resolution. 5The aim is to characterize the error in an ANN-derived composition as a function of different grids.The knowledge of the error-grid dependence is important for searching for an optimal solution for the required spectrum grid and associated data volume based on uncertainty requirements.
Additionally, we also imitate the wavelength grid and resolution of the ASPECT instrument.The ASPECT is a hyperspectral imager on board the Milani CubeSat, which is a part of the Hera mission (Michel et al. 2022).The instrument Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
will observe the binary asteroid (65803) Didymos-Dimorphos using three imaging channels that cover the Vis-NIR wavelengths from 650 to 1600 nm (ca.42 spectral bands) and one single-point channel that covers the short-wave infrared (SWIR) wavelengths from 1650 to 2500 nm (ca.30 spectral bands).All channels have a configurable step that is targeted between 25 and 35 nm.The expected ASPECT signal-to-noise ratio is higher than 50.
The ANN models for selected grids are freely accessible through a simple web interface. 6The frozen Python scripts that we used for this work can be downloaded from the Zenodo repository (Korda & Kohout 2024).Related data and metadata files and possible script updates are accessible in the GitHub repository7 as version v3.0 and higher.

Data
The neural-network models were trained using the reflectance spectra discussed in Korda et al. (2023b; see their Section 2 and Appendix A for details).Namely, we used 510 reflectance spectra of olivine (OL), orthopyroxene (OPX), clinopyroxene (CPX), and their mixtures.Most of the spectra are from the RELAB8 and C-Tape9 databases.The spectra cover wavelengths from 450 to 2450 nm, and the sample compositions are documented (for details about the samples, see Sample_Catalogue.xlsx in the datasets folder in the GitHub repository).
From the spectra, we created the following grids.
(1) First, we tested the effect of the reduction in spectral range.The spectra were truncated stepwise from both sides by 100 nm at a time (e.g., 450-2450 nm, 450-2350 nm, or 550-2450 nm) and were reinterpolated to a 10 nm step (210 unique grids in total).We note that due to the reduction in the spectral range, we were not able to perform a spectral normalization at a unique wavelength for all grids.Thus, we also tested how different wavelength positions at which we normalized the spectra affect the ANN results.This test was made using a range from 450 to 2450 nm with a step of 10 nm and a normalization wavelength shift by 100 nm (21 cases).(2) Second, we tested the effect of increasing the spectral step.We used two ranges, one range from 650 to 1850 nm, covering only the 1 μm band, and the other range from 650 to 2450 nm, covering the 1 μm and 2 μm bands.For these two ranges, we varied the step from 10 to 50 nm with a shift of 10 nm (10 unique grids in total).(3) Third, we tested whether a denser step over a particular interval increased the AAN precision with an otherwise coarse grid.We selected the wavelength range from 600 to 1600 nm and used a step of 40 nm.In this grid, we included a 200 nm wide sliding window with a double-dense step (20 nm).We shifted the window every 40 nm within the spectral range (21 unique grids in total).We note that this test is intended to simulate the configurable step of the ASPECT spectrometer within the range of its imaging channels.(4) Fourth, we replaced the simple delta-like transmission function applied in the above-mentioned tests with a Gaussian approximation of the ASPECT transmission profiles for each channel to emulate the actual ASPECT resolution.We tested the imaging channels alone (range from 650 to 1600 nm), as well as all four channels including the single-point SWIR (range from 650 to 2450 nm).For each channel, we selected steps from 10 to 50 nm with a shift of 10 nm (10 unique grids in total).The used grids are summarized in Table 1.

