Mathematical modeling AI prediction system in financial risk assessment

Abstract

The invention discloses a mathematical modeling AI prediction system in financial risk assessment, which relates to the field of financial data processing and comprises a feature principal component extraction module, a compensation alignment execution module, a momentum regulation and control decision module, a gradient direction optimization module and a risk assessment output module. According to the method, principal components are extracted through covariance matrix decomposition of the qualification-debt ratio and the cash flow fluctuation ratio, feature redundancy is eliminated, the core risk characterization efficiency is improved, a cross-market compensation matrix of transaction frequency and price fluctuation is constructed in combination with SVD and cosine similarity, and the model environment adaptability is enhanced. And analyzing momentum attenuation by adopting a dynamic sliding window of a second derivative matrix eigenvalue ratio, and establishing a regulation and control mechanism to suppress gradient oscillation. Orthogonal interference of historical momentum vectors is eliminated through Schmidt orthogonalization projection, and the accuracy of the gradient optimization direction is guaranteed. And converting abstract numerical values into interpretable risk level classification by using a hyperbolic tangent function in combination with credit rating interval mapping.

Description

TECHNICAL FIELD

[0001] The application relates to the field of financial data processing, in particular to a mathematical modeling AI prediction system in financial risk assessment. BACKGROUND

[0002] The technical field of financial data processing includes the systematic collection, processing and analysis of financial transaction data, credit records, market information and other factors. The core of this field is to achieve risk assessment, prediction and early warning through mathematical modeling and algorithm design, involving key technical links such as data cleaning, feature extraction, model training and result verification. Its technical system needs to integrate statistics, econometrics and computer science methods to build a quantifiable risk assessment framework, focusing on solving common problems such as data noise filtering, feature dimension optimization and model generalization ability improvement.

[0003] Among them, the mathematical modeling AI prediction system in financial risk assessment refers to a multi-layer perception architecture using the error back propagation algorithm. The system receives standardized asset-liability ratio, cash flow volatility and other indicators through the input layer, performs Sigmoid activation function operation in the hidden layer, calculates the default probability using the Softmax function in the output layer, and updates the weight parameters based on the stochastic gradient descent method to realize the iterative optimization of risk rating.

[0004] The prior art uses Sigmoid activation function to process hidden layer output, which is prone to gradient disappearance in extreme value area, leading to decreased sensitivity of risk assessment critical value. The fixed learning rate strategy of the stochastic gradient descent method is prone to local optimum in non-convex loss surface, affecting the convergence stability of the model. Feature engineering relies on single field data and lacks cross-market feature compensation mechanism, resulting in limited generalization ability of the model in emerging markets. The output layer directly calculates the default probability, which lacks mapping with industry rating standards, and the evaluation result lacks explainability. The momentum optimization process does not consider the cumulative error of historical vectors, which is prone to direction deviation in complex parameter space. The feature extraction process does not implement principal component dimension reduction, increasing the computational complexity of the model and reducing the accuracy of core factor identification. SUMMARY

[0005] The purpose of the present application is to provide a mathematical modeling AI prediction system in financial risk assessment to solve the problems raised in the background art.

[0006] To achieve the above purpose, the present application provides the following technical solution: a mathematical modeling AI prediction system in financial risk assessment, comprising a feature principal component extraction module: calculating the covariance matrix of asset-liability ratio and cash flow volatility, performing eigenvalue decomposition to extract the maximum eigenvalue corresponding vector, and generating a principal component direction vector group. Compensation alignment execution module: singular value decomposition is performed on transaction frequency and price fluctuation to extract left singular vector, cosine similarity is calculated column by column with principal component direction vector group to generate characteristic space compensation matrix; Momentum regulation decision module: the ratio of eigenvalues of the second-order partial derivative matrix is calculated, a sliding window is established to store the sequence, the standard deviation of the current value and the mean value is calculated, and the momentum decay rate regulation coefficient is generated; Gradient direction optimization module: calculate the dot product of the gradient and the momentum vector, and the length ratio is less than the threshold value, orthogonal projection is executed, and the optimized momentum vector is generated; Risk assessment output module: input the standardized asset-liability ratio and cash flow volatility rate into the compensation matrix operation, perform hyperbolic tangent transformation on the hidden layer output, and perform forward propagation on the optimized momentum vector and the momentum decay rate regulation coefficient to map the credit rating interval to generate the enterprise default risk grade.

[0007] Preferably, the principal component direction vector group is specifically the asset-liability ratio characteristic vector, the cash flow volatility characteristic vector, and the covariance principal component axis, the characteristic space compensation matrix includes transaction frequency alignment vector, price fluctuation compensation factor, and cross-domain similarity weight, the momentum decay rate regulation coefficient is specifically the second derivative feature ratio, the window mean offset, and the momentum decay coefficient, and the optimized momentum vector includes gradient orthogonal projection component, momentum direction reservation, and vector update orthogonal constraint. The enterprise default risk grade is specifically the credit rating mapping value, the activation function output threshold, and the risk grade classification interval.

