The aim of this research is to develop precise and dependable machine learning models for the prediction of SW (Water Saturation) using three DL and three SL techniques: LSTM, GRU, RNN, SVM, KNN and DT. These models were trained on an extensive dataset comprising various types of log data. The findings of our investigation illustrate the efficacy of data-driven machine learning models in SW prediction, underscoring their potential for a wide range of practical applications.

When evaluating and comparing algorithms, researchers must take into account several crucial factors. Accuracy and disparities in prediction are among the most significant considerations. To evaluate these factors, researchers can utilize various criteria, including Eqs.16. The Mean Percentage Error (MPE) calculates the average difference between predicted and actual values as a percentage, while the Absolute Mean Percentage Error (AMPE) measures the absolute difference between them. Additionally, the Standard Deviation (SD) determines the variability of data points around the mean. Moreover, the Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) quantify the mean and root mean squared differences between predicted and actual values, respectively. Lastly, the R2 metric assesses the fraction of diversity in the reliant variable that can be accounted for by the autonomous variable.

$$text{MPE}=frac{{{sum }_{text{i}=1}^{text{n}}(frac{{SWE}_{(text{Meas}.)}-{SWE}_{(text{Pred}.)}}{{SWE}_{(text{Meas}.)}}text{x }100)}_{text{i}}}{text{n}}$$

(1)

$$text{AMPE}=frac{{sum }_{text{i}=1}^{text{n}}left|{(frac{{SWE}_{(text{Meas}.)}-{SWE}_{(text{Pred}.)}}{{SWE}_{(text{Meas}.)}}text{x }100)}_{text{i}}right|}{text{n}}$$

(2)

$$text{SD}=sqrt{frac{{sum }_{text{i}=1}^{text{n}}{({left(frac{1}{text{n}}sum_{text{i}=1}^{text{n}}left({{SWE}_{text{Meas}.}}_{text{i}}-{{SWE}_{text{Pred}.}}_{text{i}}right)right)}_{text{i}}-(frac{1}{text{n}}sum_{text{i}=1}^{text{n}}left({{SWE}_{text{Meas}.}}_{text{i}}-{{SWE}_{text{Pred}.}}_{text{i}}right))text{imean})}^{2}}{text{n}-1}}$$

(3)

$$text{MSE}=frac{1}{text{n}}sum_{text{i}=1}^{text{n}}{left({{SWE}_{text{Meas}.}}_{text{i}}-{{SWE}_{text{Pred}.}}_{text{i}}right)}^{2}$$

(4)

$$text{RMSE}=sqrt{frac{1}{text{n}}sum_{text{i}=1}^{text{n}}{left({{SWE}_{text{Meas}.}}_{text{i}}-{{SWE}_{text{Pred}.}}_{text{i}}right)}^{2}}$$

(5)

$${text{R}}^{2}=1-frac{sum_{text{i}=1}^{text{N}}{({{SWE}_{text{Pred}.}}_{text{i}}-{{SWE}_{text{Meas}.}}_{text{i}})}^{2}}{sum_{text{i}=1}^{text{N}}{({{SWE}_{text{Pred}.}}_{text{i}}-frac{{sum }_{text{I}=1}^{text{n}}{{SWE}_{text{Meas}.}}_{text{i}}}{text{n}})}^{2}}$$

(6)

In order to forecast SW, three DL and three SL techniques: LSTM, GRU, RNN, SVM, KNN and DT, were used in this study. Each algorithm underwent individual training and testing processes, followed by independent experiments. To ensure the accuracy of the predictions, the dataset was carefully divided into three subsets. The training subset accounted for 70% of the data records, while 30% was allocated for independent testing.

Choosing the most suitable algorithm for a specific task is a crucial undertaking within the realm of data analysis and machine learning. Therefore, this research aimed to assess and compare the performance of multiple LSTM, GRU, and RNN algorithms in predicting SW. The outcomes of these algorithms, utilizing the train data values, as well as the test, have been meticulously documented and presented in Table 2. By analyzing the results, researchers can gain insights into the effectiveness of each algorithm and make informed decisions about their implementation in practical applications.

The results from the test data are presented in Table 2, highlighting the excellent performance of the RMSE, MPE and AMPE metrics for the GRU algorithm, with values of 0.0198,0.1492 and 2.0320, respectively. Similarly, for the LSTM algorithm, the corresponding values are 0.0284,0.1388 and 3.1136, while for the RNN algorithm, they are 0.0399,0.0201 and 4.0613, respectively. For SVM, KNN and DT these metrics are includes: 0.0599,0.1664 and 6.1642; 0.7873, 0.0997 and 7.4575; 0.7289,0.1758 and 8.1936. The results show the GRU model has high accuracy than other algorithms.

The R2 parameter is a crucial statistical measure for evaluating and comparing different models. It assesses the adequacy of a model by quantifying the amount of variation in the outcome variable that can be clarified by the explanatory variables. In this study, Fig.5 illustrates cross plots for predicting SW values based on the train and test data, demonstrating significantly higher prediction accuracy compared to the other evaluated models. Additionally, Fig.5 confirms that the RGU model exhibits superior prediction accuracy compared to the LSTM and RNN models.

Cross plot for predicting SW using three DL algorithms such as RGU, LSTM and RNN for test data.

To assess the precision of the GRU model, the results presented in Table 2 and Fig.5 were carefully analyzed for the train and test data. The analysis revealed that the GRU algorithm achieved low errors for SW, with RMSE values of 0.0198 and R-square values of 0.9973. The R2 values provided serve as quantitative metrics assessing the predictive prowess of ML models. The R2, denoting the coefficient of determination, gauges the extent to which the variance in the dependent variable can be foreseen from the independent variable(s), essentially showcasing how well the model aligns with observed data points. The R2 values for the GRU, LSTM, RNN, SVM, KNN and DT models stand at 0.9973, 0.9725, 0.9701, 0.8050, 0.7873 and 0.7289 respectively, reflecting their respective accuracy and reliability in predicting SW levels. Figure5 shows the cross plot for predicting SW using three DL algorithms such as RGU, LSTM, and RNN for test data. The GRU model's notably high R2 of 0.9973 underscores its exceptional correlation between predicted and observed SW values, implying that nearly 99.73% of SW data variance can be elucidated by its predictions, showcasing its precision and reliability in SW prediction tasks. Comparatively, the LSTM and RNN models, with R2 values of 0.9725 and 0.9701 respectively, also exhibit strong predictive capabilities, albeit slightly lower than the GRU model. These findings underscore the GRU model's superiority in SW prediction, attributed to its adeptness in capturing intricate temporal dependencies within SW data, thereby yielding more accurate predictions.

