A Deep-Time Atmospheric CO2 Evolution Reconstruction Method Based on Physical Information Neural Networks

Abstract

The application discloses a deep-time atmospheric CO2 evolution reconstruction method based on a physical information neural network, and belongs to the technical field of artificial intelligence inversion. The method first aligns multi-source paleoclimate data in time and estimates uncertainty; then, confidence weight negatively correlated with the estimation result is designed, a physical constraint loss and a data fitting loss fused with the confidence weight are used to jointly optimize a physical information neural network for deep-time atmospheric CO2 evolution reconstruction. The method can stably obtain a continuous atmospheric CO2 evolution curve under the conditions of sparse deep-time data, conflict of multi-source proxy indicators and high coupling of climate factors, and provides a reusable calculation method for deep-time paleoclimate quantitative inversion and carbon cycle driving mechanism analysis.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence inversion technology, and in particular relates to a method for deep-time atmospheric CO2 evolution reconstruction based on physical information neural networks. Background Technology

[0002] Deep-time atmospheric CO2 concentration is a crucial indicator for understanding the long-term evolution of the Earth's climate system, glacial cycles, and global carbon cycle feedback mechanisms. For time periods with continuous ice core records, such as the Late Pleistocene, atmospheric CO2 concentration can be directly observed through ice core bubbles. However, in earlier deep-time periods, continuous ice core records are lacking, and researchers typically rely on multi-source paleoclimate proxies, such as boron isotopes, benthic foraminifera oxygen isotopes, benthic foraminifera carbon isotopes, and authigenic neodymium isotopes, to indirectly infer changes in atmospheric CO2 concentration.

[0003] Existing methods for reconstructing deep-time atmospheric CO2 typically include spline interpolation, linear regression, empirical fitting, or inversion methods based on a single proxy index. These methods face several limitations when processing deep-time paleoclimate data. First, different data sources have different sampling intervals, chronological frames, and measurement errors, making direct comparison across a unified time axis difficult. Second, multi-source proxy indices may be affected by diagenesis, local water mass disturbances, and chronological migrations, resulting in conflicting evolutionary signals for the same geological period. Simply using averaging, interpolation, or static weighted fitting can easily lead to overly smoothed atmospheric CO2 curves or those containing non-physical oscillations.

[0004] Furthermore, the deep-time carbon cycle system is influenced by multiple mechanisms, including global ice volume, marine biological carbon pumps, deep-sea circulation, volcanic degassing, and silicate weathering, exhibiting strong nonlinearity and strong coupling characteristics. Traditional statistical models struggle to embed known physical laws into the inversion process and distinguish the independent contributions of different driving factors from highly collinear climate variables. For sparse regions of deep-time data, existing methods also tend to underestimate the uncertainties of model extrapolation, failing to reliably identify potential abrupt changes or dynamically unstable regions in the climate system.

[0005] Physical information neural networks (PINs) can embed physical constraints into the loss function of a neural network, providing a new technical approach to solving the aforementioned problems. However, traditional PINs typically rely on explicit partial differential equations or governing equations, while deep-time paleoclimate systems lack precise analytical governing equations, and the data exhibit significant irregularities, heterogeneity, and conflicts. Therefore, there is an urgent need for a deep-time atmospheric CO2 evolution reconstruction method based on customized PINs to simultaneously address issues such as multi-source data temporal alignment, index conflict handling, continuous CO2 reconstruction, carbon cycle dynamics constraints, uncertainty quantification, and driving mechanism identification. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems in the prior art, such as sparse deep-time atmospheric CO2 records, conflict of multiple source proxy indicators, easy introduction of non-physical oscillations by traditional interpolation or statistical fitting, difficulty in quantitatively identifying carbon cycle driving mechanisms, and difficulty in reliably quantifying reconstruction uncertainties. The invention proposes a deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks.

[0007] To achieve the above-mentioned objectives, the present invention specifically adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for deep-time atmospheric CO2 evolution reconstruction based on a physical information neural network, comprising the following steps:

[0009] S1. Map multi-source paleoclimate data with different sampling intervals and geological ages to a unified time grid. The multi-source paleoclimate data includes the true value of atmospheric CO2 concentration and proxy index data used to characterize the paleoclimate forcing mechanism. The true atmospheric CO2 concentration data is either direct atmospheric CO2 concentration data or proxy CO2 concentration data. Perform uncertainty estimation on the true atmospheric CO2 concentration data corresponding to each time node in the time grid to obtain the estimation results.