Neural Network
We used artificial neural networks to derive the silicate mineral composition from the reflectance spectra.The neuralnetwork models have a layered structure.Each layer performs a linear combination of its inputs h followed by a simple nonlinear operation in the form = , where o is the layer output, f is the nonlinear function, and W and b are the coefficients of the linear transformation.For each layer, the nonlinear function is fixed and W and b are set to optimize the mapping between the inputs and outputs.The inputs of the first layer are the reflectance spectra, and the outputs of the last layer are olivine, orthopyroxene, and clinopyroxene relative volumetric modal abundances and chemical compositions represented by the mineral end-members.We note that the olivine abundance equals one minus the sum of the pyroxene abundances as a consequence of the normalization of the modal abundances.
For the specific description of the model architecture, training, and configuration selection, we refer to our previous works (Korda et al. 2023a(Korda et al. , 2023b)).In these works, we intensively tested the model configuration (hyperparameters) and found a model with a nearly optimal capacity that can be used for various wavelength grids.For this work, we did not conduct any further hyperparameter search and adopted this two-hidden-layer convolutional model with 24 and 8 kernels in the first and second hidden layers, respectively.The first convolutional layer searches for the 24 most discriminant local features in the reflectance spectra.The features are found during the model training.The features are usually lines with different slopes that indicate different local gradients in reflectance around absorption bands, or V-shape curves that indicate the band centers.The second convolution layer searches for more complex features within the previous 24 feature vectors.Finally, the vectors of the complex features are combined into the predicted mineralogical parameters.

Results
We trained the neural-network models using silicate reflectance spectra interpolated to various grids.The modelpredicted composition was compared against the known composition to quantify the ANN error.For comparison, we selected two metrics, (1) the standard root-mean-square error (RMSE) metric, and (2) the "within-10-pp error" metric, indicating the fraction of predictions that are within a 10percentage-point (pp) absolute error.Before the metric evaluation, we removed orthopyroxene-clinopyroxene outliers.An outlier is defined as a sample with at least 95 vol% of pyroxene for which the predicted modal composition of orthopyroxene or clinopyroxene is more than 40 pp away from the actual value, and their presence is related to the high similarity of orthopyroxene and clinopyroxene spectra in certain rangerestricted grids.The number of outliers for a given wavelength grid seems to be constant, with a small stochastic variation.For wavelength grids that cover the range from 750 to 1050 nm at least, the number of outliers in our models is between 5% and 10% of the total pyroxene-dominated samples.We note that all of the outliers in all of the presented models were binary mixtures of orthopyroxene and clinopyroxene alone.The outliers removal is necessary to eliminate the stochasticity that highly affects the RMSE metric, so that only the variations in the metrics are detected that are related to variations in the grids.
We computed the metrics using a k-fold procedure.In the kfold, one splits the data into k equal-size parts.Subsequently, the k − 1 parts are used to train a model, and the remaining test part is evaluated.The test part is unknown for the trained model and represents new data.This is repeated k times, so all data are finally evaluated as test data.We selected k = 20 as a compromise between the approximation of accuracy metrics and computational complexity.We note that all the presented results are based on the evaluation of the test data alone and can be considered as how well the models generalize to unknown data.Additionally, we estimated the model-to-model variations caused by the stochastic training of the models.The mean and standard deviation (1σ estimate) of the RMSE and within-10pp error metrics are summarized in Table 4.The metrics were computed from predictions of 10 models evaluated using k-fold with k = 20 each.For the training of these models, we used spectra ranging from 450 to 2450 nm with a step of 10 nm.We note that the model precision is good enough to match ordinary chondrite meteorites, but it can only statistically distinguish between their subtypes H, L, and LL.

Normalization Test
Before we proceeded with the grid tests, we tested the sensitivity of our models to the normalization wavelength selection of the input reflectance spectra.The RMSE values for all quantities are plotted in Figure 1.On average, the best and worst normalization wavelengths are at 650 nm (the overall RMSE is 5.4 pp) and at 1050 nm (the overall RMSE is 6.5 pp), respectively, with an average RMSE value of 6.0 pp for all studied parameters combined.For individual parameters, the average RMSE varies between 4.9 pp for Fs (OPX) and 7.0 pp for orthopyroxene modal abundance.The within-10-pp error metric (see Figure 7) is best at 650 nm normalization, with 92.8% of the data within the limit, and it is worst at 950 nm normalization, with 89.1% of the data within the limit.

