TM / Pc material pair for sensing and removing sulfur-containing gases and a method for predicting performance

Abstract

The application discloses a TM / Pc material sulfur-containing gas sensing and removal performance prediction method, and belongs to the technical field of the cross of functional material design and artificial intelligence. The method comprises the following steps: obtaining adsorption energy and gas sensing response value and constructing a data set, constructing a multi-task deep learning network, extracting shared potential feature representation through a shared backbone network, outputting adsorption energy prediction value by a regression head, and outputting gas sensing response category probability value by a classification head; a dynamic weighted compound loss function is used to train the model, the weighted coefficient is dynamically optimized on the verification set, and a multi-task deep learning prediction model is obtained; the features of the system to be predicted are input into the model, and adsorption energy and sensing response category prediction results are output. The application can simultaneously predict adsorption energy and gas sensing response, effectively capture the internal coupling mechanism, solve the problem that the existing single-task model is difficult to balance high sensitivity and moderate adsorption energy, and improve the prediction accuracy and material screening efficiency.

Description

Technical Field

[0001] This invention relates to the field of functional materials design and artificial intelligence, and in particular to a method for predicting the sensing and removal performance of sulfur-containing gases using TM / Pc materials. Background Technology

[0002] In recent years, rapid industrialization has led to an increase in emissions of sulfur-containing gases (such as H2S, SO, SO2, and SO3), posing a serious threat to the atmospheric environment, industrial production safety, and human health. These gases are often highly toxic, flammable, or corrosive; therefore, there is an urgent social need to develop functional materials and methods for their efficient monitoring (sensing) and removal (purification).

[0003] In existing technologies, the monitoring of sulfur-containing gases primarily relies on gas sensors, and the core performance of these sensors depends on the sensing materials they employ. Transition metal phthalocyanine (TM / Pc), as a p-type organic semiconductor material, is considered a highly promising candidate for gas sensing and adsorption due to its high specific surface area, unique central metal electronic structure, and excellent chemical and thermal stability. However, TM / Pc materials contain a wide variety of transition metal (TM) central ions (up to dozens), and different target sulfur-containing gases need to be matched. If the optimal material combination is selected through traditional trial-and-error methods involving experimental synthesis and performance testing, the research and development cycle is long, costly, and extremely inefficient.

[0004] To accelerate the development of high-performance sensing and adsorption materials, researchers have introduced a high-throughput virtual screening strategy that combines density functional theory (DFT) calculations with machine learning (ML). DFT calculations can obtain key electronic structure information of the material system, such as density of states, band gap, and charge distribution. The machine learning model, based on the calculated data, can construct a quantitative mapping relationship from microstructure to macroscopic performance (such as gas adsorption energy or sensing response value), thereby enabling rapid prediction of the performance of candidate materials.

[0005] However, the aforementioned existing technologies still have the following key bottlenecks in practical applications: First, balancing the conflicting objectives of sensing and adsorption performance is difficult. Ideal gas-sensitive and purification materials need to possess both high gas sensitivity (this directly determines the sensor's minimum detection limit and responsiveness) and moderate adsorption energy (this affects the material's selectivity and regeneration recovery ability). Because these two performance indicators are inherently coupled and competitive in their physicochemical mechanisms (for example, excessive adsorption, while helping to improve the sensing signal, often leads to difficult desorption and poor recovery), any independent enhancement of one indicator may come at the cost of weakening the other.

[0006] Secondly, traditional single-task machine learning models struggle to capture multi-objective collaborative mechanisms. Existing models typically perform independent modeling for only a single performance attribute each time (e.g., predicting only the adsorption energy value, or distinguishing only the level of sensing response), lacking the ability to simultaneously learn and correlate these two interdependent physicochemical properties within the same learning framework. Consequently, such methods fail to reveal the intrinsic constraints and collaborative laws between adsorption energy and sensing response, potentially leading to the selected materials' overall performance deviating from practical application requirements, or even resulting in suboptimal solutions.

[0007] Therefore, how to provide a method that can break through the limitations of traditional single-task modeling, coordinate and balance the adsorption characteristics and sensing response characteristics of transition metal phthalocyanine materials for sulfur-containing gases within the same prediction framework, and achieve joint prediction with high sensitivity and moderate adsorption capacity has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] This invention overcomes the shortcomings of existing technologies in the design of sulfur-based toxic gas sensing and purification materials, and provides a method for predicting the sensing and removal performance of TM / Pc materials for sulfur-containing gases.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention discloses a method for predicting the sensing and removal performance of sulfur-containing gases using TM / Pc materials, comprising the following steps: Step S1: Based on density functional theory calculations, obtain the electronic structure data of the transition metal phthalocyanine material and the sulfur-containing gas adsorption system, and calculate the adsorption energy and gas sensing response value to construct a dataset; the sulfur-containing gas includes H2S, SO, SO2, and SO3. Step S2: Extract four types of input features from the dataset, including: transition metal atom features in transition metal phthalocyanines, gas molecule adsorption atom features, transition metal phthalocyanine system features, and gas molecule system features; Step S3: Construct a multi-task deep learning network, which includes a shared backbone network, a regression head, and a classification head; wherein, the shared backbone network is used to extract shared latent feature representations from the four types of input features; the regression head outputs the adsorption energy prediction value based on the shared latent feature representations; and the classification head outputs the probability value of the gas sensing response category based on the shared latent feature representations. Step S4: The multi-task deep learning network is trained using a dynamic weighted composite loss function. The dynamic weighted composite loss function is composed of a weighted sum of the loss terms of the adsorption energy regression task and the gas sensing response classification task. The weighting coefficients of the two tasks are dynamically optimized on the validation set to obtain a well-trained multi-task deep learning prediction model. Step S5: Input the four types of input features of the transition metal phthalocyanine material to be predicted and the sulfur-containing gas system into the trained multi-task deep learning prediction model, and output the adsorption energy prediction value and the gas sensing response category prediction result.