[0010] S2. Training a Physical Information Neural Network (PIN) for deep-time atmospheric CO2 evolution reconstruction; During training, the proxy index data and the corresponding geological age of each time node on the time grid are used as inputs to the PSN, and the atmospheric CO2 concentration prediction data are used as outputs. A continuous and differentiable atmospheric CO2 evolution function is formed from the atmospheric CO2 concentration prediction data of each time node, and the rate of change of atmospheric CO2 concentration is obtained. The relationship between this rate of change and multiple proxy index data is constructed as a first-order dynamic constraint, and a physical constraint loss is designed. A confidence weight that is negatively correlated with the estimation result is set to weight the CO2 concentration prediction error of each time node. The data fitting loss is established by taking the arithmetic mean of the weighted CO2 concentration prediction errors of all time nodes. The data fitting loss and the physical constraint loss are then weighted and summed to obtain the total loss. The parameters of the PSN are updated based on minimizing the total loss.

[0011] S3. Input the geological age corresponding to the specified time node and the proxy index data used for atmospheric CO2 evolution reconstruction into the trained physical information neural network, and output the atmospheric CO2 concentration prediction data at a unified time grid or specified time node to form a continuous atmospheric CO2 evolution curve, thus completing the deep-time atmospheric CO2 evolution reconstruction.

[0012] Based on the above scheme, each step can be implemented in the following preferred manner.

[0013] As a preferred embodiment of the first aspect above, in S1, the direct atmospheric CO2 concentration data includes ice core CO2 concentration data and / or blue ice CO2 concentration data; the proxy CO2 concentration data includes boron isotope proxy CO2 concentration data; and the proxy index data includes benthic foraminifera oxygen isotopes, benthic foraminifera carbon isotopes, and authigenic neodymium isotopes from different geological ages.

[0014] As a preferred option of the first aspect mentioned above, in S1, uncertainty estimation of the real atmospheric CO2 concentration data is performed using a Gaussian process regression method or a non-parametric regression method.

[0015] As a preferred embodiment of the first aspect mentioned above, in S1, when using the Gaussian process regression method to estimate the uncertainty of real atmospheric CO2 concentration data, the radial basis kernel function and the white noise kernel function are combined as the covariance function in the Gaussian process regression method; the Gaussian process regression method obtains the posterior standard deviation as the estimation result by performing nonparametric smoothing, interpolation and resampling on the real atmospheric CO2 concentration data.

[0016] As a preferred embodiment of the first aspect, in S2, the physical information neural network adopts a multi-layer fully connected neural network, which is composed of a 4-dimensional input layer, a 256-node hidden layer, multiple 128-node hidden layers, a 64-node hidden layer and a 1-dimensional output layer cascaded in sequence. The hidden layers adopt the hyperbolic tangent activation function Tanh to improve the continuous differentiability of the atmospheric CO2 evolution function in the time domain.

[0017] As a preferred embodiment of the first aspect mentioned above, in S2, the first-order dynamic constraint is used to express the rate of change of atmospheric CO2 concentration as a superposition of three weighted data and a learnable system drift parameter. The weighted data is the result of multiplying a proxy index data and a learnable physical parameter.

[0018] As a preferred embodiment of the first aspect mentioned above, in S2, the specific method for designing the physical constraint loss based on the first-order dynamic constraints is as follows: For each time node, the sum of the three weighted data and the system drift parameters is used as the physical estimate of that time node, and the difference between the rate of change of that time node and the corresponding physical estimate is used as the physical residual of that time node. The physical constraint loss is established by squaring the physical residuals of all time nodes and taking the arithmetic mean.

[0019] As a preferred embodiment of the first aspect above, in S2, the CO2 concentration prediction error is the squared error between the actual atmospheric CO2 concentration data and the predicted atmospheric CO2 concentration data at the same time node; the weighted CO2 concentration prediction error at a time node is the product of the confidence weight corresponding to that time node and the CO2 concentration prediction error at that time node; the confidence weight at a time node is the reciprocal of the estimation result at that time node.

[0020] In a second aspect, the present invention provides a deep-time atmospheric CO2 evolution reconstruction system based on a physical information neural network, for implementing the deep-time atmospheric CO2 evolution reconstruction method based on a physical information neural network as described in any of the solutions in the first aspect above.

[0021] Thirdly, the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, can realize the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks as described in any of the solutions of the first aspect above.

[0022] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the deep-time atmospheric CO2 evolution reconstruction method based on a physical information neural network as described in any of the embodiments of the first aspect above.