Range Test
In this test, we varied the wavelength range of the spectra while keeping the 10 nm step.We present the results in the form of matrix plots of the start and end wavelength values.In the matrix plots, we emphasize several regions using dashed color boxes.The box definitions are summarized in Table 2.The numerical results for a few selected wavelength ranges are summarized in Table 3.With this test, we predominantly concentrate on olivine and orthopyroxene as the two most abundant minerals observed in S-complex asteroid spectra.The clinopyroxene metrics are affected by biases (Korda et al.  2023a, 2023b) due to its overall low abundance and lack of a wide range of training data.The plots for clinopyroxene and the within-10-pp error metric can be found in Appendix B. We note that in Appendix B, we show also line versions of the matrix plots.

Olivine Abundance
In Figures 2(a) and 11(a), we show how different wavelength ranges affect the predicted modal abundances of olivine.As seen in the plots, there is a sharp boundary between the models that cover the whole 1 μm band and the models that do not have information about the blue shoulder of the band, with the models without a coverage of the blue shoulder being considerably less precise.On the other hand, when the models only cover the blue shoulder of the 1 μm band including its band center (the dashed blue boxes in the figures), their results are almost as precise as the results of the models that cover the whole 1 μm band (the dashed brown boxes in the figures).We recall that the metric values of the olivine abundance equals the metric values of the total pyroxene abundance.Therefore, we obtain a precise olivine-to-pyroxene ratio for a wavelength grid that covers the wavelengths from 750 nm and lower to 1050 nm and higher, and the 2 μm band is superfluous (compare the dashed blue and magenta boxes).

Orthopyroxene Abundance
In addition to the olivine-to-pyroxene ratio, the models also distinguish between orthopyroxene and clinopyroxene.The Note.Depending on the range, the expected uncertainty estimates for the metrics are comparable to or higher than the model-to-model variations (see Table 4).From the test, it seems that the coverage of at least one shoulder of the 1 μm band is enough to disentangle orthopyroxene and clinopyroxene (compare the dashed blue, red, and brown boxes in the figures).The 2 μm band coverage adds only a little additional information and does not significantly improve the metrics (see the dashed magenta boxes in the figures).

Olivine Composition
The olivine Fe-Mg composition is fully defined by the fayalite number Fa.The corresponding metric plots are shown in Figures 3(a) and 12(a).The metrics indicate that a simple 1 μm band center position (BIC) is not enough for our models (see the dashed yellow boxes in the figures).The results are precise when the spectra cover the whole band, including its redmost shoulder, i.e., from 750 nm and lower to 1550 nm and higher (the dashed brown boxes in the figures).When the blue shoulder of the band is not fully covered, one can obtain a reasonable estimate from the red shoulder of the band (within the spectrum range from between 850 and 1150 nm to 1550 nm and larger; see the dashed red boxes in the figures).The fayalite metrics are slowly worsening as the minimum wavelength is shifted toward higher values, with an abrupt increase at the 1250 nm starting wavelength.

Orthopyroxene Composition
The low-Ca orthopyroxene Fe-Mg composition is defined by the ferrosilite number Fs (OPX).The metrics for the orthopyroxene composition are plotted in Figures 3(b) and 12(b).The metrics show that the coverage of the whole 1 μm band is important for a high-precision model prediction (compare the dashed brown boxes with models just right of them).The model precision further improves when the models cover the 1.2 μm band and the blue shoulder of the 2 μm band (see the color gradient between the dashed brown and magenta boxes in the figures).Finally, the best results are obtained when the models cover all three absorption bands.We note that the models that only cover the 1 μm band center (the dashed yellow boxes in the figures) or the 2 μm band center (BIIC; the dashed black boxes in the figures) are significantly less precise than the previously mentioned models.Therefore, the coverage of the 1 μm band region, i.e., from 750 nm and lower to 1350 nm and higher, is a necessary condition to obtain a highprecision orthopyroxene composition.