[0010] Preferably, in step S1: The adsorption energy Calculate according to the following formula: , in, The total energy of the gas-transition metal phthalocyanine complex; The total energy of the original transition metal phthalocyanine; The total energy of isolated gas molecules; This is the corrected basis set superposition error; The gas sensing response SR is calculated according to the following formula: , , in, Electrical conductivity; The conductivity of the complex; The conductivity of the substrate; denoted as band gap; K as Boltzmann constant; T as temperature; and A as a constant.

[0011] Preferably, step S1 further includes: classifying the calculated gas sensing response SR into two categories with a threshold of 100, where SR≥100 is labeled as high response and SR<100 is labeled as low response.

[0012] Preferably, the four types of input features in step S2 specifically include: Characteristics of transition metal atoms: atomic radius, first ionization energy, Mulliken charge, Pauling electronegativity, electron affinity, d-band center; Characteristics of gas molecules adsorbed atoms: atomic type, atomic radius, electronegativity, and polarizability of the atoms at the adsorption site; Characteristics of transition metal phthalocyanine systems: band gap, dipole moment, chemical hardness, binding energy; Characteristics of a gas molecule system: highest occupied molecular orbital energy level, lowest unoccupied molecular orbital energy level, molecular dipole moment, and molecular polarizability.

[0013] Preferably, the shared backbone network in step S3 consists of three fully connected layers with the number of neurons decreasing layer by layer; each fully connected layer is followed by a LeakyReLU activation function with a negative slope of 0.01; and a progressively increasing Dropout regularization strategy is adopted, with the Dropout rate of each layer increasing sequentially.

[0014] Preferably, the regression head consists of two fully connected layers, including a Dropout layer with a fixed Dropout rate of 0.5, and the output layer is a single neuron without using an activation function; the classification head consists of two fully connected layers, with the last layer using a Sigmoid activation function to output a probability value between 0 and 1, using 0.5 as the classification threshold to distinguish between high and low responses.

[0015] Preferably, the dynamically weighted composite loss function in step S4 for: , in, This represents the mean square error loss for the adsorption energy regression task. The cross-entropy loss is used for the gas sensing response classification task; α and β are the weighting coefficients for the two tasks, respectively; the weighting coefficients α and β are dynamically optimized and adjusted based on the performance of the validation set during training.

[0016] Preferably, the training process in step S4 further includes: using five-fold hierarchical cross-validation to ensure that the ratio of high-response to low-response samples in each fold is consistent with the overall dataset; and using an early stopping mechanism to terminate training early when the validation set loss no longer decreases within a preset number of consecutive rounds.

[0017] Preferably, the training process in step S4 further includes: using the Mixup data augmentation strategy to perform linear interpolation on the training samples in the feature space to generate virtual samples and enhance the robustness of the model; the optimizer uses the Adam optimizer and the initial learning rate is set to 0.001.

[0018] Preferably, the method further includes step S6: using SHAP analysis to perform interpretability analysis on the trained multi-task deep learning prediction model, obtaining the contribution ranking of each input feature to the prediction result, so as to identify the key physicochemical factors affecting the adsorption-sensing synergistic performance.

[0019] This invention addresses the technical deficiencies in the prior art and has the following beneficial effects: By constructing a multi-task deep learning architecture that combines a shared backbone network with task-specific branches, it is possible to simultaneously learn two interrelated performance indicators—adsorption energy and gas sensing response—within a unified model. This effectively captures and characterizes the synergistic and constraint mechanisms between the two, thus overcoming the multi-objective trade-off imbalance problem caused by isolated modeling in traditional single-task models. Through a joint prediction framework, the prediction accuracy for adsorption energy (regression task) and gas sensing response (classification task) is improved, achieving a balance optimization between high sensitivity and moderate adsorption energy (i.e., good recoverability). This provides a reliable data-driven decision-making basis for designing multifunctional transition metal phthalocyanine materials with both high-performance gas detection and purification functions. Furthermore, it can elucidate the synergistic mechanism between the sensing response and adsorption thermodynamics of transition metal phthalocyanine (TM / Pc) materials for sulfur-containing gases (H2S, SO, SO2, SO3), revealing the key physicochemical factors affecting the comprehensive performance of materials at the electronic structure level, and providing clear guidance for the targeted screening and rational design of subsequent high-performance sensing and adsorption materials. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained from these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the multi-task deep learning framework in this invention. Detailed Implementation

[0022] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0023] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0024] like Figure 1 As shown, this invention discloses a method for predicting the sensing and removal performance of sulfur-containing gases using TM / Pc materials, comprising the following steps: Step S1: Based on density functional theory calculations, obtain the electronic structure data of the transition metal phthalocyanine material and the sulfur-containing gas adsorption system, and calculate the adsorption energy and gas sensing response value to construct a dataset; the sulfur-containing gas includes H2S, SO, SO2, and SO3. Step S2: Extract four types of input features from the dataset, including: transition metal atom features in transition metal phthalocyanines, gas molecule adsorption atom features, transition metal phthalocyanine system features, and gas molecule system features; Step S3: Construct a multi-task deep learning network, which includes a shared backbone network, a regression head, and a classification head; wherein, the shared backbone network is used to extract shared latent feature representations from the four types of input features; the regression head outputs the adsorption energy prediction value based on the shared latent feature representations; and the classification head outputs the probability value of the gas sensing response category based on the shared latent feature representations. Step S4: The multi-task deep learning network is trained using a dynamic weighted composite loss function. The dynamic weighted composite loss function is composed of a weighted sum of the loss terms of the adsorption energy regression task and the gas sensing response classification task. The weighting coefficients of the two tasks are dynamically optimized on the validation set to obtain a well-trained multi-task deep learning prediction model. Step S5: Input the four types of input features of the transition metal phthalocyanine material to be predicted and the sulfur-containing gas system into the trained multi-task deep learning prediction model, and output the adsorption energy prediction value and the gas sensing response category prediction result.