[0023] Fifthly, the present invention provides a computer electronic device, which includes a memory and a processor;

[0024] The memory is used to store computer programs;

[0025] The processor is configured to, when executing the computer program, implement the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks as described in any of the above-described first aspects.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] This invention unifies ice core CO2 concentration data and multiple proxy index data into the same time grid, reducing phase misalignment caused by different sampling intervals and different age frames. It uses Gaussian process regression or nonparametric regression methods to estimate the uncertainty of real atmospheric CO2 concentration data, allowing data sparsity to be explicitly expressed in subsequent model training. It constructs a continuously differentiable atmospheric CO2 evolution function using a physical information neural network, avoiding the amplification of high-frequency noise when directly performing finite difference on discrete stratigraphic data. It embeds first-order dynamic constraints into the training of the physical information neural network, ensuring that the reconstructed atmospheric CO2 evolution curve not only fits the observed data but also conforms to the preset carbon cycle evolution relationship. Finally, it uses dynamic confidence weighting to process multi-source proxy index data, reducing the interference of low-confidence scatter points or local anomalies on the atmospheric CO2 evolution curve. Attached Figure Description

[0028] Figure 1 Flowchart of the method of this invention;

[0029] Figure 2 This is a flowchart illustrating the method for calculating physical constraint loss in this invention.

[0030] Figure 3 This is a schematic diagram of the deep-time atmospheric CO2 evolution reconstruction results provided in an embodiment of the present invention;

[0031] Figure 4 This is a system block diagram of the present invention;

[0032] Figure 5 This is a schematic diagram of a computer electronic device provided by the present invention. Detailed Implementation

[0033] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in the various embodiments of the present invention can be combined accordingly without mutual conflict.

[0034] In the description of this invention, it should be understood that the terms "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features.

[0035] like Figure 1 As shown, in a preferred embodiment of the present invention, the above-mentioned deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks includes the following steps S1 to S3. This embodiment uses the atmospheric CO2 evolution reconstruction during the Pleistocene transition period from 0 to 1.5 Ma as an application scenario to illustrate the specific implementation process of the method of the present invention.

[0036] S1. Map multi-source paleoclimate data with different sampling intervals and geological ages to a unified time grid. The multi-source paleoclimate data includes the true value of atmospheric CO2 concentration and proxy index data used to characterize the paleoclimate forcing mechanism. The true atmospheric CO2 concentration data is either direct atmospheric CO2 concentration data or proxy CO2 concentration data. Perform uncertainty estimation on the true atmospheric CO2 concentration data corresponding to each time node in the time grid to obtain the estimation results.

[0037] It should be noted that in step S1 of the present invention, the direct atmospheric CO2 concentration data includes ice core CO2 concentration data and / or blue ice CO2 concentration data; the proxy CO2 concentration data includes boron isotope proxy CO2 concentration data; and the proxy index data includes benthic foraminifera oxygen isotopes, benthic foraminifera carbon isotopes, and authigenic neodymium isotopes from different geological ages.

[0038] It should be noted that in step S1 of this invention, the uncertainty of the real atmospheric CO2 concentration data is estimated by using the Gaussian Process Regression (GPR) method or a nonparametric regression method.

[0039] In step S1 of this embodiment, the Gaussian process regression method is specifically used to estimate the uncertainty of the real atmospheric CO2 concentration data. A combination of the radial basis function (RBF) kernel and the white noise kernel is used as the covariance function in the Gaussian process regression method. The Gaussian process regression method performs nonparametric smoothing, interpolation, and resampling on the real atmospheric CO2 concentration data to finally obtain the posterior standard deviation as the estimation result. The RBF kernel is used to express the correlation between the index and the smooth change of geological age; the white noise kernel is used to express measurement noise or local stratigraphic disturbance. The posterior standard deviation is used to characterize the differences in data reliability caused by sampling sparsity, measurement errors, and chronological uncertainties. Therefore, this embodiment uses it as the basis for subsequent confidence weight calculations.

[0040] It should be noted that in the uncertainty estimation of step S1, the uncertainty estimation of atmospheric CO2 concentration data is based on observations of ice core CO2 concentration data, blue ice CO2 concentration data, and surrogate CO2 concentration data. The predicted mean and posterior standard deviation on a unified time grid are obtained through Gaussian process regression. In this embodiment, the predicted mean is also used to convert the three surrogate index data into a uniform distribution; therefore, the three surrogate index data do not participate in the calculation of the posterior standard deviation.

[0041] Following step S1 above, this embodiment completes the corresponding data acquisition and data preprocessing. When the true atmospheric CO2 concentration data in multi-source paleoclimate data cannot be estimated for uncertainty using the Gaussian process regression method described above, this embodiment sets a default estimation result based on data type, measurement error, chronological error, or confidence level given in the literature.