Figure6 provides a visual representation of the calculation error for the test data, illustrating the error distribution for predicting SW using three DL algorithms (GRU, LSTM, and RNN). The plotted coordinates in the figure depict the error range for each algorithm. For the GRU algorithm, the error range is observed to be between0.0103 and 0.0727. This indicates that the predictions made by the GRU model for the test data exhibit a relatively small deviation from the actual SW values within this range. In contrast, the LSTM algorithm demonstrates a slightly wider error range, ranging from0.146 to 0.215. This suggests that the predictions generated by the LSTM model for the test data exhibit a somewhat higher variability and may deviate from the actual SW values within this broader range.

Error points for predicting SW using three DL and three SL algorithms such as GRU, LSTM, RNN, SVM, KNN and DT for test data.

Similarly, the RNN algorithm exhibits an error range between0.222 and 0.283. This indicates that the predictions made by the RNN model for the test data show a larger spread and have the potential to deviate more significantly from the actual SW values within this range. By visually comparing the error ranges for the three DL algorithms, it becomes apparent that the GRU algorithm achieves a narrower range and thus demonstrates better precision and accuracy in predicting SW for the test data. Conversely, the LSTM and RNN algorithms exhibit broader error ranges, indicating a higher degree of variability in their predictions for the same dataset. These findings further support the conclusion that the GRU algorithm outperforms the LSTM and RNN algorithms in terms of SW prediction accuracy, as it consistently produces predictions with smaller errors and tighter error bounds.

Figure7 presents an error histogram plot, depicting the prediction errors for SW using three DL and three SL algorithms such as GRU, LSTM, RNN, SVM, KNN and DT. Each histogram represents the distribution of prediction errors for each algorithm, displaying a normal distribution centered around zero with a relatively narrow spread and no noticeable positive or negative bias. This plot enables a comprehensive analysis of the algorithms' performance and aids in determining the best algorithm with a normal error distribution. Upon careful investigation, it becomes evident that the GRU algorithm exhibits a superior normal distribution of data compared to the other algorithms. The GRU algorithm's performance is characterized by a more accurate standard deviation and a narrower spread of prediction errors. This indicates that the GRU algorithm consistently produces more precise and reliable predictions for SW. By comparing the results presented in Table 2 and analyzing the error histogram plot in Fig.7, we can conclude that the performance accuracy of the algorithms can be ranked as follows: GRU>LSTM>RNN>SVM>KNN>DT.

Histogram plot for SW prediction using three DL and three SL algorithms such as GRU, LSTM, RNN, SVM, KNN and DT.

Figure8 illustrates the error rate of the three DL and three SL algorithms such as GRU, LSTM, RNN, SVM, KNN and DT as a function of iteration for SW prediction. The findings of this study indicate that the GRU and LSTM algorithms initially exhibit higher error values that progressively decrease over time. However, this pattern is not observed in the RNN algorithm. Upon analyzing the figure, it becomes evident that the LSTM algorithm achieves higher accuracy than the other algorithms at the beginning of the iteration. At the threshold of 10 iterations, the LSTM algorithm surpasses the GRU algorithm with a lower error value. However, in the subsequent iterations, specifically at iteration 31, the GRU algorithm outperforms the LSTM algorithm with superior performance accuracy. In contrast, the RNN algorithm shows a consistent decrease in performance accuracy from the start to the end of the iterations, without displaying significant fluctuations. When focusing on the zoomed-in portion of the figure, specifically repetitions 85100, the ongoing performance trends of these algorithms become more apparent. It is evident from the analysis that the GRU algorithm consistently outperforms the other algorithms in terms of performance accuracy. The LSTM algorithm follows, with a decrease in accuracy over the iterations. On the other hand, the RNN algorithm exhibits a declining performance accuracy without any notable changes or fluctuations. These findings emphasize the superiority of the GRU algorithm in terms of performance accuracy when compared to the LSTM and RNN algorithms. The GRU algorithm consistently maintains a higher level of accuracy throughout the iterations, while the LSTM and RNN algorithms experience fluctuations and decreasing accuracy over time.

Iteration plot for SW prediction using three DL and three SL algorithms such as GRU, LSTM, RNN, SVM, KNN and DT.

Pearson's coefficient (R) is a widely used method for assessing the relative importance of input-independent variables compared to output-dependent variables, such as SWL. The coefficient ranges between1 and+1 and represents the strength and direction of the correlation. A value of+1 indicates a strong positive correlation, -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation. Equation7 illustrates the calculation of Pearson's correlation coefficient, which is a statistical measure of the linear relationship between two variables. It allows researchers to quantify the extent to which changes in one variable are associated with changes in another variable. By applying Pearson's coefficient, researchers can determine the level of influence that input-independent variables have on the output-dependent variable, SWL.

$$R=frac{sum_{i=1}^{n}({Z}_{i}-overline{Z })({Q}_{i}-overline{Q })}{sqrt{{sum }_{i=1}^{n}{({Z}_{i}-overline{Z })}^{2}}sqrt{{sum }_{i=1}^{n}{({Q}_{i}-overline{Q })}^{2}}}$$

(7)

A coefficient of+1 indicates a perfect positive correlation, suggesting that the input-independent variables have the greatest positive impact on the output-dependent variable. Conversely, a coefficient of1 represents a perfect negative correlation, indicating that the input-independent variables have the greatest absolute impact on the output-dependent variable. When the coefficient is close to 0, it suggests that there is no significant correlation between the variables, indicating that changes in the input-independent variables do not have a substantial effect on the output-dependent variable. Pearson's correlation coefficient is a valuable tool for assessing the relationship between variables and understanding their impact. It provides researchers with a quantitative measure to determine the relative importance of input-independent variables compared to the output-dependent variable, SWL.

By heat map shows Fig.9, a comparison of Pearson correlation coefficients can be made to gain insights into the relationship between input variables and SW. The results reveal several significant correlations between the variables. Negative correlations are observed with URAN and DEPTH, indicating an inverse relationship with SW. This suggests that higher values of URAN and DEPTH are associated with lower SW values. On the other hand, positive correlations are observed with CGR, DT, NPHI, POTA, THOR, and PEF. These variables show a direct relationship with SW, meaning that higher values of CGR, DT, NPHI, POTA, THOR, and PEF are associated with higher SW values. The comparison of Pearson correlation coefficients provides valuable insights into the relationship between input variables and SW.