[0025] This method constructs a shared-task-specific hierarchical neural network architecture and combines it with multi-source feature data generated by density functional theory calculations to achieve joint prediction of adsorption energy (regression task) and gas sensing response (classification task). This technical solution consists of the following four core modules: (1) Data generation module: Based on density functional theory calculation, the electronic structure characteristics of the adsorption system of TM / Pc material and sulfur-based gas (H2S, SO, SO2, SO3) are obtained.

[0026] Technical measures: Gaussian 16 software was used, with the ωB97XD functional employed. The 6-311G(d,p) basis set was used for non-metallic atoms, and the LANL2TZ basis set was used for metallic atoms to perform structure optimization and frequency calculation. Calculate the adsorption energy according to equation (1) : (1), in , , , and the total energy of the gas-TM / Pc complex, isolated gas molecules, and original TM / Pc, respectively, and the basis set superposition error is corrected by the Counterpoise method (balance correction method); The sensing response SR is calculated according to equations (2) and (3): (2), (3), in, Electrical conductivity; The conductivity of the complex; The conductivity of the substrate; denoted as band gap; K as Boltzmann constant; T as temperature; and A as a constant.

[0027] Its function is to provide high-fidelity label data (adsorption energy) and input features (electronic structure descriptors) for subsequent machine learning models.

[0028] (2) Feature Engineering Module: Extracts four types of input features from the atomic scale, molecular scale, and system scale; Technical measures: Constructing four types of input feature vectors

[0029]

[0030] Feature sources: Some features were obtained through simple DFT calculations, while others were read directly from the periodic table.

[0031] Function: To quantify physicochemical information into numerical features, enabling deep learning models to learn the mapping relationship between structure and performance. To ensure the numerical stability of model training, before inputting features into the model, the Min-Max normalization method is used to scale all features to the [0, 1] interval. The normalization parameters are calculated based on the training set and applied to the validation and test sets.

[0032] (3) Multi-task deep learning network module: Common representations are extracted using a shared backbone network, and adsorption energy and sensing response are output through task-specific branches respectively; Its network structure is as follows Figure 2 As shown, it includes: (A) Shared Backbone It consists of three fully connected layers, with the number of neurons decreasing layer by layer. Each fully connected layer is followed by a LeakyReLU activation function (with a negative slope of 0.01) to alleviate the neuron "death" problem. A progressive dropout strategy (a regularization technique that randomly discards some neuron outputs with a specified probability during training to suppress overfitting) is employed: the dropout rate is lower in the first layer and gradually increases in subsequent layers, for example, set to 0.1, 0.2, and 0.3 respectively, to balance feature extraction and regularization. Input: a feature vector composed of the four types of features mentioned above; Output: a high-dimensional latent feature representation, serving both tasks. The LeakyReLU activation function is a linear unit activation function with leakage correction. When the input is negative, its output is the input value multiplied by a small fixed slope (e.g., 0.01), rather than being directly set to zero, to alleviate the neuron "deactivation" problem of standard ReLU.

[0033] (B) Task-specific branch Regression Head: Used to predict adsorption energies (Eads); consists of two fully connected layers with a fixed dropout rate of 0.5, and the output layer is a single neuron (without an activation function). Classification Head: Used to predict whether the sensor response SR exceeds the threshold of 100 (high response = 1, low response = 0); it consists of two fully connected layers, the last layer of which uses the Sigmoid activation function to output a probability value between 0 and 1, with 0.5 as the classification threshold, that is, output probability p ≥ 0.5 is judged as high response, and p < 0.5 is judged as low response.

[0034] Connection relationship: The output of the shared backbone network is fed into both the regression head and the classification head. The two branches are computed in parallel, without interfering with each other, but sharing the underlying feature representation.

[0035] Function: The shared backbone network forces the model to learn common representations of adsorption energy and sensing response, while task-specific branches retain their own uniqueness, thereby capturing the intrinsic coupling mechanism between the two objectives.

[0036] (4) Model training and optimization module: adopts dynamic weighted composite loss function, five-fold hierarchical cross-validation, early stopping mechanism and Mixup data augmentation strategy.

[0037] Its dynamic weighted composite loss function for: (4), in, This represents the mean square error loss for the adsorption energy regression task. α represents the cross-entropy loss for the gas sensing response classification task; α and β are the weighting coefficients for the two tasks, respectively; after each training round, the weighting coefficients α and β are dynamically adjusted based on the model's overall performance on the validation set to adaptively balance the training progress of the two tasks and avoid one task dominating the learning direction of the entire network.

[0038] Stratified 5-Fold Cross-Validation: Ensures that the proportion of high / low response samples in each fold is consistent with the overall ratio.