[0008] Preferably, the characteristic principal component extraction module includes a data covariance calculation submodule, a characteristic root vector decomposition submodule, and a principal component vector screening submodule: Data covariance calculation submodule: obtain the asset-liability ratio time series and the cash flow volatility time series in the source field credit record data set, calculate the arithmetic mean of the two sequences respectively, multiply the data at each time point by the deviation of the corresponding mean value, sum the product results of all time points and divide by the total number of data points, and establish a risk factor covariance matrix; Characteristic root vector decomposition submodule: call the risk factor covariance matrix, set a unit vector and perform a linear transformation defined by the matrix on the vector, solve the scaling ratio when the transformed vector and the original vector remain unchanged in direction, and combine all scaling ratios and their corresponding unit vectors to obtain a covariance characteristic root vector set; Principal component vector screening submodule: according to all scaling ratios in the covariance characteristic root vector set, perform a numerical size comparison operation, determine the largest scaling ratio, extract the unit vector corresponding to the scaling ratio in the covariance characteristic root vector set, and take the unit vector as the core direction to generate the principal component direction vector group.

[0009] Preferably, the compensation alignment execution module comprises a singular vector extraction submodule, a similarity matrix construction submodule, and a compensation direction calibration submodule. The singular vector extraction submodule obtains the time series of transaction frequency and price fluctuation in the target field market information data set, forms a data matrix from the two groups of sequence data, performs singular value decomposition on the matrix, extracts the left singular vector matrix obtained after decomposition, and generates a market information left singular vector group; The similarity matrix construction submodule calls the market information left singular vector group and the principal component direction vector group, calculates the dot product of the corresponding vectors in the two vector groups column by column, divides each dot product result by the product of the magnitudes of the corresponding two vectors, and combines all the cosine similarity calculation results according to the original sequence to establish a cross-domain feature similarity matrix. The compensation direction calibration submodule performs eigenvalue decomposition on the cross-domain feature similarity matrix, compares the numerical values of all eigenvalues, selects the feature vector corresponding to the largest eigenvalue, and uses the feature vector as a compensation reference for dimension adjustment and transformation to generate a feature space compensation matrix.

[0010] Preferably, the momentum regulation decision module comprises a curvature ratio calculation submodule, a historical sequence construction submodule, and a decay parameter generation submodule. The curvature ratio calculation submodule calls the hidden layer weight parameter update record, calculates the second-order partial derivative matrix of the loss function with respect to the weight parameter, performs eigenvalue decomposition on the matrix, selects the maximum eigenvalue and the minimum eigenvalue of the matrix, divides the maximum eigenvalue by the minimum eigenvalue, and obtains the curvature ratio of the loss function. The historical sequence construction submodule stores the latest loss function curvature ratio in a queue structure according to a preset window length, determines whether the number of data points in the current queue exceeds the window length setting value, removes the earliest stored data point in the queue if it exceeds, and establishes a dynamic sequence of ratio changes. The decay parameter generation submodule calls the dynamic sequence of ratio changes, calculates the arithmetic mean of all data points in the sequence, extracts the loss function curvature ratio of the current iteration period, analyzes the standard deviation between the current ratio and the arithmetic mean of the sequence, normalizes the standard deviation, and generates a momentum decay rate regulation coefficient.

[0011] Preferably, the gradient direction optimization module comprises a vector direction scalar submodule and an orthogonal projection execution submodule. The vector direction scalar submodule obtains the dot product value between the current gradient vector and the historical momentum vector, calculates the Euclidean norm of each vector, divides the dot product value by the product of the two norms, and takes the quotient as a quantitative indicator of direction consistency to obtain the vector direction cosine value. The orthogonalization projection execution submodule: calls the vector direction cosine value and the historical momentum vector, sets a direction deviation judgment threshold, judges whether the vector direction cosine values of the continuous iteration periods are all lower than the threshold, if the judgment is yes, calculates the dot product of the historical momentum vector and the current gradient vector, divides the dot product by the square of the gradient vector module length, multiplies the quotient by the current gradient vector, obtains a projection component, and generates an optimized momentum vector.

[0012] Preferably, the risk assessment output module comprises an input feature compensation submodule, a hidden layer activation output submodule, a forward propagation operator submodule and a risk level calibration submodule. The input feature compensation submodule: obtains the standardized asset-liability ratio and cash flow volatility ratio data, integrates the two groups of data into an input vector, calls a feature space compensation matrix, performs matrix multiplication operation on the input vector and the matrix, performs weighted summation on each element of the operation result, and obtains compensated feature data flow; The hidden layer activation output submodule: calls the compensated feature data flow, takes it as the input of the hidden layer neuron, applies the hyperbolic tangent function to each input data point for nonlinear transformation, calculates the difference between the natural logarithm exponential and the negative exponential divided by their sum, recombines all the transformed values into a vector to establish a nonlinear activation vector; The forward propagation operator submodule: calls the nonlinear activation vector, the optimized momentum vector and the momentum decay rate control coefficient, performs weighted summation on the nonlinear activation vector and the output layer weight parameter, and linearly superimposes the sum value and the corresponding component of the optimized momentum vector, the superimposition ratio is scaled by the momentum decay rate control coefficient, and an initial risk assessment value is obtained; The risk level calibration submodule: obtains the initial risk assessment value, and collects preset credit rating interval division thresholds, compares the initial risk assessment value with the upper and lower limits of each interval threshold in value, judges the specific rating classification to which it belongs, takes the classification as the final evaluation conclusion output, and generates the enterprise default risk level.