[0042] It should be noted that in step S1 of this invention, the time grid is generated according to a preset time step and covers a preset time interval. Specifically, in step S1 of this embodiment, the time interval covered by the time grid is 0 to 1.5 million years (Mega-annum, Ma), and the time step is 1 millennium.

[0043] S2. Training a Physical Information Neural Network (PIN) for deep-time atmospheric CO2 evolution reconstruction. During training, the proxy index data and the corresponding geological age of each time node on the time grid are used as inputs to the PSN, and the atmospheric CO2 concentration prediction data are used as outputs. A continuously differentiable atmospheric CO2 evolution function is formed from the atmospheric CO2 concentration prediction data of each time node, and the rate of change of atmospheric CO2 concentration is obtained. The relationship between this rate of change and multiple proxy index data is constructed as a first-order dynamic constraint, and a physical constraint loss is designed. A confidence weight that is negatively correlated with the estimation result is set to weight the CO2 concentration prediction error of each time node. The data fitting loss is established by taking the arithmetic mean of the weighted CO2 concentration prediction errors of all time nodes. The data fitting loss and the physical constraint loss are then weighted and summed to obtain the total loss. The parameters of the PSN are updated based on minimizing the total loss.

[0044] It should be noted that in step S2 of the present invention, the physical information neural network adopts a multi-layer fully connected neural network, which is composed of a 4-dimensional input layer, a 256-node hidden layer, multiple 128-node hidden layers, a 64-node hidden layer and a 1-dimensional output layer cascaded in sequence. The hidden layer adopts the hyperbolic tangent activation function Tanh to improve the continuous differentiability of the atmospheric CO2 evolution function in the time domain.

[0045] It should be noted that in step S2 of this invention, the atmospheric CO2 evolution function essentially refers to the potential dynamic law of atmospheric CO2 concentration changing with time nodes. Therefore, the rate of change of atmospheric CO2 concentration can be directly obtained. Specifically, in this embodiment, automatic differentiation is used to directly obtain the above-mentioned rate of change by differentiating the atmospheric CO2 evolution function represented by the physical information neural network with respect to the input time node t. Unlike the finite difference method based on the difference between adjacent samples, the automatic differentiation used in this embodiment can reduce the amplification effect of uneven formation sampling intervals and local noise on the calculation of the rate of change.

[0046] It should be noted that in step S2 of this invention, the first-order dynamic constraint is used to express the rate of change of atmospheric CO2 concentration as a superposition of three weighted data and a learnable system drift parameter. The weighted data is the result of multiplying a proxy index data and a learnable physical parameter.

[0047] In step S2 of this embodiment, the evolution of the atmospheric carbon pool on a million-year timescale is approximated as a first-order dynamic constraint modulated by multiple proxy index data, and its expression is:

[0048]

[0049] in, The rate of change of atmospheric CO2 concentration; Time node The corresponding oxygen isotopes of benthic foraminifera; Time node Corresponding benthic foraminifera carbon isotopes; Time node The corresponding authigenic neodymium isotopes; , , is a learnable physical parameter; Bias is a learnable system drift parameter.

[0050] Furthermore, in this embodiment, the physical parameters and system drift parameters in the first-order dynamic constraints are all set as learnable parameters. The physical information neural network optimizes the above parameters simultaneously during the training process so that it fits the atmospheric CO2 concentration value and satisfies the physical constraint loss. This allows the physical information neural network to quantify the relative contributions of global ice volume and temperature feedback, marine biological carbon pumps, and deep-sea circulation reorganization to atmospheric CO2 evolution during the training process.

[0051] It should be noted that in step S2 of the present invention, by Figure 2 As shown, the specific method for designing physical constraint loss based on first-order dynamic constraints is as follows: For each time node, the sum of the three weighted data and the system drift parameters is used as the physical estimate of that time node, and the difference between the rate of change of that time node and the corresponding physical estimate is used as the physical residual of that time node. The physical constraint loss is established by averaging the squares of the physical residuals of all time nodes.

[0052] In step S2 of this embodiment, the aforementioned physical constraint loss The function form is:

[0053]

[0054] in, Number of time points; For the i-th time node; Let be the rate of change of atmospheric CO2 concentration at the i-th time point; This is the physical estimate for the i-th time node; , , These are the oxygen isotopes, carbon isotopes, and authigenic neodymium isotopes of benthic foraminifera at the i-th time node, respectively. Let be the physical residual at the i-th time point. The result of averaging the squared physical residuals is the physical constraint loss value.