Heat map plot for SW prediction using three DL and three SL algorithms such as GRU, LSTM, RNN, SVM, KNN and DT.

These findings can be utilized to develop predictive models of SW based on the input variables. By incorporating the correlations into the models, researchers can enhance their accuracy and reliability in predicting SW values. The expression of the relationships between the input variables and SW in the form of Eq.8 allows for quantitative analysis of the data. This equation provides a mathematical representation of the correlations, enabling researchers to quantitatively evaluate the impact of the input variables on SW.

$$SWE=propto left(text{CGR},text{ DT},text{ NPHI},text{ POTA},text{ THOR},text{ PEF}right) and SWE=propto frac{1}{left(URAN, DEPTHright)}$$

(8)

Read more here:
Deep learning algorithm-enabled sediment characterization techniques to determination of water saturation for tight ... - Nature.com

In the following section, we will give details about the methodologies that make up our proposed workflow for predicting the conductivity and band gap of spinel oxide materials: DFT for band structure calculation, principal layer, Greens functions, Landauer formalism for electric conductivity, and machine learning and band structure fitting to tight binding Hamiltonian.

All DFT calculations were done using the Vienna ab-initio simulation package (VASP)25 with the PerdewBurkeErnzerhof (PBE) functional26. We align the spins in a ferrimagnetic arrangement with Nel collinear configuration, where the magnetic moment of tetrahedral cations is opposing that of octahedral cations. Following convergence tests, the calculations for the cubic cells utilized a 600 eV plane wave energy cut-off and a 333 k-point mesh, centered at the -point. The self-consistent electronic minimization employed a 0.1meV threshold and ionic relaxation had a force threshold of 0.01eV/. The band structure was calculated using k-points along high symmetry lines, selected based on the implementation in the pymatgen27 library as described in ref28. The k-point file is available in the SI. The Hubbard U values applied to Mn, Co, Fe, Ni, and O atoms were 3.9, 3.5, 4.5, 5.5, and 0 eV, respectively, where all U values were used based on previous literature works29,30,31,32,33,34,35. The unit cell of all the spinels in the dataset consists of 56 atoms, 32 of which are oxygen, 16 of which are transition metal ions in tetrahedral sites and 8 transition metal ions in octahedral sites (Fig.8). The dataset contains 190 different combinations of this cell as explained later in the results.

An example of normal spinel oxide unit cell geometry (Co16Ni8O32). The red spheres are oxygen ions, gray are nickel ions in tetrahedral sites and blue are cobalt ions in octahedral sites.

For calculating the current, we followed the well-established approach of LandauerBttiker for quantum transport36,37. In this formalism, we postulate that there is a potential between two electron reservoirs that possess an equilibrium distribution and has dissimilar chemical potentials. These reservoirs act as sources and drains of electrons for the left and right electrodes, respectively. The device, which we intend to evaluate its current, constitutes the scattering region located between the electrodes. The variance in the electrochemical potentials of the reservoirs represents the applied bias on the scattering region. The LandauerBttiker is

$$I=frac{2e}{h}underset{-infty }{overset{infty }{int }}Tleft(Eright)left[fleft(E-{upmu }_{L}right)-fleft(E-{upmu }_{R}right)right]dE$$

(1)

where (fleft(E-{upmu }_{L}right)) and (fleft(E-{upmu }_{R}right)) are the FermiDirac electron distributions with ({upmu }_{L}) and ({upmu }_{R}) the chemical potentials of the left and right electrodes, respectively. (Tleft(Eright)) is the transmission function of an electron from left to right electrodes through the scattering region. In this setup the system is divided into principal layers that interact only with the nearest neighbors layer and each layer is described by a tight-binding Hamiltonian, ({H}_{i}), where i is the layer number. Since each electrode is semi-infinite, this approach introduces an infinite problem. Fortunately, this problem is solved by using Greens function. The scattering region which must interest us is a finite region that can be obtained by

$${{varvec{G}}}_{{varvec{S}}}={left(left(E+ieta right){{varvec{S}}}_{{varvec{S}}}-{{varvec{H}}}_{S}-{boldsymbol{Sigma }}_{L}-{boldsymbol{Sigma }}_{R}right)}^{-1}$$

(2)

where E is the energy of the system and (eta) is a small number. ({{varvec{S}}}_{{varvec{S}}}) is the overlap matrix of the scattering region The overlap matrix terms are defined as the overlap integral between associate vectors of the Hamiltonian basis. ({{varvec{H}}}_{{varvec{S}}}) is a block matrix representing the scattering region, and the effect of the semi-infinite electrodes is contained through the finite self-energy matrices ({{varvec{Sigma}}}_{{varvec{L}}backslash {varvec{R}}}) of electrode left (L) and right (R) electrodes.

The transmission formula can be obtained from the LandauerBttiker formalism and quantum scattering theory36,37,38,39, and it is given by

$${mathbf{T}}left( {mathbf{E}} right) = {text{Tr}}left{ {{{varvec{Gamma}}}_{{mathbf{L}}} {mathbf{G}}_{{mathbf{S}}}^{dag } {{varvec{Gamma}}}_{{mathbf{R}}} {mathbf{G}}_{{mathbf{S}}} } right}$$

(3)

where ({Gamma }_{Lbackslash R}) is called the broadening matrix and it is given by the expression

$${{varvec{Gamma}}}_{{{mathbf{L}}backslash {mathbf{R}}}} = {text{i}}left( {{{varvec{Sigma}}}_{{{varvec{L}}backslash {varvec{R}}}} -{varvec{varSigma}}_{{{varvec{L}}backslash {varvec{R}}}}^{dag } } right)$$

(4)

A technique for deriving finite self-energy matrices is available in the literature40,41. This procedure results in the following terms for the left electrodes self-energy.

$$hat{user2{Sigma }}_{{varvec{L}}} = {varvec{H}}_{{user2{L^{prime}},{varvec{L}}}}^{dag } {varvec{g}}_{{varvec{L}}} {varvec{H}}_{{user2{L^{prime}},{varvec{L}}}}^{{}}$$

(5)

where ({{varvec{H}}}_{{{varvec{L}}}^{boldsymbol{^{prime}}},{varvec{L}}}) is the coupling Hamiltonian between the scattering region and the left electrode. And ({{varvec{g}}}_{{varvec{L}}}) is given by a recursive formula,

$$g_{L}^{{left( {n + 1} right)}} = left[ {{varvec{H}}_{{varvec{L}}} - {varvec{H}}_{{user2{L^{prime}},{varvec{L}}}}^{dag } {varvec{g}}_{{varvec{L}}}^{{left( {varvec{n}} right)}} {varvec{H}}_{{user2{L^{prime}},{varvec{L}}}}^{{}} } right]^{ - 1}$$