[0039] Early Stopping Mechanism: The maximum number of training rounds is 2000. Training is terminated early when the total loss on the validation set no longer decreases within 50 consecutive rounds, and the model weights with the minimum loss on the validation set are restored to prevent overfitting.

[0040] Mixup data augmentation: This method uses linear interpolation to generate virtual samples from training samples in the feature space, enhancing the model's generalization ability and robustness to noise on finite datasets. Specifically, for any two training sample feature vectors and their labels, pairwise linear interpolation is performed by sampling mixing coefficients λ from a beta distribution (a continuous probability distribution defined on the interval [0, 1]). This strategy is applied to approximately 20% of the training batches, improving the model's robustness to noise and outliers.

[0041] Optimizer: The Adam optimizer is used, with an initial learning rate of 0.001.

[0042] Purpose: To ensure that the model achieves good generalization ability with limited data, while balancing the optimization objectives of the two tasks.

[0043] Specifically, the specific implementation of the method of the present invention for jointly predicting the adsorption energy and gas sensitivity of transition metal phthalocyanine (TM / Pc) materials to sulfur-based toxic gases (H2S, SO, SO2, SO3) based on a multi-task deep learning framework is as follows: Step 1: DFT Dataset Construction Procedure: Gaussian 16 software was used, employing the ωB97XD functional. The 6-311G(d,p) basis set was used for non-metallic atoms, and the LANL2TZ basis set was used for metallic atoms. Optimization was performed on 28 TM / Pc and four gas molecule structures. The adsorption energy E was calculated. ads =E gas -TM / Pc—E gas —E TM / Pc Counterpoise correction is used to correct for basis set superposition error. The sensing response SR = |σ| is calculated. substrate −σ adsorption ∣ / σadsorption ×100%. A threshold of 100 was set to divide SR into high response (1) and low response (0). A total of 78 adsorption systems were obtained. These 78 adsorption systems cover various stable adsorption configurations of 28 TM / Pc materials and 4 sulfur-containing gases, constituting the dataset of this invention, providing a sufficient data foundation for subsequent model training and evaluation.

[0044] Step 2: Feature Extraction Extract four types of input features (approximately 20 dimensions): (i) TM atomic characteristics: atomic radius rTM, first ionization energy ITM, Mulliken charge MCTM, electronegativity NTM, electron affinity ATM, d-band center; (ii) Characteristics of gas adsorbed atoms: atomic radius, electronegativity, polarizability; (iii) Characteristics of TM / Pc system: band gap GapTM, dipole moment DTM, chemical hardness η (a measure of a substance’s ability to resist electron cloud deformation or charge transfer, calculated from the band gap), binding energy Ebind; (iv) Characteristics of gas molecular systems: HOMO level, LUMO level, molecular dipole moment, polarizability.

[0045] Use Min-Max normalization to scale the features to [0, 1].

[0046] Step 3: MTDL Model Construction Shared backbone network: 3 fully connected layers (din→128→64→32), each followed by LeakyReLU activation (negative slope 0.01) and progressive Dropout (0.1 / 0.2 / 0.3). Here, din is the total dimension of the input feature vector, which is approximately 20 dimensions in this embodiment (the dimension after concatenating the four types of features).

[0047] Regression head (predicting Eads): 2 fully connected layers (32→16→1), with Dropout (0.5) after the first layer, and no activation function in the output layer.

[0048] Classification head (predicting whether SR is ≥100): 2 fully connected layers (32→16→1), the first layer is followed by Dropout(0.5), the output layer uses the Sigmoid activation function to output the high response probability p, and classifies with a threshold of 0.5.

[0049] Step 4: Model Training Data partitioning: The training and validation sets are randomly partitioned in a 4:1 ratio to maintain the same proportions of each class as the complete dataset. Five-fold stratified cross-validation is used on the training set.

[0050] Loss function: Ltotal =α⋅L reg +β⋅L cls L reg For MSE, L cls Let α be the cross-entropy. The weights α and β are dynamically optimized on the validation set.

[0051] Hyperparameters: Adam optimizer, learning rate 0.001, batch size 16, maximum number of epochs 2000, early stopping patience 50 epochs, gradient clipping max_norm=1.0. Mixup data augmentation was used (λ∼Beta(0.2, 0.2), applied to approximately 20% of the training batches).

[0052] The model is implemented using the PyTorch framework and trained on an NVIDIA RTX 3060 GPU in minutes. PyTorch is an open-source programming framework for deep learning research, with tensor computation and automatic differentiation mechanisms at its core.

[0053] Step 5: Application of Model Prediction Input 20-dimensional features of the system to be predicted → Normalization → MTDL forward propagation → Output E^ ads And probability p^. For example, Fe / Pc for SO: predict E^ ads =−0.91 eV (true -0.90), p^=0.998 (high response). Screening criteria: Materials that simultaneously meet the requirements of adsorption energy in the range of -1.0 to -0.78 eV (moderate adsorption strength) and sensing response ≥100 are considered candidates with excellent overall performance.

[0054] Step 6: SHAP Interpretability Analysis (SHAP is an abbreviation for SHApley Additive exPlanations) The SHAP library is used to calculate the contribution of each feature. Feature importance ranking: r TM >I TM Gap TM >MC TM >ε d HOMO g This indicates that the prediction is dominated by the electronic properties of the metal center. This analysis, based on the entire test set and averaging the differences between samples, provides a transparent and quantitative basis for understanding the model's decision-making logic and guiding further experimental synthesis.