[0055] It should be noted that in step S2 of the present invention, the CO2 concentration prediction error is the squared error between the actual atmospheric CO2 concentration data and the predicted atmospheric CO2 concentration data at the same time node; the weighted CO2 concentration prediction error at a time node is the product of the confidence weight corresponding to that time node and the CO2 concentration prediction error at that time node; the confidence weight at a time node is the reciprocal of the estimation result at that time node.

[0056] In step S2 of this embodiment, the above-mentioned data fitting loss The function form is:

[0057]

[0058] in, Let be the confidence weight corresponding to the i-th time node; This is the predicted atmospheric CO2 concentration data for the i-th time point; This represents the actual atmospheric CO2 concentration data at the i-th time point; The prediction error of CO2 concentration at the i-th time point; Let be the weighted CO2 concentration prediction error at the i-th time point. Similarly, the arithmetic mean of the weighted CO2 concentration prediction error is the data fitting loss value.

[0059] Furthermore, in the aforementioned data fitting loss, a dynamic confidence weight is established based on the level of uncertainty represented by the S1 estimation result. This ensures that the confidence weight corresponding to the CO2 concentration prediction error is small for real atmospheric CO2 concentration data with high uncertainty, and vice versa. Specifically, the confidence weight is set as the reciprocal of the estimation result in this embodiment. By assigning different confidence weights to real atmospheric CO2 concentration data at different time points, this invention enables high-confidence real atmospheric CO2 concentration data to play an anchoring role in the corresponding interval and reduces the interference of low-confidence real atmospheric CO2 concentration data on the training of the physical information neural network.

[0060] Therefore, based on the above data fitting loss and physical constraint loss, the total loss constructed in this embodiment can be expressed as:

[0061]

[0062] in, The weights for the physical constraint loss.

[0063] Furthermore, in this embodiment, the time interval from 0 to 0.8 million years is considered a high-confidence time interval. This means that the confidence level of direct atmospheric CO2 concentration data is high (low uncertainty) within this time interval. Therefore, when using direct atmospheric CO2 concentration data as the true atmospheric CO2 concentration data within this time interval, the confidence weight of ice core CO2 concentration data and / or blue ice CO2 concentration data needs to be increased. When using proxy CO2 concentration data as the true atmospheric CO2 concentration data, the confidence weight of boron isotope proxy CO2 concentration data is correspondingly reduced. For the deep-time interval from 0.8 to 1.5 million years, where direct atmospheric CO2 concentration data is missing or sparse, this embodiment multiplies the total loss mentioned above by the additional weights to obtain the final total loss, replacing the original total loss. This allows the physical information neural network to rely more robustly on macroscopic carbon cycle dynamics for extrapolation when facing high-noise proxy scatter points.

[0064] Additionally, it should be noted that in step S2 of this invention, the training of the physical information neural network further includes standardizing the input proxy index data and the output atmospheric CO2 concentration prediction data; minimizing the total loss using Adam or other gradient optimization algorithms; and synchronously updating the weights, biases, and learnable physical parameters and learnable system drift parameters in the first-order dynamic constraints of the physical information neural network. After training, the atmospheric CO2 concentration prediction data output by the physical information neural network is destandardized to obtain the atmospheric CO2 concentration prediction value in ppm.

[0065] S3. Input the geological age corresponding to the specified time node and the proxy index data used for atmospheric CO2 evolution reconstruction into the trained physical information neural network, and output the atmospheric CO2 concentration prediction data at a unified time grid or specified time node to form a continuous atmospheric CO2 evolution curve, thus completing the deep-time atmospheric CO2 evolution reconstruction.

[0066] It should be noted that in step S3 of this embodiment, the trained physical information neural network can be used to reconstruct the deep-time atmospheric CO2 evolution and output the atmospheric CO2 evolution curve. This curve can be used to describe the long-term evolution trend of deep-time atmospheric CO2, the amplitude changes of glacial-interglacial periods, and the ground state changes of different climate stages.

[0067] After training, by Figure 3As can be seen, the trained Physical Information Neural Network (PIN) can output atmospheric CO2 evolution curves from 0 to 1.5 Ma. In this embodiment, the PIN maintains a high fitting ability in the high confidence interval, and the atmospheric CO2 evolution curves can continuously pass through the main evolution intervals jointly constrained by ice core CO2 concentration data, blue ice CO2 concentration data, and surrogate CO2 concentration data. It can also be used to describe the changes in the atmospheric CO2 ground state and glacial-interglacial amplitude during the Middle Pleistocene transition period. Furthermore, this embodiment trains K independent PINs based on different random seeds or different initialization parameters, thereby obtaining K atmospheric CO2 evolution curves. The mean of these K atmospheric CO2 evolution curves forms the final atmospheric CO2 evolution curve, and its variance is used as an uncertainty estimate of the PIN's cognition, yielding the total uncertainty and 95% confidence interval. Here, K represents the number of ensemble models.