Step Test
In this test, we interpolated spectra with wavelength steps varying from 10 to 50 nm.The RMSE of the model predictions is shown in Figure 4.Even though there are often clear trends of increasing RMSE with increasing wavelength step, the differences are always small in amplitude.On average, the 650-1850 nm and 650-2450 nm grids have an RMSE between 6.9 and 7.4 pp.The highest RMSE increase (as the slope of the linear fit) equals 0.21 pp per 10 nm step increase [Fs (CPX); 650-2450 nm].Therefore, the maximum RMSE penalty related to the step coarsening from 10 to 50 nm is 0.9 pp.The within-10-pp error metric (see Figure 14) shows similar results.On average, its values are between 86.9% and 89.7% for the 650-1850 nm and 650-2450 nm grids.The highest metric decrease equals −0.84 pp per 10 nm step increase [En (CPX); 650-2450 nm] giving a maximum negative penalty of −3.4 pp from the 10 nm step to the 50 nm step.

Dense Sliding-window Test
In this test, we took spectra covering the whole 1 μm band with a coarse 40 nm step and inserted a denser 200 nm wide sliding window of a denser 20 nm step.The RMSE of the model predictions is plotted in Figure 5. On average, the best and worst window positions are between 640 and 840 nm (the overall RMSE is 6.6 pp) and between 1200 and 1400 nm (the overall RMSE is 7.2 pp), respectively.The window-positionaveraged RMSE value for all quantities is 6.9 pp and between 6.2 pp (olivine abundance) and 7.5 pp (clinopyroxene abundance).The differences in the within-10-pp error metric are small as well (see Figure 15).The best window position is between 920 and 1120 nm (89.3% of the data within the limit), and the worst is between 1200 and 1400 nm (87.0% of the data within the limit).

Step Test with ASPECT Resolution
In the last test, we imitated the ASPECT observations with variable wavelength steps from 10 to 50 nm.The results from this test can be directly compared to the results from Section 4.3.The RMSE of the model predictions is plotted in Figure 4.The approximate step of the ASPECT is highlighted using larger points.Similarly to the test in Section 4.3, there are lowamplitude trends of an increasing RMSE with increasing step.On average, the ASPECT 650-1600 nm (imaging channels alone) and ASPECT 650-2450 nm (imaging and single-point channels) grids have an RMSE between 7.4 and 8.6 pp.The highest RMSE increase equals 0.35 pp per 10 nm step increase [Fs (OPX); ASPECT 650-1600 nm], so the maximum RMSE penalty due to the step coarsening from 10 to 50 nm is 1.4 pp.The within-10-pp error metric is shown in Figure 14.On average, the ASPECT 650-1600 nm and ASPECT 650-2450 nm grids have metric values between 82.8% and 86.9%.The highest metric decrease equals −1.3 pp per 10 nm step increase [Wo (CPX); ASPECT 600-1600 nm], giving a maximum negative penalty of −5.3 pp from a 10 nm step to a 50 nm step.In most of the cases, the metrics for the non-ASPECT resolution spectra indicate a higher precision.