[0013] Compared with the prior art, the present application has the following advantages: The principal component direction of the asset-liability ratio and the cash flow volatility ratio is extracted through covariance matrix feature decomposition, the redundant feature dimension is eliminated, the core risk factor representation efficiency is improved, the compensation matrix of the transaction frequency and the price volatility is constructed through cross-domain singular value decomposition combined with cosine similarity calculation, the model cross-market environment adaptability is enhanced, the momentum decay control mechanism is established through the dynamic sliding window analysis of the second derivative matrix eigenvalue ratio, the gradient shock phenomenon in the parameter update process is relieved, the orthogonal interference component in the historical momentum vector is removed through the Schmidt orthogonalization projection, the gradient direction optimization accuracy is maintained, the abstract numerical value is converted into an interpretable risk level classification through the hyperbolic tangent activation function combined with the credit rating interval mapping, and the matching degree of the evaluation result and the business scene is improved. Attached Figure Description

[0014] Figure 1 This is a system module block diagram of a mathematical modeling AI prediction system for financial risk assessment according to the present invention. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] like Figure 1 As shown, the present invention provides a technical solution: a mathematical modeling AI prediction system for financial risk assessment, the system comprising: The principal component extraction module acquires the credit record dataset from the source domain, calculates the covariance matrix of the debt-to-equity ratio and cash flow volatility, performs eigenvalue decomposition to extract the eigenvector corresponding to the largest eigenvalue, and generates a principal component direction vector set. Compensation Alignment Execution Module: Based on the target domain market information dataset, the module extracts the left singular vector by performing singular value decomposition on the transaction frequency and price fluctuations. It then calculates the cosine similarity between the left singular vector and the principal component direction vector group column by column, and generates a feature space compensation matrix based on the direction of the largest eigenvector of the similarity matrix. Momentum control decision module: calls the hidden layer weight parameter update record, calculates the eigenvalue ratio of the second-order partial derivative matrix of the loss function, establishes a sliding window to store the historical ratio sequence, calculates the standard deviation of the current ratio and the window mean, and generates the momentum decay rate control coefficient. Gradient direction optimization module: Calculates the ratio of the dot product magnitude of the current gradient vector to that of the historical momentum vector. When the ratio is lower than the threshold multiple times in a row, it performs Schmidt orthogonalization projection, retains the gradient direction components, and generates the optimized momentum vector. Risk assessment output module: The standardized debt-to-equity ratio and cash flow volatility are input into the compensation matrix for calculation. The output of the hidden layer is subjected to hyperbolic tangent transformation. The forward propagation is performed by combining the optimized momentum vector and momentum decay rate control coefficient, and mapped to the credit rating range to generate the enterprise default risk level.

[0017] The principal component direction vector group is specifically asset-liability ratio characteristic vector, cash flow volatility characteristic vector, and covariance principal component axis, the characteristic space compensation matrix includes transaction frequency alignment vector, price volatility compensation factor, and cross-domain similarity weight, the momentum decay rate regulation coefficient is specifically second derivative characteristic ratio, window mean offset, and momentum decay coefficient, the optimized momentum vector includes gradient orthogonal projection component, momentum direction reservation, and vector update orthogonal constraint, and the enterprise default risk level is specifically credit rating mapping value, activation function output threshold, and risk level classification interval.