[0068] Figure 3 In this embodiment, a red curve represents the final atmospheric CO2 evolution curve, gray dots represent ice core CO2 concentration data, and blue triangles represent blue ice CO2 concentration data. The results show that in the Late Pleistocene interval of 0–0.8 Ma, which is absolutely constrained by polar ice cores, the final atmospheric CO2 evolution curve obtained by this invention exhibits high fidelity, maintaining an evolutionary trajectory consistent with both ice core CO2 concentration data and blue ice CO2 concentration data. Statistical results show that the coefficient of determination between the predicted atmospheric CO2 concentration data and the actual atmospheric CO2 concentration data within this interval is as high as 0.90, demonstrating the powerful nonlinear feature extraction and fitting capabilities of the physical information neural network. Furthermore, when observing the proxy index data, it can be found that some ocean records at specific geological ages deviate significantly from the main global mixed atmospheric signal represented by polar ice cores. This deviation reflects local carbonate chemical disturbances or dating errors. Thanks to the adaptive error masking mechanism embedded in the loss function, the physical information neural network successfully rejected the interference of these noisy strata scattered points during the assimilation evolution, conformed to the more reliable ice core evolution baseline, and effectively filtered out the spurious interpolations caused by multi-index conflicts.

[0069] Based on the learnable physical parameters obtained through training, this embodiment can also extract the relative contributions of different proxy index data. Specifically, benthic foraminifera oxygen isotopes are used to characterize global ice volume and temperature feedback; benthic foraminifera carbon isotopes are used to characterize the state of marine biological carbon pumps or deep-sea carbon reservoirs; and authigenic neodymium isotopes are used to characterize deep-sea circulation and water mass reorganization. By comparing the normalized contributions of these three physical parameters, the relative constraint strength of the proxy index data on the rate of change of atmospheric CO2 concentration can be quantified.

[0070] Specifically, this embodiment, by stripping or masking a single proxy index data and retraining the physical information neural network, allows observation of the deviation of the obtained atmospheric CO2 evolution curve from the atmospheric CO2 evolution curve obtained under the three proxy index data. For simplicity, the atmospheric CO2 evolution curve obtained after stripping or masking a single proxy index data is used as the comparison curve, and the atmospheric CO2 evolution curve obtained by retaining all three proxy index data is used as the base curve. If the comparison curve deviates significantly from the base curve after stripping a certain proxy index data, it indicates that the climate mechanism corresponding to that proxy index data has a strong independent contribution to CO2 evolution; if the comparison curve changes little compared to the base curve, it indicates that the effect of that proxy index data may be partially compensated by other proxy index data. Therefore, Table 1 not only shows the relative contributions of different proxy index data, but also illustrates that this invention can identify the independence, compensatory relationship, or coupling relationship between different climate mechanisms.

[0071] Table 1: Ablation Experiment Results

[0072] In Table 1, Comparison Method 1 is a scheme that removes the oxygen isotopes of benthic foraminifera based on the method of the present invention; Comparison Method 2 is a scheme that removes the carbon isotopes of benthic foraminifera based on the method of the present invention; and Comparison Method 3 is a scheme that removes the authigenic neodymium isotopes based on the method of the present invention. Physical parameters 1, 2, and 3 correspond to the oxygen, carbon, and neodymium isotopes of benthic foraminifera, respectively. The coefficient of determination of the method of the present invention is 0.90, and the three physical parameters show a clear weight distribution: physical parameter 2 is dominant, physical parameter 3 is second, and physical parameter 1 is last. This confirms the synergistic effect of the three proxy indicators in CO2 evolution.

[0073] Meanwhile, Comparative Method 1 removed the benthic foraminifera oxygen isotopes, which represent the thermodynamic forcing of ice volume. The results showed that the predictive performance of the physical information neural network was only slightly affected, with the coefficient of determination remaining stable at 0.87. However, a dramatic compensatory reorganization occurred in the underlying feature variance: the weight of benthic foraminifera carbon isotopes surged to 77.88%, almost completely taking over the explanatory variance originally belonging to benthic foraminifera oxygen isotopes. This phenomenon was verified by Comparative Method 2. Even without the constraint of core biophysical carbon pump indicators, the coefficient of determination remained at 0.88, and benthic foraminifera oxygen isotopes rapidly compensated and occupied 73.42% of the weight. The high substitutability of benthic foraminifera carbon isotopes and oxygen isotopes in mathematical constraints profoundly reveals that, on an orbital scale, there is a strong co-evolutionary relationship between ice volume expansion and cooling and deep-sea carbon sequestration. This homology confirms that simple ice volume expansion is not an independent external forcing triggering MPT, but rather a co-evolutionary response to the evolution of the deep-sea carbon cycle.