(6)

The initial guess is ({{varvec{g}}}_{{varvec{L}}}^{left({varvec{n}}right)}={{varvec{H}}}_{{{varvec{L}}}^{boldsymbol{^{prime}}},{varvec{L}}}) and the iterative procedure continues until ({left({{varvec{g}}}_{{varvec{L}}}^{left({varvec{n}}-1right)}-{{varvec{g}}}_{{varvec{L}}}^{left({varvec{n}}right)}right)}_{ij}^{2}le {updelta }^{2}), where (updelta) is a small number in the order of 11015, this convergence criterion is achieved within few iterations. A similar procedure is done for the right self-energy (for symmetric electrodes and bias ({{varvec{g}}}_{{varvec{L}}}={{varvec{g}}}_{{varvec{R}}})). ({boldsymbol{Sigma }}_{{varvec{L}}}) takes the size of the scattering Hamiltonian and has a block element only in the top left of the left self-energy matrix and in the bottom right of the right self-energy,

$${boldsymbol{Sigma }}_{{varvec{L}}}=left(begin{array}{ccccc}{widehat{Sigma }}_{L}& 0& cdots & 0& 0\ 0& 0& 0& cdots & 0\ vdots & 0& 0& cdots & vdots \ 0& vdots & cdots & ddots & 0\ 0& 0& cdots & 0& 0end{array}right)$$

(7)

Our system is divided into the so-called principal layers42,43,44 where each layer consists of four unit cells of spinel oxide as illustrated in Fig.9. Using only four unit cells is sufficient to capture all the necessary information from the TB Hamiltonians that were adjusted to fit the DFT band structure. The layers are interconnected by a coupling Hamiltonian, effectively forming an endless wire. The Hamiltonian of a single layer of our system was defined as follows

$$H_{layer} = left( {begin{array}{*{20}c} {{varvec{H}}_{00} } & {{varvec{H}}_{010} } & {{varvec{H}}_{001} } & 0 \ {{varvec{H}}_{010}^{dag } } & {{varvec{H}}_{00} } & 0 & {{varvec{H}}_{001} } \ {{varvec{H}}_{001}^{dag } } & 0 & {{varvec{H}}_{00} } & {{varvec{H}}_{010} } \ 0 & {{varvec{H}}_{001}^{dag } } & {{varvec{H}}_{010}^{dag } } & {{varvec{H}}_{00} } \ end{array} } right)$$

(8)

where the elements in the Hamiltonian matrix are blocks of matrices. The blocks along the diagonal correspond to a tight-binding Hamiltonian (the tight-binding Hamiltonians defined in the next section) of each of the four unit cells within a single layer of spinel oxide. The block matrices along the off-diagonal represent the tight-binding Hamiltonian matrix elements that connect each unit cell with its neighboring cells within the same layer. The subscripts used for H indicate the spatial directions between a unit cell and its adjacent neighbors. The block matrix below defines the coupling between each layer and its neighboring layers,

A schematic representation of a wire built from principal layers of four unit cells each. The layers are coupled in the 100 direction.

$${H}_{layerCoupling}=left(begin{array}{cccc}{{varvec{H}}}_{100}& 0& 0& 0\ 0& {{varvec{H}}}_{100}& 0& 0\ 0& 0& {{varvec{H}}}_{100}& 0\ 0& 0& 0& {{varvec{H}}}_{100}end{array}right)$$

(9)

To maintain a manageable size for the Hamiltonians and take advantage of the electrodes being made of the same material, we opted to use only two layers to represent our material in the scattering region. This approach essentially yields an infinite material through which the current can flow. The Hamiltonian for the scattering region is expressed as follows:

$$H_{s} = left( {begin{array}{*{20}c} {{varvec{H}}_{{{varvec{layer}}}} } & {{varvec{H}}_{{{varvec{layerCoupling}}}} } \ {{varvec{H}}_{{{varvec{layerCoupling}}}}^{dag } } & {{varvec{H}}_{{{varvec{layer}}}} } \ end{array} } right)$$

(10)

The size of the scattering Hamiltonian is composed of 22 blocks representing two layers and their connection, and each block is composed of 44 block matrices that include ({{varvec{H}}}_{00},{{varvec{H}}}_{100},{{varvec{H}}}_{010},{{varvec{H}}}_{001}) , where these matrices have the size of 88 (since in this work we fitted to eight bands). Thus, in total the size of ({H}_{s}) is 6464.

The project emphasizes material property prediction and follows a workflow suited for such a task. The workflow includes the following steps: building a dataset by collecting and cleaning data and dividing it into a train and test set, selecting features, training the model by selecting an appropriate model, tuning hyperparameters, and optimizing it. The model's performance is evaluated on the test set and compared to other models, and finally, the model is used for making predictions.

To prepare for model training and testing, the dataset is first divided into two sets: a training set and a test set. The latter is used to evaluate the model's ability to predict properties on new data that it has not seen during training. It's a mistake to train and test on the same data since the model can overfit the training data and perform poorly on new data. A standard approach is to partition 80% of the dataset for training and reserve the remaining 20% for testing.

To set up a dataset for machine learning (ML) models, it should be divided into features and target variables. Features are independent variables grouped into a vector that serves as input for the ML model. Choosing informative and independent features is crucial for model performance. A single input vector represents a sample, and the order of features must remain consistent. The target variables are the properties to be predicted. For the materials in this project, A and B elements and stoichiometric numbers x and y from the formula AyBy8A16xBxO32 are the most representative features. Oxygen has a constant value and doesn't add information to the feature vector. The A and B atoms are represented by their atomic number values: Mn=25, Fe=26, Co=27, and Ni=28. Features normalization and scaling are important to ensure a proper functioning of some ML algorithms and to speed up gradient descent. In this project, we applied standardization using Scikit-learn module45, which involves removing the mean value and scaling to unit variance.