[0018] The characteristic principal component extraction module includes a data covariance calculation submodule, a characteristic root vector decomposition submodule, and a principal component vector screening submodule. The data covariance calculation submodule: obtains the asset-liability ratio time series and cash flow volatility time series in the source field credit record dataset, calculates the arithmetic mean of the two sequences respectively, multiplies the data at each time point with the deviation of the corresponding mean, sums the product results of all time points and divides by the total number of data points, establishes the risk factor covariance matrix, obtains the asset-liability ratio time series and cash flow volatility time series in the source field credit record dataset, the specific operation is: from the financial database, call the annual financial report of A company in the latest five years, extract the asset-liability ratio data point set, denoted as sequence X, for example X = {0.60, 0.62, 0.58, 0.65, 0.63}, and extract the cash flow volatility data point set, here the cash flow volatility is obtained by calculating the standard deviation of the change rate of net operating cash flow of each year relative to the previous year, denoted as sequence Y, for example Y = {0.15, 0.18, 0.12, 0.20, 0.17}, next calculate the arithmetic mean of the two sequences, the arithmetic mean of the asset-liability ratio sequence X μx = (0.60 + 0.62 + 0.58 + 0.65 + 0.63) / 5 = 0.616, the arithmetic mean of the cash flow volatility sequence Y μy = (0.15 + 0.18 + 0.12 + 0.20 + 0.17) / 5 = 0.164, then multiply the data at each time point with the deviation of the corresponding mean, take the first year's data as an example, the deviation product is (0.60 - 0.616) × (0.15 - 0.164) = (-0.016) × (-0.014) = 0.000224, sum the product results of all five time points to get the total sum 0.00228, then divide the total sum by the total number of data points 5, get the covariance of asset-liability ratio and cash flow volatility Cov(X, Y) = 0.00228 / 5 = 0.000456, according to the same principle, calculate the variance of asset-liability ratio Var(X) = 0.000624 and the variance of cash flow volatility Var(Y) = 0.000824, combine these calculation results to establish the risk factor covariance matrix; The eigenvalue vector decomposition submodule: call the risk factor covariance matrix, set the unit vector and perform the matrix defined linear transformation on the vector, solve the scaling ratio when the transformed vector and the original vector keep the same direction, and combine all the scaling ratios and their corresponding unit vectors to get the covariance eigenvalue vector set, call the risk factor covariance matrix, the specific value of the matrix C is [[0.000624, 0.000456], [0.000456, 0.000824]], set a two-dimensional unit vector v and perform the linear transformation defined by the matrix C on the vector, that is, calculate Cv, solve the scaling ratio λ when the transformed vector Cv and the original vector v keep the same direction, which is the eigenvalue, the solving process needs to establish and solve the characteristic equation det(C - λI) = 0, where I is the unit matrix, and det is the determinant calculation symbol, the equation expands to (0.000624 - λ)(0.000824 - λ) - (0.000456)(0.000456) = 0, after arranging, a quadratic equation about λ is obtained λ^2 - 0.001448λ + 0.0000003058 = 0, solving this equation can get two eigenvalues, i.e. scaling ratios, respectively λ1 ≈ 0.001185 and λ2 ≈ 0.000263, next, for each scaling ratio obtained, bring it into the equation (C - λI)v = 0 to solve its corresponding unit vector, for λ1 = 0.001185, (C - λ1I)v1 = 0 is converted into a linear equation system: -0.000561x1 + 0.000456x2 = 0 and 0.000456x1 - 0.000361x2 = 0, the characteristic vector v1 is proportional to [0.630, 0.777] is obtained, for λ2 = 0.000263, similarly, the characteristic vector v2 is proportional to [0.777, -0.630] is obtained, combine all the scaling ratios and their corresponding unit vectors to get the covariance eigenvalue vector set; The principal component vector screening submodule: according to all scale ratios in the covariance characteristic root vector set, performing a numerical size comparison operation, judging the largest numerical scale ratio, extracting the unit vector corresponding to the scale ratio in the covariance characteristic root vector set, taking the unit vector as the core direction, generating the principal component direction vector group, according to all scale ratios in the covariance characteristic root vector set, that is, the characteristic values λ1 ≈ 0.001185 and λ2 ≈ 0.000263, performing a numerical size comparison operation, judging the numerical size of the two, and determining that 0.001185 is greater than 0.000263 through direct comparison, so the largest numerical scale ratio is λ1 = 0.001185, and the variance proportion explained by the characteristic value is λ1 / (λ1 + λ2) = 0.001185 / (0.001185 + 0.000263) ≈ 81.8%, which indicates that the direction carries the main part of the data variation information, and then the unit vector corresponding to the largest scale ratio in the covariance characteristic root vector set is extracted, that is, v1, and the direction vector is [0.630, 0.777], which represents the direction of the linear combination of the asset-liability ratio and the cash flow volatility ratio in the original data. The vector represents the direction of the linear combination of the asset-liability ratio and the cash flow volatility ratio in the original data. The unit vector is taken as the core direction for subsequent analysis, and the vectors of other directions are discarded in this step. The selected core direction vector is separately constructed into a set to generate the principal component direction vector group.