[0074] It should also be noted that the time interval range, time step, number of network layers, number of hidden layer nodes, activation function, number of training rounds, optimization algorithm, and number of ensemble models in the above embodiments are all preferred implementations. Those skilled in the art can make adaptive adjustments based on different deep-time ranges, different paleoclimate databases, or different computing resources; such adjustments do not affect the essence of the technical solution of this invention.

[0075] It should also be noted that the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks in the above embodiments can essentially be executed by a computer program or module. Therefore, similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a deep-time atmospheric CO2 evolution reconstruction system based on physical information neural networks, corresponding to the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks provided in the above embodiments, such as... Figure 4 As shown, it includes:

[0076] The data acquisition module is used to map multi-source paleoclimate data with different sampling intervals and geological ages to a unified time grid. The multi-source paleoclimate data includes the true value of atmospheric CO2 concentration and proxy index data used to characterize the paleoclimate forcing mechanism. The true atmospheric CO2 concentration data is either direct atmospheric CO2 concentration data or proxy CO2 concentration data. Uncertainty estimation is performed on the true atmospheric CO2 concentration data corresponding to each time node in the time grid to obtain the estimation results.

[0077] The model training module is used to train a physical information neural network for deep-time atmospheric CO2 evolution reconstruction. During training, the proxy index data and the corresponding geological age of each time node on the time grid are used as inputs to the physical information neural network, and the atmospheric CO2 concentration prediction data are used as outputs. The atmospheric CO2 concentration prediction data of each time node form a continuously differentiable atmospheric CO2 evolution function and obtain the rate of change of atmospheric CO2 concentration. The relationship between this rate of change and multiple proxy index data is constructed as a first-order dynamic constraint and a physical constraint loss is designed. A confidence weight that is negatively correlated with the estimation result is set to weight the CO2 concentration prediction error of each time node. The data fitting loss is established by taking the arithmetic mean of the weighted CO2 concentration prediction errors of all time nodes. The data fitting loss and the physical constraint loss are then weighted and summed to obtain the total loss. The parameters of the physical information neural network are updated based on minimizing the total loss.

[0078] The results acquisition module is used to input the geological age and proxy index data required for atmospheric CO2 evolution reconstruction corresponding to a specified time node into a trained physical information neural network, and output atmospheric CO2 concentration prediction data at a unified time grid or a specified time node to form a continuous atmospheric CO2 evolution curve and complete the deep-time atmospheric CO2 evolution reconstruction.

[0079] It is understood that the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks described in S1-S3 above can essentially be implemented by a computer program. Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer program product corresponding to the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks provided in the above embodiments. This product includes a computer program / instruction, which, when executed by a processor, can implement the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks as described in the above embodiments.

[0080] Similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer electronic device corresponding to the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks provided in the above embodiments, such as... Figure 5 As shown, it includes a memory and a processor;

[0081] The memory is used to store computer programs;

[0082] The processor is configured to implement the deep-time atmospheric CO2 evolution reconstruction method based on physical information neural networks in the above embodiments when executing the computer program.

[0083] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a portion of the technical solution, 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 steps of the methods described in the various embodiments of the present invention.

[0084] Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer-readable storage medium corresponding to the deep time-based atmospheric CO2 evolution reconstruction method based on physical information neural network provided in the above embodiments. The storage medium stores a computer program, which, when executed by a processor, can realize the deep time-based atmospheric CO2 evolution reconstruction method based on physical information neural network in the above embodiments.

[0085] Specifically, in the computer-readable storage medium of the above three embodiments, the stored computer program is executed by a processor, which can perform the aforementioned steps S1 to S3.

[0086] It is understood that the aforementioned storage media may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Furthermore, the storage media may also be various media capable of storing program code, such as USB flash drives, external hard drives, magnetic disks, or optical discs.

[0087] It is understood that the processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0088] It should also be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the embodiments provided in this application, the division of steps or modules in the system and method is merely a logical functional division, and there may be other division methods in actual implementation. For example, multiple modules or steps may be combined or integrated together, and a module or step may also be split.