[0055] Implementation results: Compared with single-task models (RF, XGBoost, GBDT, SVM), the MTDL model of this invention achieved the following results on the test set: classification accuracy of 0.83 (31.7% improvement over the best SVM), regression R²=0.86, and RMSE=0.46 eV (23.3% reduction over the best RF).

[0056] In this embodiment, the method further includes the following steps: The latent feature vectors extracted by the shared backbone network from the target input sample are obtained. At the same time, the partial derivatives of the latent feature vectors with the regression head loss and the classification head loss are respectively used to obtain the first gradient vector representing the sensitive change direction of the adsorption energy and the second gradient vector representing the sensitive change direction of the sensing response. Unit perturbations are applied to the potential feature vectors along the directions of the first gradient vector and the second gradient vector, respectively. The changes in the output of the classification head and the output of the regression head after the perturbations are observed. Based on this, a task cross-influence matrix is ​​constructed. The non-main diagonal elements of the task cross-influence matrix reflect the perturbation effect of the adsorption energy sensitive direction on the sensor response output and the perturbation effect of the sensor response sensitive direction on the adsorption energy output, respectively. Singular value decomposition is performed on the task cross-influence matrix to extract the first left singular vector and the first right singular vector corresponding to the largest singular value, as well as the second left singular vector and the second right singular vector corresponding to the second largest singular value. The subspace spanned by the first left singular vector and the first right singular vector is defined as the first coupling subspace, and the subspace spanned by the second left singular vector and the second right singular vector is defined as the second coupling subspace. The first coupling subspace and the second coupling subspace are orthogonal to each other and respectively retain the dominant mode and the secondary dominant mode of the cross-influence between the two tasks. The potential feature vectors are projected onto the first coupling subspace and the second coupling subspace respectively to obtain the first coupling representation component and the second coupling representation component. The cross-correlation norm of the first coupled characterization component and the second coupled characterization component is calculated. This cross-correlation norm is used as a quantitative measure of the coupling strength between the adsorption energy and the sensing response in the transition metal phthalocyanine-sulfur-containing gas adsorption system corresponding to the input sample, and is output. The cross-correlation norm is the matrix norm corresponding to the interaction structure matrix constructed based on the two component vectors, such as the Frobenius norm, which measures the degree of correlation between the two subspace characterization components.

[0057] The task cross-influence matrix, with the perturbation direction as the row and the observation task as the column, quantifies the degree of cross-influence of the sensitive direction perturbation of one task on the output of another task in the latent feature space.

[0058] It should be noted that in the joint prediction of adsorption energy and sensing response, existing methods typically only focus on the prediction accuracy of each task, lacking an effective means to quantitatively characterize the inherent coupling between them. For the transition metal phthalocyanine-sulfur-containing gas adsorption system, there is a physically inherent competition and constraint relationship between adsorption energy and sensing response. If this coupling strength cannot be quantitatively assessed, it is difficult to determine whether the prediction results truly reflect the intrinsic characteristics of the material system, and it is also impossible to effectively identify the prediction reliability of the model within the coupling blind zone of the two tasks. In view of this, this embodiment utilizes a pre-trained shared backbone network to obtain the latent feature vector extracted by it for the target input sample. The partial derivatives of this latent feature vector are obtained by applying the regression head loss and the classification head loss respectively, yielding the first gradient vector and the second gradient vector, which respectively characterize the sensitive change directions of adsorption energy and sensing response in the latent feature space. By applying unit perturbations along the two gradient directions to the latent feature vectors respectively, and observing the changes in the outputs of the classification head and regression head before and after the perturbations, a task cross-influence matrix is ​​constructed. The elements located on the non-main diagonal positions in the matrix quantify the perturbation effect of the adsorption energy sensitive direction on the sensing response output, as well as the perturbation effect of the sensing response sensitive direction on the adsorption energy output, thereby explicitly characterizing the mutual influence relationship between the two tasks in numerical form.

[0059] Furthermore, singular value decomposition is performed on the task cross-influence matrix to extract the first left and first right singular vectors corresponding to the largest singular value, and the second left and second right singular vectors corresponding to the second largest singular value. Based on this, the subspace spanned by the first left and first right singular vectors is defined as the first coupling subspace, and the subspace spanned by the second left and second right singular vectors is defined as the second coupling subspace. The first and second coupling subspaces are orthogonal to each other, respectively preserving the dominant and secondary dominant transmission modes of the cross-influence between adsorption energy and sensing response, that is, the two most important and independent feature transformation directions of mutual perturbation between the two tasks. The coupling subspace mentioned here refers to the subspace in the latent feature space that is jointly dominated by the two tasks and can reflect the cross-influence structure between the tasks.

[0060] The aforementioned latent feature vectors are projected onto the first and second coupled subspaces respectively to obtain the first and second coupled characterization components. The cross-correlation norm of the two coupled characterization components is used as a quantitative measure of the coupling strength between the adsorption energy and sensing response corresponding to the input sample, and is output. The cross-correlation norm refers to the matrix norm corresponding to the interaction structure matrix constructed based on the two component vectors, and is used to measure the degree of correlation between the characterization components in the two coupled subspaces.

[0061] This embodiment achieves the quantitative output of the coupling strength between adsorption energy and sensing response in each transition metal phthalocyanine-sulfur-containing gas adsorption system to be predicted. The coupling strength value can be directly used to evaluate the reliability of the model's prediction results for the current sample: the higher the coupling strength, the more significant the mutual constraint between the two tasks in this sample region, and the more realistically the joint prediction results of the two tasks reflect the intrinsic physicochemical competition relationship of the material, rather than the accidental fitting of the model or data bias.