Discussion
The standard empirical relations state that (1) the olivine-topyroxene ratio is a function of the 1 μm and 2 μm band areas (Cloutis et al. 1986;Burbine et al. 2003;Dunn et al. 2010) Adams 1974;Cloutis 1985).In other words, the olivine-topyroxene ratio can be computed for a spectrum that covers the two major bands, while the 1 μm band alone is sufficient for the olivine and pyroxene compositions.
These assumptions are only partially confirmed by our models.Surprisingly, a high precision of the model-predicted olivine-to-pyroxene ratio can be achieved for spectra that only cover the blue shoulder of the 1 μm band.The additional information coming from the 2 μm band does not significantly improve the predictions.The reason may be that the models distinguish different olivine and pyroxene contributions to the shape of the 1 μm band, where olivine contributes more to its width and pyroxene contributes more to its depth.Moreover, the band-area relation assumes that a sample has a restricted range of the olivine-to-pyroxene ratio, but this information is often not known in advance.The exact range of the composition ratio is hard to define because different authors provided different relations (see, e.g., Figure 1 in Dunn et al. 2010).If we filter only such samples for which the olivine-topyroxene ratio is within the model assumptions (in the modeloptimized range), then the RMSEs of the standard empirical relations are 15.1 pp for Cloutis et al. (1986), 12.2 pp for Burbine et al. (2003), and 11.1 pp for Dunn et al. (2010).Without the ratio assumption, the RMSEs are between 33 and 38 pp.The worsening is related to the high portion of pure olivine and pyroxene samples in our data (71% of the total samples).Our model gives good results already with only a narrow spectral range from about 750 to about 1050 nm and gives valid results for any olivine-pyroxene ratio, from pure olivine to pure pyroxene.
The three olivine absorption bands become more pronounced as the iron content in olivine increases.The most significant observed changes are in the position and width of the bands, especially for the redmost band.For this reason, the overall band center can be used alone to estimate the iron content in olivine, but the overall band shape carries much more precise information.We observe this effect on the model predictions as well.The model trained with spectra that cover the combined 1 μm band minimum has an RMSE of ≈12 pp (wavelength range from 950 to 1250 nm).When the whole 1 μm band is included, the error decreases to ≈6 pp, and when only the red shoulder of the 1 μm band is covered, the error is ≈8 pp.We note that using the equation from Dunn et al. (2010) and using only samples whose fayalite number fulfills 17 < Fa < 31, the RMSE equals 6.5 pp.Including data outside this range, the RMSE rises to 21 pp.The result with the restricted fayalite number has a precision comparable to our ANN model.The ANN model, however, is valid for any fayalite number larger than 3 (minimum of our data set), but the detection of absorption bands might be the limiting factor.
In the case of orthopyroxene composition, the model behaves as expected from the empirical relations.The key region in the spectrum is the 1 μm band.The 1 μm band gives us an orthopyroxene composition estimate with an RMSE of ≈6.4 pp.The advantage of the 1 μm band over the 2 μm band is also observed in the standard empirical relations and may be related to the sharper nature of the 1 μm band, which enables a more precise localization of its center compared to the 2 μm band.Dunn et al. (2010) fitted the ferrosilite-1 μm band-center relation for ferrosilite numbers between 16 and 26.Using only samples with the ferrosilite number in this interval, the relationbased RMSE equals 6.7 pp.Gaffey et al. (2002) listed the relations between the ferrosilite number and the 2 μm band center.Using the low-Wo equation for the orthopyroxene ferrosilite number and the same actual ferrosilite interval, we obtain an RMSE of ≈19 pp.This high error is probably due to the clinopyroxene contribution to the 2 μm band.When we only use the equation to pure orthopyroxene samples, the RMSE drops to 14 pp.When the range constraints are released, the RMSEs of the two methods are between 22 pp and 23 pp.Similarly as for olivine, our model uses the whole band shape information to improve its predictions of the orthopyroxene composition, and the ANN-modeled ferrosilite has a similar precision as the equation of Dunn et al. (2010) in the restricted composition range, while the ANN model is valid for Fs > 7 at least (minimum of our data set).The model most likely works down to low Fs numbers until the 1 μm band is still apparent.When the models only cover the 1 μm band center, the RMSE is almost twice larger than when the models cover the whole band.The model predictions improve as the models cover the other diagnostic orthopyroxene bands, and the best results are obtained for the models that cover all three diagnostic bands (RMSE of ≈5 pp).
As the wavelength range changed during the range test, we could not use a unique wavelength for normalization of the spectra.Therefore, we also tested how the position of the normalization affects the model predictions to verify that the variations in the metrics are due to variations in the ranges and not due to the position of the normalization wavelength.Even though the models were trained using the normalized spectra and we did not expect any dependence, the accuracy metrics are slightly better for a normalization outside of the absorption bands.Perhaps the lowest RMSE is for a normalization at 650 nm, but the differences in metrics are very subtle to exclude some positions.For practical usage, we recommend a normalization at wavelengths with a high signal-to-noise ratio.
The range test was made using a constant wavelength step.Therefore, we further tested how the wavelength step affects the model predictions.Naturally, the expected behavior is that the error increases as the step increases, but we did not observe any significant increase in the error even for a coarse coverage of 50 nm step.We described above why a coarser spectrum coverage does not decrease the model precision.The models use the whole band shape to estimate the composition, and the spectrum changes slowly with wavelength.Therefore, even a coarser coverage can represent the overall shape well.
The accuracy metrics computed during the range test indicate that the most important region for the olivine and pyroxene abundances and compositions is between 750 and 1550 nm.This approximately fits the wavelength range of the step-tunable imaging channels of the ASPECT instrument.For these reasons, we restricted the wavelength range to the ASPECT-like range and increased the wavelength coverage in the specific parts of the spectrum.We do not observe any significant changes in the metrics of any quantity, regardless of which part of the spectrum is better resolved.This test further supports the results that the model predictions do not strongly depend on the wavelength step, either constant or adaptive.
Finally, we performed realistic tests for spectra as seen by the ASPECT instrument via the application of the ASPECT instrument spectral filter transmission characteristic.The tests with an increasing wavelength step were made for the imaging channels alone and for the imaging and single-point channels together.Compared with the previous results, the metrics for the low-resolution ASPECT spectra are usually worse.On the other hand, the changes due to the resolution are typically lower than 1 pp for the RMSE metric and lower than 5 pp for the within-10-pp error metric.
All the previous tests were made using noiseless spectra.To obtain metric estimates for noisy data, we additionally tested how noise in the ASPECT spectra propagates through our models with an ASPECT-targeted step of 30 nm.We assumed that the noise follows the normal distribution.We added 200 different realizations of the noise with various signal-to-noise ratios to the spectra and continued with the pre-processing (automatic denoising and normalization) and evaluation of the resulting spectra.For the evaluation, we used a single model to avoid model-to-model variations and spectra that were not used during the model training.The results are listed in Table 5.Both metrics show worse results for the noisy data, but the changes are mostly small in amplitude.For the expected ASPECT observation, i.e., a signal-to-noise ratio 50, the maximum increase in the RMSE is 1.12 pp and 0.53 pp for ASPECT 650-1600 nm and ASPECT 650-2450 nm, respectively.Similarly, the maximum decrease in the within-10-pp error metric is 4.5 pp and 4.6 pp for ASPECT 650-1600 nm and ASPECT 650-2450 nm, respectively.The mean worsening in metrics are 0.37 pp and 0.24 pp (RMSE) and 2.3 pp and 1.7 pp (within-10-pp error) for ASPECT 650-1600 nm and ASPECT 650-2450 nm, respectively.
We note that the RMSE values of these tests are comparable with previous results by Korda et al. (2023a), where we used the k-fold procedure with k = 100.Therefore, k = 20 used in this work is enough to estimate the accuracy metrics correctly.