For the regression problems, which are predicting current from compositions, predicting current from bandwidth and prediction of bandgaps, we have chosen to utilize five different machine learning algorithms for comparison of their performance. For predicting current from composition these algorithms include kernel ridge regression (KRR), support vector regression (SVR), random forests (RF), neural networks (NN), and an ensemble model which takes the average result of all other four algorithms. For the prediction of current from bandwidth and for the bandgap prediction we used the XGboost algorithm46. These algorithms were chosen as they each have unique strengths in handling different types of data and relationships. Specifically, NN were chosen due to their ability to model complex, non-linear relationships, which is often the case in predicting material properties like electronic conductivity and band gaps; SVR was selected for its effectiveness in high-dimensional spaces, which is common in material science data. It also has strong theoretical foundations in statistical learning theory; KRR was chosen for its ability to handle non-linear relationships through the use of kernel functions. It also has the advantage of being less sensitive to outliers; RF was selected for its robustness and ease of use. It performs well with both linear and non-linear data.

ML models are functions defined by parameters. During training, the model optimizes the parameters to fit the data. Hyperparameters, like regularization values or architecture of a neural network, are tuned by the user. To avoid overfitting and ensure models perform well with new predictions, cross-validation procedures are used. The training set is split into k-folds, and the model is trained on k-1 folds and evaluated on the remaining fold (validation set) k times. The average performance is reported, and once hyperparameters are tuned, the model is trained on the whole training set and tested. In evaluating the model, selecting an appropriate metric is crucial. For this work, we have chosen the mean absolute error (MAE) as it provides a natural measurement of the accuracy of a model that predicts physical values such as current. Additionally, we have used R2 to measure the linearity between the predicted values of the models and the true values that were calculated.

Traditional tight-binding fitting schemes entail tuning numerous parameters that represent the atomic structure and do not always yield precise results47. A more common approach is utilizing Wannier functions, obtained by transforming extended Bloch functions from DFT calculations, which derive tight-binding parameters from ab-inito results without the need for fitting48,49. However, this method demands extensive system knowledge and a trial-and-error process due to the numerous parameters involved. Our objective is to rapidly and precisely compute the tight-binding Hamiltonian for approximately two hundred material samples.

Our approach follows the method proposed by Wang et al., where a parametrized tight-binding Hamiltonian is obtained by employing the back-propagation technique to fit the real-space tight-binding matrices to the DFT band structure50. Here we implemented the same approach but with pyTorch51 library instead of TensorFlow52 as done by the original authors. In TB theory the reciprocal space Hamiltonian for a desired K vector is,

$${H}^{TB}(k)={sum }_{R}{e}^{ikcdot R}{H}^{R}$$

(11)

where R is a lattice vector of selected real-space Hamiltonian matrices and ({H}^{R}) is the corresponding TB Hamiltonian. H0 (R=(000)) is the real-space TB Hamiltonian matrix of the unit cell, ({H}^{R}ne 0) (R=(100), (010), (001), etc.) are the Hamiltonian matrices that couple the unit cell Hamiltonian to the adjacent unit cells in the direction of R vectors. The TB band structure is obtained from the eigenvalues ({{varepsilon }^{TB}}_{n,k}) for every desired k vector via,

$${H}_{k}^{TB}{psi }_{n,k}^{TB}={{varepsilon }^{TB}}_{n,k}{psi }_{n,k}^{TB}$$

(12)

where ({{varepsilon }^{TB}}_{n,k}) is the energy of the n-th band at reciprocal vector k. To fit the TB bands to the DFT bands, the mean squared error loss L between the TB and DFT eigenvalues is minimized,

$$L=frac{1}{N}frac{1}{{N}_{k}}{{sum }_{i=1}^{N}{sum }_{k}{left({varepsilon }_{i,k}^{TB}-{varepsilon }_{i,k}^{DFT}right)}^{2}}$$

(13)

The loss is computed for all bands and k-points, where N represents the total number of bands and Nk represents the number of sampled k-points. The TB Hamiltonians parameters (HR) are updated iteratively using the Adam gradient descent algorithm53. The back-propagation procedure is used to calculate the derivative of the loss with respect to HRs. The gradient descent algorithm seeks to minimize the loss by moving in the direction of the steepest descent, which is opposite to the direction of the gradient, according to the general formula,

$${H}_{l+1}^{R}={H}_{l}^{R}-alpha frac{partial L}{partial {H}_{l}^{R}}$$

(14)

The variable "l" represents either an epoch number (epoch defines the number of times the entire data set, in this case all the k points, has worked through the learning algorithm) or a single iteration over all k points. In this context, an epoch is considered complete after the loss function has accumulated all the eigenvalues in the band structure, which occurs after calculating all ({H}^{TB}(k)) values. The derivative of the loss with respect to HR is given with matrix derivative algorithmic differentiation rules54.

The fitting process has a predefined numerical threshold (means squared error<(3cdot {10}^{-5} {text{eV}}^{2}), as defined in Eq.13) for the loss function, which serves as a criterion to terminate the fitting. Additionally, we introduced another criterion that halts the fitting if the loss increases for more than ten epochs due to spikes or jumps in the loss function during training. If the loss was already low, we consider the results of the fitting process. However, if the loss was high, we re-run the process with slightly different initial random weights in the Hamiltonians.

To determine the R vectors for the fitting process, we conducted tests with various vectors, up to 24 in total. After experimentation, we concluded that the three main directions and their opposite directions were sufficient for achieving a highly accurate fitting of the bands. The size of the matrices used in the fitting process is defined by the number of bands being fitted. For instance, for eight bands, the matrix size is 88.

More:
From density functional theory to machine learning predictive models for electrical properties of spinel oxides ... - Nature.com

The arms race for the next AI breakthrough is upon us -- and for good reason. While the news cycles are quick to point to fears around job displacement, bias, security risks, and weaponization, there is reason to be optimistic about this technology if we proceed carefully. We are stepping into the future of an AI-enabled world, and the competitive landscape for AI innovation should have only one bias in mind: a bias towards humanity.

AI should be viewed as a tool for enhancing human capabilities and productivity rather than one that replaces them. AI has the potential to amplify creativity, solve complex problems faster, and tackle tasks that are lengthy, tedious or impossible for humans. By positioning AI as a partner in progress, we can foster an environment where technological advancement serves to elevate human potential. From the perspective of the enterprises and innovators that are building this technology, its important that these tools are built with that idea at the core.

These improvements are lifesaving in certain sectors. In healthcare, AI algorithms are deployed and being refined to allow practitioners to diagnose diseases quickly and accurately, spotting early signs of conditions like cancer, diabetic retinopathy and heart disease from imaging scans that surpass the human eye by itself. AI systems can also speed up drug discovery and development by predicting molecular behavior and identifying promising drug candidates much faster than traditional methods. That significantly reduces the time and cost to bring new medicines to market.