[0062] In this embodiment, the method further includes the following steps: For all samples in the dataset, the feature vector obtained by concatenating the four types of input features of each sample is used as the original coordinate point of the sample in the original feature space, and the original coordinate points of all samples are collected to form the original feature point cloud. For each original coordinate point of the original feature point cloud, calculate the Euclidean distance between the sample and its k nearest neighbors, and take the median of the Euclidean distance as the local scale parameter. Based on the local scale parameter, construct a local feature neighborhood for each original coordinate point, where k is the integer part of the square root of the total number of samples in the dataset. Starting from the local feature neighborhood, using the Euclidean distance between the original coordinate points as a metric, a distance-based simple complex manifold is constructed sequentially. During the construction process, the occurrence and extinction times of homology classes in the complex under different distance thresholds are recorded to generate a continuous graph reflecting the evolution of the topological structure of the feature space. The zeroth-order continuous cohomology feature reflecting the connectivity of the feature space, the first-order continuous cohomology feature reflecting the void structure of the feature space, and the second-order continuous cohomology feature reflecting the higher-dimensional cavity of the feature space are extracted from the continuous graph, and the persistence measure of the Betty interval of each order of continuous cohomology is calculated. The persistence measures of the Betty intervals of the zeroth, first, and second order continuous cohomology are concatenated into a topological feature vector, which represents the topological invariant of the feature space in which the input sample is located. The topological feature vector is concatenated with the original feature vector obtained by concatenating the four types of input features to form an augmented feature vector. The augmented feature vector is then used as the input of the shared backbone network in the multi-task deep learning network, enabling the shared backbone network to simultaneously learn the electronic structure features of the material system and its topological structure features in the high-dimensional feature space from the augmented feature vector.

[0063] It should be noted that in existing prediction methods combining DFT and machine learning, the input features typically only include local physicochemical descriptors such as the electronic structure and atomic properties of the material. While these features can capture the microscopic properties of a single adsorption system, they neglect the macroscopic distribution and intrinsic clustering structure of multiple samples in the overall feature space. For the transition metal phthalocyanine-sulfur-containing gas adsorption system, the combination of different transition metal centers and different gas molecules will form a specific distribution pattern in the feature space. The connectivity, void, and high-dimensional cavity structures contained in this distribution pattern reflect the intrinsic correlation between different material-gas combinations. If the model learns only from the independent features of each sample, it is difficult to capture this global topological information that determines the coordinated change of adsorption energy and sensing response across samples. To solve the above problem, this embodiment first concatenates the four types of input features of all samples in the constructed dataset, using the concatenated feature vector of each sample as the original coordinate point of that sample in the original feature space, and summing all the original coordinate points to form the original feature point cloud. The original feature space refers to the high-dimensional vector space spanned by each input feature dimension as the coordinate axis; the original feature point cloud refers to the set of coordinate points of all samples in this space.

[0064] Then, based on the local scale parameter, a local feature neighborhood is defined for each original coordinate point, centered on that point and with the local scale parameter as the reference radius. The local feature neighborhood refers to a local spherical region in the feature space centered on a sample point and containing its nearest neighbor samples. Its function is to provide a distance reference benchmark adapted to the local sample density for subsequent complex construction. Starting from the local feature neighborhood of each sample point, distance-based simplex manifolds are constructed sequentially using the Euclidean distance between the original coordinate points as a metric. A simplex manifold is a topological structure composed of points, edges, triangles, and their higher-dimensional generalization units, used to approximate the shape contour of the feature point cloud in space. The construction process is driven by a progressively increasing distance threshold: as the distance threshold gradually increases from zero, for any two original coordinate points, if the Euclidean distance between them is less than the current distance threshold, an edge is formed between the two points, creating a one-dimensional skeleton of the simplex; when there are edges between every pair of three points, a triangular facet is formed with these three points as vertices; higher-dimensional simplexes follow the same rules. In this process, the occurrence and extinction times of homology classes in a simplicial complex manifold under different distance thresholds are recorded. Here, a homology class refers to an equivalence class in a simplicial complex that shares the same topological features, such as rings, holes, or cavities; the occurrence time refers to the minimum distance threshold corresponding to the initial formation of a homology class; and the extinction time refers to the distance threshold corresponding to the filling or destruction of the homology class. Plotting the occurrence and extinction times of all homology classes as point pairs on a two-dimensional plane yields a persistence graph reflecting the evolution of the feature space's topology with distance scales.

[0065] From the generated persistence graph, zeroth-order persistence homology features, first-order persistence homology features, and second-order persistence homology features are extracted respectively. The zeroth-order persistence homology feature reflects the generation and merging process of connected components between sample points in the feature space with respect to distance thresholds, i.e., connectivity features; the first-order persistence homology feature reflects the appearance and disappearance process of one-dimensional ring or void structures in the feature space, i.e., void structure features; and the second-order persistence homology feature reflects the appearance and disappearance process of two-dimensional cavities in the feature space, i.e., higher-dimensional cavity features. For each homology class in each order of persistence homology feature, the persistence metric of its Betty interval is calculated. The Betty interval refers to the interval formed by the appearance time and disappearance time corresponding to each homology class in the persistence graph. The persistence metric can be characterized by the difference between the appearance time and disappearance time of the homology class; the larger the difference, the wider the distance scale range of the homology class, i.e., the stronger the stability and the more representative the topological structure. For example, if a first-order homology class appears at a distance threshold of 0.3 and disappears at a distance threshold of 0.9, then its Betty interval persistence measure is 0.6. In this manner, the persistence measure of each homology class in each order of sustained homology is calculated separately.