[0019] The compensation alignment execution module includes a singular vector extraction submodule, a similarity matrix construction submodule, and a compensation direction calibration submodule: The singular vector extraction submodule: obtain the time series of transaction frequency and price volatility in the target field market information data set, construct a data matrix with the two sets of sequence data, perform singular value decomposition operation on the matrix, extract the left singular vector matrix obtained after decomposition, generate the market information left singular vector group, obtain the time series of transaction frequency and price volatility in the target field market information data set, for example, collect the daily average transaction frequency of five representative companies (companies A to E) in a certain industry in the emerging market in the past one complete trading week (5 trading days), denoted as sequence F = {1200, 1500, 1100, 1800, 1300} (unit: pen / day), and calculate the daily price volatility, which is calculated by (the highest price of the day - the lowest price of the day) / the closing price of the day, denoted as sequence P = {0.025, 0.031, 0.021, 0.042, 0.028}, and construct a 5x2 data matrix M with the two sets of sequence data, each row of the matrix M represents a company, and the two columns represent the transaction frequency and the price volatility, respectively, perform singular value decomposition operation on the matrix M, which decomposes the matrix M into the product of three matrices M = UΣV^T, where U is a 5x5 orthogonal matrix, whose columns form the left singular vector, Σ is a 5x2 diagonal matrix, the values on the diagonal are singular values, and V is a 2x2 orthogonal matrix, whose columns form the right singular vector, in this process, the left singular vector matrix U obtained after decomposition is extracted, the column vectors of the matrix U represent the linear combination direction in the company dimension, and all the column vectors of the matrix U are taken as a group of reference vectors to generate the market information left singular vector group; The similarity matrix construction submodule: call the market information left singular vector group and the principal component direction vector group, calculate the dot product of the corresponding vectors in the two vector groups column by column, and divide each dot product result by the product of the corresponding two vector lengths, combine all the cosine similarity calculation results according to the original sequence, and establish a cross-domain feature similarity matrix. Call the market information left singular vector group and the principal component direction vector group generated in the previous step. The market information left singular vector group here is a 5x5 matrix U, and the principal component direction vector group is assumed to be calculated on the source domain data through the same number of company samples, which is also a 5x1 vector P, such as P = [0.45, 0.55, 0.30, 0.60, 0.35]^T. Now calculate the dot product of the corresponding vectors in the two vector groups column by column, taking the first column vector u1 = [0.48, 0.52, 0.33, 0.58, 0.29]^T of U and the principal component vector P as an example. The dot product u1·P = (0.48×0.45) + (0.52×0.55) + (0.33×0.30) + (0.58×0.60) + (0.29×0.35) = 0.216 + 0.286 + 0.099 + 0.348 + 0.1015 = 1.0505, and divide each dot product result by the product of the corresponding two vector lengths. The length of vector u1 is ||u1|| = sqrt(0.48^2 + 0.52^2+ 0.33^2 + 0.58^2 + 0.29^2) = sqrt(0.2304 + 0.2704 + 0.1089 + 0.3364 +0.0841) = sqrt(1.0302) ≈ 1.015, and the length of vector P is ||P|| = sqrt(0.45^2 + 0.55^2 +0.30^2 + 0.60^2 + 0.35^2) = sqrt(0.2025 + 0.3025 + 0.09 + 0.36 + 0.1225) =sqrt(1.0775) ≈ 1.038, then the cosine similarity is 1.0505 / (1.015 × 1.038) ≈ 0.998. Repeat this calculation process for each column of U matrix and vector P. If the principal component direction vector group contains multiple vectors, perform this operation for each principal component vector. Combine all the calculated cosine similarity results according to the original sequence to establish a cross-domain feature similarity matrix. The compensation direction calibration sub-module: the eigenvalue decomposition is performed on the cross-domain feature similarity matrix, the numerical values of all eigenvalues are compared, the eigenvector corresponding to the maximum eigenvalue is screened out, the eigenvector is taken as a compensation reference for dimension adjustment and transformation, a feature space compensation matrix is generated, the eigenvalue decomposition is performed on the cross-domain feature similarity matrix, assuming that the cross-domain feature similarity matrix S generated in the previous process is a 2x2 matrix, the numerical value is S = [[0.95, 0.25],[0.25, 0.85]], the eigenvalue decomposition is performed, that is, a scalar λ and a non-zero vector v are found to make Sv=λv, which needs to solve the characteristic equation det(S - λI) = 0, wherein I is a unit matrix, the equation is specifically (0.95 - λ)(0.85 - λ) -(0.25)(0.25) = 0, after expansion, λ^2 - 1.8λ + 0.8075 - 0.0625 = 0, that is, λ^2 - 1.8λ +0.745 = 0, two eigenvalues λ1 ≈ 1.154 and λ2 ≈ 0.646 are obtained by solving the quadratic equation, then the numerical values of all eigenvalues are compared, 1.154 is greater than 0.646, therefore the maximum eigenvalue λ1 = 1.154 is screened out, then the eigenvector corresponding to the maximum eigenvalue is solved, by solving the equation (S - λ1I)v = 0, that is, [[-0.204, 0.25], [0.25,-0.304]]v = 0, the eigenvector v1 is proportional to [0.78, 0.63], the eigenvector is taken as a compensation reference for dimension adjustment and transformation, and the specific operation is that the vector [0.78, 0.63]^T is taken as the first column, and its orthogonal vector [-0.63, 0.78]^T is calculated as the second column, to form a 2x2 transformation matrix, and a feature space compensation matrix is generated.