Web Application
To make the models easily accessible, we developed a simple and intuitive web interface10 (see Figure 6).First, the user needs to upload a data file.The data file must be a text file containing wavelengths (the first column or row) and spectra (the other columns or rows).Second, the user selects the types of models to be evaluated (taxonomy and/or composition) and presses "Compute".An automatic algorithm finds the best pretrained model based on the wavelength grid (range and mean step) of the uploaded data.This model is used to evaluate the data.The model predictions can be downloaded as a CSV file.The user data file is deleted as soon as it is no longer needed or when any error occurs during the data handling.
Except for the data evaluation, the interface enables basic data pre-processing.One can limit the wavelength range, denoise data using the Gaussian filter, and replace incorrect measurements (where reflectance is negative or not defined) or outliers with the interpolated values.The raw and preprocessed data can be visualized using the "Plot spectra" button.The pre-processed data can be downloaded using the "Download pre-processed data" button.If any pre-processing is selected, the pre-processed data are used as inputs of the neuralnetwork models.
The composition models were trained using fresh olivinepyroxene-rich samples, and their outputs are always normalized to the sum of the olivine, orthopyroxene, and clinopyroxene volumetric abundances.This may cause issues when one inputs spectra that are dominated by other minerals.Therefore, we recommend the following usage.First, evaluate both the taxonomy and composition models.Second, ignore the results of the composition model when the predicted taxonomies indicate different mineral compositions (i.e., a taxonomy different from S-complex, V-type, and A-type).Third, when the predicted taxonomies are dominated by the spaceweathered types (mostly S-type), the predicted relative olivine abundance, orthopyroxene-to-clinopyroxene ratio, and fayalite number are artificially lowered (Korda et al. 2023a(Korda et al. , 2023b)).One should keep this in mind when using or interpreting the predicted results.