[0066] Next, the persistence measures of all Betty intervals of the zeroth, first, and second order continuous cohomology are concatenated into a topological feature vector in a predetermined order. This topological feature vector represents the topological invariants of the feature space in which the input sample resides at the current scale, i.e., the essential structural information unaffected by coordinate scaling or continuous deformation. Finally, the topological feature vector is concatenated with the original feature vector obtained by concatenating the four types of input features to form an augmented feature vector. This augmented feature vector is used as the input to the shared backbone network in a multi-task deep learning network, enabling the shared backbone network to simultaneously learn the electronic structure features of the material system and its topological structure features in the high-dimensional feature space determined by multiple samples during training or inference. Thus, the model can not only perceive the individual physicochemical properties of each sample but also its aggregation position and structural role in the overall data distribution, thereby improving the model's ability to represent the coupling relationship between adsorption energy and sensing response.

[0067] In summary, compared with existing technologies such as single-task machine learning models, including Random Forest (RF), eXtreme Gradient Boosting (XGBoost), Gradient Boosting Decision Tree (GBDT), and Support Vector Machine (SVM), the method proposed in this invention for jointly predicting the adsorption energy and gas sensitivity of transition metal phthalocyanine materials to sulfur-based toxic gases based on a multi-task deep learning (MTDL) framework has the following technical advantages: I. Significant improvement in prediction accuracy 1. Performance improvement for classification tasks (gas sensing response prediction) Using a sensing response threshold of 100 as the classification standard (≥100 for high response, <100 for low response), the MTDL model of this invention performs as follows on the independent test set:

[0068] The accuracy of this invention (0.83) is 31.7% higher than that of the optimal single-task model SVM (0.63); the F1 score of this invention (0.83) is 31.7% higher than that of SVM (0.63); and the recall of this invention (0.88) is 39.7% higher than that of SVM (0.63).

[0069] The above results demonstrate that by jointly learning adsorption energy and sensing response, this invention can better capture discriminative patterns related to sensing performance and exhibits significantly better generalization ability than single-task models under conditions of unseen data.

[0070] 2. Performance improvement of regression task (adsorption energy prediction)

[0071] The coefficient of determination R² (0.86) of this invention is higher than all single-task models, indicating that the model has the strongest explanatory power for the variance of adsorption energy. The root mean square error (RMSE) of this invention (0.46 eV) is 23.3% lower than that of the optimal single-task model RF (0.60 eV). The mean absolute error (MAE) of this invention (0.35 eV) is 23.9% lower than that of RF (0.46 eV). Here, R² is a statistic measuring the goodness of fit of the regression model, representing the proportion of the variance in the dependent variable that can be explained by the independent variable. RMSE is the root mean square error, and MAE is the mean absolute error.

[0072] II. Successfully capturing the intrinsic coupling mechanism between adsorption energy and sensing response Existing single-task models model adsorption energy and sensing response as independent targets, failing to reveal their synergistic relationship. This invention forces the model to learn common representations of the two tasks by sharing a backbone network, effectively capturing their inherent coupling mechanism.

[0073] Experimental evidence: The MTDL model of this invention achieved an R² of 0.73 in cross-validation, which is significantly higher than the 0.48~0.58 of the single-task model. On the independent test set, the R² of MTDL (0.86) is higher than the cross-validation result (0.73), indicating that the model has good generalization ability, and the joint optimization framework is always better than the single-task model on the independent test set.

[0074] III. Model Interpretability: Revealing Key Physicochemical Factors This invention reveals the key features affecting prediction results and their importance ranking through SHAP analysis, providing physically interpretable guidance for materials design, which is difficult to achieve with existing black-box machine learning models.

[0075] SHAP feature importance ranking (from highest to lowest): 1. Transition metal atomic radius rTM 2. First Ionization Energy (ITM) 3. Bandgap™ in TM / Pc systems 4. Transition metal Mulliken charge MCTM 5. The center of the d-band on the surface of a pure metal is εd. 6. HOMO energy levels of gas molecules HOMOg This ranking indicates that the adsorption-sensing synergistic performance is mainly dominated by the electronic properties of the metal center, and is also jointly regulated by the electronic structure of the substrate and the electron-donating ability of the gas phase, providing a clear direction for subsequent material design.

[0076] IV. Successful screening of high-performance TM / PC sensing and adsorption materials Technical Results: This invention, through DFT calculations combined with MTDL predictions, successfully screened candidate materials with excellent performance against sulfur-based gases from 28 TM / Pc materials.

[0077] The Fe / Pc sensing response to SO reached a high value of 1628.21, far exceeding the screening criteria for candidate sensing materials. By applying an electric field (ranging from −0.006 to +0.006 au), the adsorption energy can be further tuned, increasing the sensing response by several orders of magnitude (up to 10 au). 22 (magnitude).

[0078] V. Significantly reduced computational efficiency and design cycle Compared with the traditional "trial and error" experimental screening, this invention combines DFT calculation with MTDL prediction to achieve high-throughput virtual screening of material properties: Traditional experimental methods: synthesizing a TM / Pc material and testing its performance on four gases takes an average of several weeks to several months; The method of this invention: the performance prediction of 28 TM / Pc materials on 78 adsorption systems of four gases can be completed in a few hours; the design cycle is expected to be shortened by 2 to 3 orders of magnitude.