[0020] The momentum regulation decision module includes a curvature ratio calculation sub-module, a historical sequence construction sub-module, and a decay parameter generation sub-module. The curvature ratio calculation submodule: call the hidden layer weight parameter update record, calculate the second-order partial derivative matrix of the loss function to the weight parameter, perform eigenvalue decomposition operation on the matrix, screen the maximum eigenvalue and the minimum eigenvalue of the matrix, divide the maximum eigenvalue by the minimum eigenvalue to obtain the curvature ratio of the loss function, call the hidden layer weight parameter update record, specifically, in the t-th iteration of model training, for a hidden layer neuron containing two weight parameters w1 and w2, the second-order partial derivative matrix of the loss function L to the two weight parameters, that is, the Hessian matrix H, is calculated, for example, the H matrix calculated in a certain iteration is [[12, 3], [3, 6]], perform eigenvalue decomposition operation on the matrix, which finds the eigenvalue λ by solving the characteristic equation det(H - λI) = 0, where I is the unit matrix, the equation is (12 - λ)(6 - λ) -3*3 = 0, after expansion, λ^2 - 18λ + 72 - 9 = 0, that is, λ^2 - 18λ + 63 = 0, solve this quadratic equation to get two eigenvalues, that is, λ_max ≈ 14.32 and λ_min ≈ 3.68, screen the maximum eigenvalue and the minimum eigenvalue of the matrix, that is, by numerical comparison, determine that 14.32 is the maximum eigenvalue and 3.68 is the minimum eigenvalue, these two values respectively represent the maximum and minimum curvature directions of the loss function in the parameter space, divide the maximum eigenvalue by the minimum eigenvalue, that is, 14.32 divided by 3.68, to obtain the curvature ratio of the loss function; The historical sequence construction submodule: according to the preset window length, the latest loss function curvature ratio value is stored in a queue structure, whether the current queue data point number exceeds the window length setting value is judged, if it exceeds, the earliest stored data point in the queue is removed, the dynamic sequence of the ratio change is established, according to the preset window length, the window length is set to 10, this setting is based on the dynamic tracking of the recent 10 iteration history, the latest loss function curvature ratio value, that is, the 3.89 calculated in the last process, is stored in a first-in first-out queue structure, assuming that the current queue has stored 9 ratio value data from the previous 10 iterations, the content is [3.5, 4.1, 4.0, 3.8, 4.2, 4.5, 4.3, 3.9, 3.7], after the new value 3.89 is added to the tail of the queue, the queue is updated to [3.5, 4.1, 4.0, 3.8, 4.2, 4.5, 4.3, 3.9, 3.7, 3.89], the current queue data point number is judged, which is 10 at this time, which does not exceed the window length setting value 10, so no removal operation is performed, if in the next iteration, the queue has 10 data points [4.1, 4.0, 3.8, 4.2, 4.5, 4.3, 3.9, 3.7, 3.89, 4.05], when the new value 4.15 is added, the queue length becomes 11, at this time it is judged that the window length is exceeded, so the earliest stored data point in the queue, that is, the head of the queue 4.1 is removed, so that the queue length returns to 10, and the dynamic sequence of the ratio change is established; The attenuation parameter generation submodule: call the ratio change dynamic sequence, calculate the arithmetic mean of all data points in the sequence, extract the loss function curvature ratio of the current iteration period, analyze the standard deviation between the current ratio and the arithmetic mean of the sequence, normalize the standard deviation, generate the momentum attenuation rate control coefficient, call the ratio change dynamic sequence, which is [4.0, 3.8, 4.2, 4.5, 4.3, 3.9, 3.7, 3.89, 4.05, 4.15], calculate the arithmetic mean of all data points in the sequence, that is, (4.0 + 3.8 + 4.2 + 4.5 + 4.3 + 3.9 + 3.7 + 3.89 + 4.05 + 4.15) / 10 = 40.49 / 10 = 4.049, extract the loss function curvature ratio of the current iteration period, that is, the last value in the sequence 4.15, analyze the absolute value of the deviation between the current ratio and the arithmetic mean of the sequence, that is, |4.15 - 4.049| = 0.101, and calculate the standard deviation σ of the entire sequence, which is 0.276. The absolute deviation value is normalized according to the standard deviation of the sequence, and the calculation method of this processing is deviation normalized value = |current value - average value| / standard deviation, and the numerical value obtained is 0.101 / 0.276 ≈ 0.366. This normalized value reflects the deviation of the current curvature ratio from the recent historical fluctuations. Add this value to a benchmark attenuation rate of 0.1, and set an upper limit of 0.9, that is, 0.1 + 0.366 = 0.466, which does not exceed 0.9, so it is directly adopted, and the momentum attenuation rate control coefficient is generated.