Related:What You Need to Know about AI as a Service

Another example is in education. AI breakthroughs are establishing a more personalized process by adapting content and pacing it to individual learners needs. Machine learning can identify areas where students struggle, provide tailored resources, and enhance engagement through interactive and immersive experiences. This can help teachers create more tailored learning processes for each of their students, including those with special needs, so no one student gets left behind.

This just scratches the surface. AI has the potential to play a role in a variety of industries from manufacturing, supply chain, entertainment, environmental conservation, and much more.

Despite fears surrounding job displacement, history has shown that technological advancements lead to more jobs, not fewer. The advent of AI is no exception. It's true that repetitive tasks that are tedious in nature and easily structured, such as data processing and extraction from documents, will slowly start being automated away. However, these systems will have to be overseen by specialists and experts to ensure everything is running in a user-friendly way.

Related:Is an AI Bubble Inevitable?

By automating these routine tasks, AI frees humans to engage in more creative, strategic, and interpersonal roles. This transition underscores the importance of retraining initiatives to prepare the workforce for the jobs of the future. As the workforce evolves alongside technology, AI will serve more as a job creator rather than a job destroyer, as long as companies invest in upskilling their employees with the necessary capabilities to understand, leverage, implement, and improve technology.

We're already seeing evidence of this phenomenon. Big companies are starting to create new opportunities revolving around machine-learning or Gen AI capabilities. As Aaron Mok of Business Insider points out, job postings on LinkedIn that mention GPT have grown 20-fold from 2022 to 2023. He goes on to point out how Meta, Netflix, Apple and even non-tech companies in the healthcare, education, and legal industries have posted listings for AI-related jobs. Those who learn how to operate this technology effectively will have a growing number of employment opportunities.

Related:Overcoming AIs 5 Biggest Roadblocks

Theres a Pandora's box opening up as it relates to AI as it plays an increasingly significant role in creative and inventive processes, raising questions about authorship and ownership. At what point does a user take what is being given to them from an AI algorithm without challenging it? What are the ethical considerations of a consumer or an employee taking those considerations or recommendations and then parading them as their own work versus the work that's being done by the AI engine?

Addressing these concerns requires a multi-stakeholder approach, including policymakers, legal experts, technologists, and creators, to redefine intellectual property frameworks that recognize the contributions of both humans and AI. This could involve exploring new licensing models, establishing AI as a tool under human direction, establishing regulations and laws, and ensuring that creators are fairly compensated for AI-assisted work.

A human-centric approach should guide AI in all its developments. This involves ensuring transparency, accountability, and fairness in AI systems, with a focus on minimizing biases and increasing accessibility. Its important that AI systems also consider those with disabilities or sensory impairments to make their lives easier rather than creating more walls. Addressing AI bias requires a multifaceted approach, including diversifying datasets, implementing fairness metrics, and incorporating diverse perspectives in AI development teams.

By adopting a proactive, collaborative, and regulation-informed approach, we can harness the benefits of AI while safeguarding against its risks. The arms race of AI is here; but we can ensure that practitioners and thought leaders are always within arms reach of any AI implementation introduced into our daily lives.

Read this article:
Focus on Humanity in the Age of the AI Revolution - InformationWeek

Machine learning stocks are gaining traction as the interest in artificial intelligence (AI) and machine learning soars, especially after the launch of ChatGPT by OpenAI. This technology has given us a glimpse of its potential, sparking curiosity about its future applications, and has led to my list of machine learning stocks to buy.

Machine learning stocks present a promising opportunity for growth, with the potential to create significant wealth. As per analyst forecasts, I think around a decade from now is when we will see these companies go parabolic and reach their full growth potential.

These companies leverage machine learning for various applications, including diagnosing life-threatening diseases, preventing credit card fraud, developing chatbots and exploring advanced tech like artificial general intelligence. The future will only get better from here.

So if youre looking for machine learning stocks to buy with substantial upside potential, keep reading to discover three top picks.

Source: Lori Butcher / Shutterstock.com

DraftKings (NASDAQ:DKNG) leverages machine learning to enhance its online sports betting and gambling platform. The company has shown significant growth, with recent revenue increases and expansion in legalized betting markets.

DKNG has significantly revised its revenue outlook for 2024 upwards, expecting it to be between $4.65 billion and $4.9 billion, marking an anticipated year-over-year growth of 27% to 34%. This adjustment reflects higher projections compared to their earlier forecast ranging from $4.50 billion to $4.80 billion. Additionally, the company has increased its adjusted EBITDA forecast for 2024, now ranging from $410 million to $510 million, up from the previous estimate of $350 million to $450 million.

DraftKings has also announced plans to acquire the gambling company Jackpocket for $750 million in a cash-and-stock deal. This acquisition is expected to further enhance DraftKings market presence and capabilities in online betting.

I covered DKNG before, and I still think its one of the best meme stocks that investors can get behind. The companys stock price has risen 72.64% over the past year, and it seems theres still plenty of fuel left in the tank to surge higher.

Source: Sundry Photography / Shutterstock

Cloudflare (NYSE:NET) provides a cloud platform that offers a range of network services to businesses worldwide. The company uses machine learning to enhance its cybersecurity solutions.

Cloudflare has outlined a robust strategy for 2024, focusing on advancing its cybersecurity solutions and expanding its network services. The company expects to generate total revenue between $1.648 billion and $1.652 billion for the year. This revenue forecast reflects a significant increase in their operational scale.

NET is another stock that is leveraging machine learning to its full advantage. Ive been bullish on this company for some time and continue to be so. Notably, Cloudflare is expanding its deployment of inference-tuned graphic processing units (GPUs) across its global network. By the end of 2024, these GPUs will be deployed in nearly every city within Cloudflares network.

NET has been silently integrating many parts of its network within the internets fabric for millions of users, such as through its DNS service, Cloudflare WARP; reverse proxy for website owners; and much more. Around 30% of the 10,000 most popular websites globally use Cloudflare. Many of NETs services can be accessed free of charge.

It is following a classic tech stock strategy of expanding its users, influence and reach over reaching immediate profits, and its financials have slowly scaled with this performance.

Source: VDB Photos / Shutterstock.com

CrowdStrike (NASDAQ:CRWD) is a leading cybersecurity company that uses machine learning to detect and prevent cyber threats.

In its latest quarterly report on Mar. 5, CRWD reported a 102% earnings growth to 95 cents per share and a 33% revenue increase to $845.3 million. Analysts expect a 57% earnings growth to 89 cents per share in the next report and a 27% EPS increase for the full fiscal year ending in January.