[0079] VI. Summary of Technical Effects

[0080] In summary, by introducing a multi-task deep learning framework, this invention achieves significantly better technical results than existing technologies in terms of prediction accuracy, model interpretability, material screening efficiency, and depth of understanding of the adsorption-sensing coupling mechanism.

[0081] It should also be noted that this invention is equally applicable to the prediction of other two-dimensional material sensing / adsorption systems. For example, TM / Pc can be replaced with other modifiable transition metal substrates, such as MoS2, graphene, or MXene; simultaneously, sulfur-containing gases can be extended to other environmentally toxic and harmful gases, such as NO. X NH3 or volatile organic compounds. Simply follow the procedure in step 1 to recalculate and generate a dataset for the new system, and retrain or fine-tune the MTDL model to achieve accurate predictions under the same architecture.

[0082] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0083] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0084] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0085] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0086] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0087] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting TM / Pc material pair sensing and removal performance for sulfur-containing gases, characterized by, Includes the following steps: Step S1: Based on density functional theory calculations, obtain the electronic structure data of the transition metal phthalocyanine material and the sulfur-containing gas adsorption system, and calculate the adsorption energy and gas sensing response value to construct a dataset; the sulfur-containing gas includes H2S, SO, SO2, and SO3. Step S2: Extract four types of input features from the dataset, including: transition metal atom features in transition metal phthalocyanines, gas molecule adsorption atom features, transition metal phthalocyanine system features, and gas molecule system features; Step S3: Construct a multi-task deep learning network, which includes a shared backbone network, a regression head, and a classification head; wherein, the shared backbone network is used to extract shared latent feature representations from the four types of input features; the regression head outputs the adsorption energy prediction value based on the shared latent feature representations; and the classification head outputs the probability value of the gas sensing response category based on the shared latent feature representations. Step S4: The multi-task deep learning network is trained using a dynamic weighted composite loss function. The dynamic weighted composite loss function is composed of a weighted sum of the loss terms of the adsorption energy regression task and the gas sensing response classification task. The weighting coefficients of the two tasks are dynamically optimized on the validation set to obtain a well-trained multi-task deep learning prediction model. Step S5: Input the four types of input features of the transition metal phthalocyanine material to be predicted and the sulfur-containing gas system into the trained multi-task deep learning prediction model, and output the adsorption energy prediction value and the gas sensing response category prediction result.

2. The method for predicting the sensing and removal performance of sulfur-containing gases using TM / Pc materials according to claim 1, characterized in that, In step S1: the adsorption energy calculated according to the formula: ， Etot = Egas + Epm + Ecorr Etot = Epm + Ecorr Etot = Egas + Ecorr Ecorr = Ecorr (basis set superposition error) The gas sensing response SR is calculated according to the following formula: ， ， in, Electrical conductivity; The conductivity of the complex; The conductivity of the substrate; denoted as band gap; K as Boltzmann constant; T as temperature; and A as a constant.

3. The method for predicting the sensing and removal performance of sulfur-containing gases using TM / Pc materials according to claim 1, characterized in that, Step S1 further includes: performing binary classification labeling on the calculated gas sensing response SR with a threshold of 100, labeling SR≥100 as high response class and SR<100 as low response class.

4. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The four types of input features mentioned in step S2 specifically include: Characteristics of transition metal atoms: atomic radius, first ionization energy, Mulliken charge, Pauling electronegativity, electron affinity, d-band center; Characteristics of gas molecules adsorbed atoms: atomic type, atomic radius, electronegativity, and polarizability of the atoms at the adsorption site; Characteristics of transition metal phthalocyanine systems: band gap, dipole moment, chemical hardness, binding energy; Characteristics of a gas molecule system: highest occupied molecular orbital energy level, lowest unoccupied molecular orbital energy level, molecular dipole moment, and molecular polarizability.

5. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The shared backbone network in step S3 consists of three fully connected layers with the number of neurons decreasing layer by layer; each fully connected layer is followed by a LeakyReLU activation function with a negative slope of 0.01; and a progressively increasing Dropout regularization strategy is adopted, with the Dropout rate of each layer increasing sequentially.

6. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The regression head consists of two fully connected layers, including a Dropout layer with a fixed Dropout rate of 0.5, and the output layer is a single neuron without using an activation function; the classification head consists of two fully connected layers, with the last layer using a Sigmoid activation function to output a probability value between 0 and 1, using 0.5 as the classification threshold to distinguish between high and low responses.

7. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The dynamic weighted compound loss function in the step S4 is: ， in, This represents the mean square error loss for the adsorption energy regression task. The cross-entropy loss is used for the gas sensing response classification task; α and β are the weighting coefficients for the two tasks, respectively; the weighting coefficients α and β are dynamically optimized and adjusted based on the performance of the validation set during training.

8. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The training process in step S4 also includes: using five-fold hierarchical cross-validation to ensure that the ratio of high-response to low-response samples in each fold is consistent with the overall dataset; and using an early stopping mechanism to terminate training early when the validation set loss no longer decreases within a preset number of consecutive rounds.

9. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The training process in step S4 further includes: using the Mixup data augmentation strategy to perform linear interpolation on the training samples in the feature space to generate virtual samples and enhance the robustness of the model; the optimizer uses the Adam optimizer and the initial learning rate is set to 0.

001.

10. The method of claim 1, wherein the TM / Pc material is selected from the group consisting of TM / Pc materials listed in Table 1. The method also includes step S6: using SHAP analysis to perform interpretability analysis on the trained multi-task deep learning prediction model, obtaining the contribution ranking of each input feature to the prediction result, in order to identify key physicochemical factors affecting the adsorption-sensing synergistic performance.

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