[0021] The gradient direction optimization module includes a vector direction scalar submodule and an orthogonal projection execution submodule: The vector direction scalar sub-module obtains the current gradient vector and the historical momentum vector, calculates the dot product value between the two vectors, and calculates the respective Euclidean norms, divides the dot product value result by the product of the two norms, and takes the quotient as a quantitative indicator of direction consistency, obtains the vector direction cosine value, obtains the current gradient vector and the historical momentum vector, and this process occurs in the iteration step of neural network weight update. Assuming that the current gradient vector g_t calculated for two weight parameters [w1, w2] in the network at the tth iteration is [0.7, -0.3], and the historical momentum vector m_{t-1} obtained from the previous time t-1 is [0.6, 0.2], the dot product value between the two vectors, i.e., the inner product of g_t and m_{t-1}, is calculated, and the calculation process is (0.7 x 0.6) + ((-0.3) x 0.2) = 0.42 - 0.06 = 0.36. The respective Euclidean norms are calculated, the norm ||g_t|| of the current gradient vector g_t is calculated as the square root of (0.7^2 + (-0.3)^2), i.e., the square root of (0.49 + 0.09), which is √0.58 approximately equal to 0.762, and the norm ||m_{t-1}|| of the historical momentum vector m_{t-1} is calculated as the square root of (0.6^2 + 0.2^2), i.e., the square root of (0.36 + 0.04), which is √0.40 approximately equal to 0.632. The dot product value 0.36 is divided by the product of the two norms, i.e., 0.36 / (0.762 x 0.632) ≈ 0.36 / 0.4816 ≈ 0.747, which is taken as a quantitative indicator of direction consistency, and the vector direction cosine value is obtained. The orthogonal projection execution submodule: call the vector direction cosine value and the historical momentum vector, set the direction deviation judgment threshold, judge whether the vector direction cosine values of the continuous iteration periods are all lower than the threshold, if the judgment is yes, calculate the dot product of the historical momentum vector and the current gradient vector, divide the dot product by the square of the gradient vector length, multiply the quotient by the current gradient vector, obtain the projection component, generate the optimized momentum vector, call the vector direction cosine value and the historical momentum vector, assume that the vector direction cosine value sequence of the last three consecutive iterations is obtained from the previous steps and historical records [0.08, 0.05, 0.09], and set the direction deviation judgment threshold to 0.1, which is set according to the stability experience of gradient change in the training process, and is used to determine whether the gradient and momentum direction have deviated significantly, judge whether the vector direction cosine values of the continuous iteration periods are all lower than the threshold, that is, compare the size of 0.08, 0.05, 0.09 and the threshold 0.1, because the three values are all less than 0.1, so the judgment is yes, then execute the subsequent operation for the historical momentum vector m_{t-1}=[0.5, -0.8] and the current gradient vector g_t=[0.9, 0.2] of the current iteration period, calculate the dot product of the two vectors, that is, (0.5 × 0.9) + ((-0.8) × 0.2) = 0.45 - 0.16 = 0.29, divide the dot product 0.29 by the square of the gradient vector length, the square of the gradient vector length is 0.9^2 + 0.2^2 = 0.81 + 0.04 = 0.85, the result of division is 0.29 / 0.85 ≈0.341, multiply the quotient by the current gradient vector, that is, 0.341 × [0.9, 0.2]= [0.307, 0.068], the result is the projection component of the historical momentum in the current gradient direction, subtract the projection component from the historical momentum vector, that is, [0.5, -0.8]- [0.307, 0.068] = [0.193, -0.868], generate the optimized momentum vector.

[0022] The risk assessment output module includes an input feature compensation submodule, a hidden layer activation output submodule, a forward propagation operator submodule, and a risk level calibration submodule. The input feature compensation submodule: obtain the standardized asset-liability ratio and cash flow volatility ratio data, integrate the two sets of data into an input vector, call the feature space compensation matrix, perform matrix multiplication operation on the input vector and the matrix, and obtain the compensated feature data stream by weighted sum of each element of the operation result. Obtain the standardized asset-liability ratio and cash flow volatility ratio data, which is for a specific evaluation enterprise, for example, B company. After Z-score standardization, the asset-liability ratio of B company is 0.7, and the cash flow volatility ratio is 0.3. Integrate the two sets of data into an input vector X = [0.7, 0.3]T. Call the feature space compensation matrix C generated in the previous step. Assume that the matrix is [[0.78, -0.63], [0.63, 0.78]]. Perform matrix multiplication operation on the input vector X and the matrix C. The calculation process is C multiplied by X, that is, [[0.78, -0.63], [0.63, 0.78]] × [0.7, 0.3]T. The first element of the result vector is (0.78 × 0.7) + ((-0.63) × 0.3) = 0.546 - 0.189 = 0.357, and the second element is (0.63 × 0.7) + (0.78 × 0.3) = 0.441 + 0.234 = 0.675. This operation projects the original financial risk indicators into a new feature space generated by data-driven. This process does not directly perform weighted sum, but through matrix transformation, it completes the linear reorganization of features. The calculated vector [0.357, 0.675] is used as the data basis for the next step of processing, and the compensated feature data stream is obtained. The hidden layer activation output submodule: calls the compensated feature data stream, takes it as the input of the hidden layer neurons, applies the hyperbolic tangent function to each input data point for nonlinear transformation, calculates the difference between the natural logarithm exponential and the negative exponential divided by their sum, recombines all the transformed values into a vector, establishes a nonlinear activation vector, calls the compensated feature data stream, that is, the vector Y = [0.357, 0.675], takes it as the input of the hidden layer containing two neurons, applies the hyperbolic tangent function to each input data point for nonlinear transformation, the specific expression of the function is tanh(x) = (e^x - e^-x) / (e^x + e^-x), for the first input data point 0.357, calculate e^0.357 ≈ 1.429 and e^-0.357 ≈ 0.699, then tanh(0.357) ≈ (1.429 - 0.699) / (1.429 + 0.699) = 0.73 / 2.128 ≈ 0.343, for the second input data point 0.675, calculate e^0.675 ≈ 1.964 and e^-0.675 ≈ 0.509, then tanh(0.675) ≈ (1.964 - 0.509) / (1.964 + 0.509) = 1.455 / 2.473 ≈ 0.588, this transformation compresses the linear combination signal of the input into the interval of -1 to 1, recombines all the transformed values into a vector, that is, [0.343, 0.588], establishes a nonlinear activation vector; The forward propagation operator module: call the nonlinear activation vector, the optimized momentum vector and the momentum decay rate control coefficient, perform weighted summation on the nonlinear activation vector and the output layer weight parameter, and linearly superimpose the sum value and the corresponding component of the optimized momentum vector, and the superposition ratio is scaled by the momentum decay rate control coefficient, obtain the initial risk assessment value, call the nonlinear activation vector A = [0.343, 0.588], and the optimized momentum vector M = [0.193, -0.868] and the momentum decay rate control coefficient α = 0.466 determined in the previous step, perform weighted summation on the nonlinear activation vector and the weight parameter W = [0.7, -0.5] of the output layer, calculate the output signal S = (0.343 × 0.7) + (0.588 × (-0.5)) = 0.2401 - 0.294 = -0.0539, and linearly superimpose the sum value and the corresponding component of the optimized momentum vector, the momentum term contribution value here is the dot product of the momentum vector M and the weight vector W multiplied by the control coefficient α, that is, α × (M ·W) = 0.466 × ((0.193 × 0.7) + ((-0.868) × (-0.5))) = 0.466 × (0.1351 +0.434) = 0.466 × 0.5691 ≈ 0.2652, finally add the two parts, that is, -0.0539 + 0.2652 = 0.2113, obtain the initial risk assessment value; The risk level calibration submodule: obtain the initial risk assessment value, and collect the preset credit rating interval threshold value, compare the numerical value of the initial risk assessment value with the upper and lower limits of each interval threshold value, determine the specific rating classification it belongs to, and output the classification as the final evaluation conclusion. Generate enterprise default risk level, obtain the initial risk assessment value, whose value is 0.2113, and collect a set of preset credit rating interval threshold value, which is set by referring to historical default data statistical distribution, for example, the rating is divided into five levels, AAA level (very low risk) corresponds to an assessment value greater than 0.9, AA level (low risk) corresponds to (0.7, 0.9], A level (medium risk) corresponds to (0.4, 0.7], B level (higher risk) corresponds to (0.1, 0.4], and C level (high risk) corresponds to less than or equal to 0.1. Compare the numerical value of the initial risk assessment value 0.2113 with the upper and lower limits of each interval threshold value. Since 0.1 < 0.2113 ≤ 0.4, it is determined that the specific rating classification to which the assessment value belongs is B level. Output the classification as the final evaluation conclusion, and generate the enterprise default risk level.