Adding to the bull case for CRWD is that it has has partnered with Google Cloud by Alphabet (NASDAQ:GOOG, GOOGL) to enhance AI-native cybersecurity solutions, positioning itself strongly against competitors like Palo Alto Networks (NASDAQ:PANW).

Many contributors here at Investorplace have identified CRWD as one of the best cybersecurity stocks for investors to buy, and I am in agreement here. Its aggressive EPS growth and stock price appreciation (140.04% over the past year), make it a very attractive pick for long-term investors.

On the date of publication, Matthew Farley did not have (either directly or indirectly) any positions in the securities mentioned in this article. The opinions expressed are those of the writer, subject to the InvestorPlace.com Publishing Guidelines.

Matthew started writing coverage of the financial markets during the crypto boom of 2017 and was also a team member of several fintech startups. He then started writing about Australian and U.S. equities for various publications. His work has appeared in MarketBeat, FXStreet, Cryptoslate, Seeking Alpha, and the New Scientist magazine, among others.

Go here to read the rest:
The 2034 Millionaire's Club: 3 Machine Learning Stocks to Buy Now - InvestorPlace

Krakauer, J. W., Ghazanfar, A. A., Gomez-Marin, A., MacIver, M. A. & Poeppel, D. Neuroscience needs behavior: correcting a reductionist bias. Neuron 93, 480490 (2017).

Article CAS PubMed Google Scholar

Anderson, D. J. & Perona, P. Toward a science of computational ethology. Neuron 84, 1831 (2014).

Article CAS PubMed Google Scholar

Egnor, S. E. R. & Branson, K. Computational analysis of behavior. Annu. Rev. Neurosci. 39, 217236 (2016).

Article CAS PubMed Google Scholar

Datta, S. R., Anderson, D. J., Branson, K., Perona, P. & Leifer, A. Computational neuroethology: a call to action. Neuron 104, 1124 (2019).

Article CAS PubMed PubMed Central Google Scholar

Falkner, A. L., Grosenick, L., Davidson, T. J., Deisseroth, K. & Lin, D. Hypothalamic control of male aggression-seeking behavior. Nat. Neurosci. 19, 596604 (2016).

Article CAS PubMed PubMed Central Google Scholar

Ferenczi, E. A. et al. Prefrontal cortical regulation of brainwide circuit dynamics and reward-related behavior. Science 351, aac9698 (2016).

Article PubMed PubMed Central Google Scholar

Kim, Y. et al. Mapping social behavior-induced brain activation at cellular resolution in the mouse. Cell Rep. 10, 292305 (2015).

Article CAS PubMed Google Scholar

Gunaydin, L. A. et al. Natural neural projection dynamics underlying social behavior. Cell 157, 15351551 (2014).

Article CAS PubMed PubMed Central Google Scholar

Graving, J. M. et al. DeepPoseKit, a software toolkit for fast and robust animal pose estimation using deep learning. eLife 8, e47994 (2019).

Article CAS PubMed PubMed Central Google Scholar

Mathis, A. et al. DeepLabCut: markerless pose estimation of user-defined body parts with deep learning. Nat. Neurosci. 21, 12811289 (2018).

Article CAS PubMed Google Scholar

Pereira, T. D. et al. Fast animal pose estimation using deep neural networks. Nat. Methods 16, 117125 (2019).

Article CAS PubMed Google Scholar

Geuther, B. Q. et al. Robust mouse tracking in complex environments using neural networks. Commun. Biol. 2, 124 (2019).

Article PubMed PubMed Central Google Scholar

Gris, K. V., Coutu, J.-P. & Gris, D. Supervised and unsupervised learning technology in the study of rodent behavior. Front. Behav. Neurosci. 11, 141 (2017).

Schaefer, A. T. & Claridge-Chang, A. The surveillance state of behavioral automation. Curr. Opin. Neurobiol. 22, 170176 (2012).

Article CAS PubMed PubMed Central Google Scholar

Robie, A. A., Seagraves, K. M., Egnor, S. E. R. & Branson, K. Machine vision methods for analyzing social interactions. J. Exp. Biol. 220, 2534 (2017).

Article PubMed Google Scholar

Vu, M.-A. T. et al. A shared vision for machine learning in neuroscience. J. Neurosci. 38, 16011607 (2018).

Article CAS PubMed PubMed Central Google Scholar

Goodwin, N. L., Nilsson, S. R. O., Choong, J. J. & Golden, S. A. Toward the explainability, transparency, and universality of machine learning for behavioral classification in neuroscience. Curr. Opin. Neurobiol. 73, 102544 (2022).

Article CAS PubMed PubMed Central Google Scholar

Newton, K. C. et al. Lateral line ablation by ototoxic compounds results in distinct rheotaxis profiles in larval zebrafish. Commun. Biol. 6, 115 (2023).

Article Google Scholar

Jernigan, C. M., Stafstrom, J. A., Zaba, N. C., Vogt, C. C. & Sheehan, M. J. Color is necessary for face discrimination in the Northern paper wasp, Polistes fuscatus. Anim. Cogn. 26, 589598 (2022).

Article PubMed PubMed Central Google Scholar

Dahake, A. et al. Floral humidity as a signal not a cue in a nocturnal pollination system. Preprint at bioRxiv https://doi.org/10.1101/2022.04.27.489805 (2022).

Dawson, M. et al. Hypocretin/orexin neurons encode social discrimination and exhibit a sex-dependent necessity for social interaction. Cell Rep. 42, 112815 (2023).

Article CAS PubMed Google Scholar

Baleisyte, A., Schneggenburger, R. & Kochubey, O. Stimulation of medial amygdala GABA neurons with kinetically different channelrhodopsins yields opposite behavioral outcomes. Cell Rep. 39, 110850 (2022).

Article CAS PubMed Google Scholar

Cruz-Pereira, J. S. et al. Prebiotic supplementation modulates selective effects of stress on behavior and brain metabolome in aged mice. Neurobiol. Stress 21, 100501 (2022).

Article CAS PubMed PubMed Central Google Scholar

Linders, L. E. et al. Stress-driven potentiation of lateral hypothalamic synapses onto ventral tegmental area dopamine neurons causes increased consumption of palatable food. Nat. Commun. 13, 6898 (2022).

Article CAS PubMed PubMed Central Google Scholar

Slivicki, R. A. et al. Oral oxycodone self-administration leads to features of opioid misuse in male and female mice. Addiction Biol. 28, e13253 (2023).

Article CAS Google Scholar

Miczek, K. A. et al. Excessive alcohol consumption after exposure to two types of chronic social stress: intermittent episodes vs. continuous exposure in C57BL/6J mice with a history of drinking. Psychopharmacology (Berl.) 239, 32873296 (2022).