[0089] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network, characterized in that, Includes the following steps: S1. Map multi-source paleoclimate data with different sampling intervals and geological ages to a unified time grid. The multi-source paleoclimate data includes the true value of atmospheric CO2 concentration and proxy index data used to characterize the paleoclimate forcing mechanism. The true atmospheric CO2 concentration data is either direct atmospheric CO2 concentration data or proxy CO2 concentration data. Perform uncertainty estimation on the true atmospheric CO2 concentration data corresponding to each time node in the time grid to obtain the estimation results. S2. Training a Physical Information Neural Network (PIN) for deep-time atmospheric CO2 evolution reconstruction; During training, the proxy index data and the corresponding geological age of each time node on the time grid are used as inputs to the PSN, and the atmospheric CO2 concentration prediction data are used as outputs. A continuous and differentiable atmospheric CO2 evolution function is formed from the atmospheric CO2 concentration prediction data of each time node, and the rate of change of atmospheric CO2 concentration is obtained. The relationship between this rate of change and multiple proxy index data is constructed as a first-order dynamic constraint, and a physical constraint loss is designed. A confidence weight that is negatively correlated with the estimation result is set to weight the CO2 concentration prediction error of each time node. The data fitting loss is established by taking the arithmetic mean of the weighted CO2 concentration prediction errors of all time nodes. The data fitting loss and the physical constraint loss are then weighted and summed to obtain the total loss. The parameters of the PSN are updated based on minimizing the total loss. S3. Input the geological age corresponding to the specified time node and the proxy index data used for atmospheric CO2 evolution reconstruction into the trained physical information neural network, and output the atmospheric CO2 concentration prediction data at a unified time grid or specified time node to form a continuous atmospheric CO2 evolution curve, thus completing the deep-time atmospheric CO2 evolution reconstruction.

2. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 1, characterized in that, In S1, the direct atmospheric CO2 concentration data includes ice core CO2 concentration data and / or blue ice CO2 concentration data; the proxy CO2 concentration data includes boron isotope proxy CO2 concentration data; and the proxy index data includes benthic foraminifera oxygen isotopes, benthic foraminifera carbon isotopes, and authigenic neodymium isotopes from different geological ages.

3. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 1, characterized in that, In S1, uncertainty estimation of the real atmospheric CO2 concentration data is performed using Gaussian process regression or nonparametric regression methods.

4. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 3, characterized in that, In S1, when using the Gaussian process regression method to estimate the uncertainty of real atmospheric CO2 concentration data, the radial basis kernel function and the white noise kernel function are combined as the covariance function in the Gaussian process regression method. The Gaussian process regression method obtains the posterior standard deviation as the estimation result by performing nonparametric smoothing, interpolation and resampling on the real atmospheric CO2 concentration data.

5. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 1, characterized in that, In S2, the physical information neural network adopts a multi-layer fully connected neural network, which consists of a 4-dimensional input layer, a 256-node hidden layer, multiple 128-node hidden layers, a 64-node hidden layer, and a 1-dimensional output layer cascaded in sequence. The hidden layers adopt the hyperbolic tangent activation function Tanh to improve the continuous differentiability of the atmospheric CO2 evolution function in the time domain.

6. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 2, characterized in that, In S2, the first-order dynamic constraint is used to express the rate of change of atmospheric CO2 concentration as a superposition of three weighted data and a learnable system drift parameter. The weighted data is the result of multiplying a proxy index data and a learnable physical parameter.

7. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 6, characterized in that, In S2, the specific method for designing physical constraint loss based on first-order dynamic constraints is as follows: For each time node, the sum of the three weighted data and the system drift parameters is used as the physical estimate of that time node, and the difference between the rate of change of that time node and the corresponding physical estimate is used as the physical residual of that time node. The physical constraint loss is established by averaging the squares of the physical residuals of all time nodes.

8. The method for reconstructing deep-time atmospheric CO2 evolution based on a physical information neural network as described in claim 1, characterized in that, In S2, the CO2 concentration prediction error is the squared error between the actual atmospheric CO2 concentration data and the predicted atmospheric CO2 concentration data at the same time node; the weighted CO2 concentration prediction error at a time node is the product of the confidence weight corresponding to that time node and the CO2 concentration prediction error at that time node; the confidence weight at a time node is the reciprocal of the estimation result at that time node.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the deep-time atmospheric CO2 evolution reconstruction method based on a physical information neural network as described in any one of claims 1 to 8.

10. A computer electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to, when executing the computer program, implement the deep-time atmospheric CO2 evolution reconstruction method based on a physical information neural network as described in any one of claims 1 to 8.

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