Conclusions
We used an established neural-network model and tested the model precision using reflectance spectra of olivine and pyroxene interpolated to various wavelength grids.The tests included the normalization position, various wavelength steps (both constant and adaptive), various wavelength ranges, and various spectral resolutions.From the tests, we obtain the following results.(1) The position of the normalization wavelength most likely does not affect the model predictions.
(2) A denser coverage in a specific part of the 1 μm band does not affect the model predictions.(3) An increased wavelength step up to 50 nm does not affect the model predictions.(4) The important wavelength region for the olivine-to-pyroxene ratio is between 750 and 1050 nm.(5) The important region to distinguish orthopyroxene from clinopyroxene is between 750 and 1250 nm.(6) The important region for the olivine composition is between 750 and 1550 nm.(7) The important region for the orthopyroxene composition is between 750 and 1350 nm.Therefore, to obtain high-precision olivine and pyroxene modal abundances and chemical compositions, the spectra should cover wavelengths from 750 nm and lower to 1550 nm and larger with a step of 50 nm and smaller.
We approximated the ASPECT instrument spectral filter transmission characteristic and tested the error-step and errornoise dependences.Both dependences are weak, with a typical change lower than 1 pp in the RMSE metric and lower than 5 pp for the within-10-pp error metric, both for a step increase from 10 to 50 nm and a signal-to-noise ratio of ≈ 50.Similar differences in the metrics were observed between non-ASPECT and ASPECT-like spectra.
We created a simple web interface through which everybody can pre-process and evaluate reflectance spectra using our models.The pretrained models are provided for many different wavelength grids, and they predict Bus-DeMeo taxonomy classes and the olivine and pyroxene modal and chemical compositions.The model predictions can be downloaded in the form of a CSV file.Note.Models were trained on spectra covering 450-2450 nm with a step of 10 nm.The evaluation was made using k-fold with k = 20.

Figure 1 .
Figure 1.Dependence of the RMSE on the normalization wavelength of the spectra.

Figure 2 .
Figure 2. RMSE of the mineral modal abundance predictions for different wavelength ranges.The dashed color boxes indicate important wavelength regions to which the metric values are assigned.

Figure 3 .
Figure 3. RMSE of the mineral chemical composition predictions for different wavelength ranges.The dashed color boxes indicate important wavelength regions to which the metric values are assigned.
,(2) the olivine composition is a function of the 1 μm band center(King & Ridley 1987;sunshine & Pieters 1998), and(3) the orthopyroxene composition is a function of the 1 μm band center or the 2 μm band center(Burns et al. 1972;

Figure 4 .
Figure 4. Dependence of the RMSE on the wavelength step.The input data for the ASPECT 650-1600 nm and ASPECT 650-2450 nm grids imitate the transmission properties of the ASPECT instrument.The values for the approximate ASPECT step are highlighted.

Figure 5 .
Figure 5. Dependence of the RMSE on the position of the dense window.

Figure 9 .
Figure 9. RMSE of the mineral composition predictions for different wavelength ranges.The dashed color boxes indicate important wavelength regions to which the metric values are assigned.

Table 1
Summary of the Wavelength Grids and Spectral Resolutions We Used for Each Test

Table 2
Definitions of the Boxes Used in the Matrix Plots a 850-1150 for the fayalite number.b 1550-1750 for the fayalite number.

Table 3
The Metric Values for the Selected Wavelength Ranges

Table 5
Changes in the Accuracy Metrics for ASPECT-like Spectra with Different Signal-to-noise Ratios (S/N) Computed as Noisy Minus Noiseless

Table 4
Mean Model Accuracy and Model-to-model Variations in the Metrics