Article CAS PubMed Google Scholar

Cui, Q. et al. Striatal direct pathway targets Npas1+ pallidal neurons. J. Neurosci. 41, 39663987 (2021).

Article CAS PubMed PubMed Central Google Scholar

Chen, J. et al. A MYT1L syndrome mouse model recapitulates patient phenotypes and reveals altered brain development due to disrupted neuronal maturation. Neuron 109, 37753792 (2021).

Article CAS PubMed PubMed Central Google Scholar

Rigney, N., Zbib, A., de Vries, G. J. & Petrulis, A. Knockdown of sexually differentiated vasopressin expression in the bed nucleus of the stria terminalis reduces social and sexual behaviour in male, but not female, mice. J. Neuroendocrinol. 34, e13083 (2021).

Winters, C. et al. Automated procedure to assess pup retrieval in laboratory mice. Sci. Rep. 12, 1663 (2022).

Article CAS PubMed PubMed Central Google Scholar

Neira, S. et al. Chronic alcohol consumption alters home-cage behaviors and responses to ethologically relevant predator tasks in mice. Alcohol Clin. Exp. Res. 46, 16161629 (2022).

Article PubMed PubMed Central Google Scholar

Kwiatkowski, C. C. et al. Quantitative standardization of resident mouse behavior for studies of aggression and social defeat. Neuropsychopharmacology 46, 15841593 (2021).

Yamaguchi, T. et al. Posterior amygdala regulates sexual and aggressive behaviors in male mice. Nat. Neurosci. 23, 11111124 (2020).

Article CAS PubMed PubMed Central Google Scholar

Nygaard, K. R. et al. Extensive characterization of a Williams syndrome murine model shows Gtf2ird1-mediated rescue of select sensorimotor tasks, but no effect on enhanced social behavior. Genes Brain Behav. 22, e12853 (2023).

Article CAS PubMed PubMed Central Google Scholar

Ojanen, S. et al. Interneuronal GluK1 kainate receptors control maturation of GABAergic transmission and network synchrony in the hippocampus. Mol. Brain 16, 43 (2023).

Article CAS PubMed PubMed Central Google Scholar

Hon, O. J. et al. Serotonin modulates an inhibitory input to the central amygdala from the ventral periaqueductal gray. Neuropsychopharmacology 47, 21942204 (2022).

Article CAS PubMed PubMed Central Google Scholar

Murphy, C. A. et al. Modeling features of addiction with an oral oxycodone self-administration paradigm. Preprint at bioRxiv https://doi.org/10.1101/2021.02.08.430180 (2021).

Neira, S. et al. Impact and role of hypothalamic corticotropin releasing hormone neurons in withdrawal from chronic alcohol consumption in female and male mice. J. Neurosci. 43, 76577667 (2023).

Article CAS PubMed PubMed Central Google Scholar

Lapp, H. E., Salazar, M. G. & Champagne, F. A. Automated maternal behavior during early life in rodents (AMBER) pipeline. Sci. Rep. 13, 18277 (2023).

Article CAS PubMed PubMed Central Google Scholar

Barnard, I. L. et al. High-THC cannabis smoke impairs incidental memory capacity in spontaneous tests of novelty preference for objects and odors in male rats. eNeuro 10, ENEURO.0115-23.2023 (2023).

Article PubMed PubMed Central Google Scholar

Ausra, J. et al. Wireless battery free fully implantable multimodal recording and neuromodulation tools for songbirds. Nat. Commun. 12, 1968 (2021).

Article CAS PubMed PubMed Central Google Scholar

Friard, O. & Gamba, M. BORIS: a free, versatile open-source event-logging software for video/audio coding and live observations. Methods Ecol. Evol. 7, 13251330 (2016).

Article Google Scholar

Spink, A. J., Tegelenbosch, R. A. J., Buma, M. O. S. & Noldus, L. P. J. J. The EthoVision video tracking systema tool for behavioral phenotyping of transgenic mice. Physiol. Behav. 73, 731744 (2001).

Article CAS PubMed Google Scholar

Lundberg, S. shap. https://github.com/shap/shap

Lauer, J. et al. Multi-animal pose estimation, identification and tracking with DeepLabCut. Nat. Methods 19, 496504 (2022).

Article CAS PubMed PubMed Central Google Scholar

Pereira, T. D. et al. SLEAP: a deep learning system for multi-animal pose tracking. Nat Methods 19, 486495 (2022).

Segalin, C. et al. The Mouse Action Recognition System (MARS) software pipeline for automated analysis of social behaviors in mice. eLife 10, e63720 (2021).

Article CAS PubMed PubMed Central Google Scholar

Breiman, L. Random forests. Mach. Learn. 45, 532 (2001).

Article Google Scholar

Liaw, A. & Wiener, M. Classification and regression by randomForest. R News 2/3 https://journal.r-project.org/articles/RN-2002-022/RN-2002-022.pdf (2022).

Goodwin, N. L., Nilsson, S. R. O. & Golden, S. A. Rage against the machine: advancing the study of aggression ethology via machine learning. Psychopharmacology 237, 25692588 (2020).

Article CAS PubMed PubMed Central Google Scholar

Lundberg, S. M. et al. From local explanations to global understanding with explainable AI for trees. Nat. Mach. Intell. 2, 5667 (2020).

Article PubMed PubMed Central Google Scholar

Ribeiro, M. T., Singh, S., & Guestrin, C. Why should I trust you?: explaining the predictions of any classifier. Preprint at arXiv https://doi.org/10.48550/arXiv.1602.04938 (2016).

Sundararajan, M., Taly, A. & Yan, Q. Axiomatic attribution for deep networks. In Proc. of the 34th International Conference on Machine Learning 33193328 (MLR Press, 2017).

Hatwell, J., Gaber, M. M. & Azad, R. M. A. CHIRPS: explaining random forest classification. Artif. Intell. Rev. 53, 57475788 (2020).

Article Google Scholar

Lundberg, S. & Lee, S.-I. A unified approach to interpreting model predictions. Preprint at arXiv https://doi.org/10.48550/arXiv.1705.07874 (2017).

Verma, S., Dickerson, J. & Hines, K. Counterfactual explanations for machine learning: a review. Preprint at arXiv https://doi.org/10.48550/arXiv.2010.10596 (2020).

Here is the original post:
Simple Behavioral Analysis (SimBA) as a platform for explainable machine learning in behavioral neuroscience - Nature.com