[0023] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting; it is not intended to exclude myriad other embodiments of the present application that other inventors can develop based on the same general inventive concepts embodied by the described embodiments. That is, although the present application is described in terms of particular embodiments and illustrative figures, it should be apparent that the scope of the present application is not limited to these specific embodiments.

[0024] While the embodiments of the application have been shown and described herein, it will be understood by those skilled in the art that many changes, modifications, substitutions and alterations to these embodiments can be made without departing from the spirit and scope of the present application, which is defined by the appended claims and their equivalents.

Claims

1. A mathematical modeling AI prediction system in financial risk assessment, characterized by: The system comprises: Characteristic principal component extraction module: calculate the covariance matrix of the asset-liability ratio and the cash flow volatility ratio, perform eigenvalue decomposition to extract the maximum eigenvalue corresponding vector, and generate a principal component direction vector group; Compensation alignment execution module: singular value decomposition is performed on the transaction frequency and price fluctuation to extract the left singular vector, and the cosine similarity is calculated column by column with the principal component direction vector group to generate a characteristic space compensation matrix; Momentum regulation decision module: calculate the ratio of the eigenvalues of the second-order partial derivative matrix, establish a sliding window to store the sequence, calculate the standard deviation of the current value and the mean value, and generate a momentum decay rate regulation coefficient; Gradient direction optimization module: calculate the dot product of the gradient and the momentum vector, and if the length ratio is less than a threshold, perform orthogonal projection to generate an optimized momentum vector; Risk assessment output module: input the standardized asset-liability ratio and cash flow volatility ratio into the compensation matrix operation, perform hyperbolic tangent transformation on the hidden layer output, and perform forward propagation on the optimized momentum vector and the momentum decay rate regulation coefficient to map the credit rating interval to generate the enterprise default risk grade.

2. The mathematical modeling AI prediction system in financial risk assessment according to claim 1, wherein: The principal component direction vector group is specifically an asset-liability ratio characteristic vector, a cash flow volatility ratio characteristic vector, and a covariance principal component axis. The characteristic space compensation matrix includes a transaction frequency alignment vector, a price fluctuation compensation factor, and a cross-domain similarity weight. The momentum decay rate regulation coefficient is specifically a second-order derivative feature ratio, a window mean offset, and a momentum decay coefficient. The optimized momentum vector includes a gradient orthogonal projection component, a momentum direction retention amount, and a vector update orthogonal constraint. The enterprise default risk grade is specifically a credit rating mapping value, an activation function output threshold, and a risk grade classification interval.

3. The AI prediction system for mathematical modeling in financial risk assessment according to claim 1, wherein: The characteristic principal component extraction module comprises a data covariance calculation submodule, an eigenvalue vector decomposition submodule, and a principal component vector screening submodule: The data covariance calculation submodule: obtains the asset-liability ratio time series and the cash flow volatility ratio time series in the source field credit record dataset, respectively calculates the arithmetic mean of the two sequences, performs product operation on the data at each time point and the deviation of the corresponding mean value, sums the product results of all time points and divides by the total number of data points to establish a risk factor covariance matrix; The eigenvalue vector decomposition submodule: calls the risk factor covariance matrix, sets a unit vector and performs a linear transformation defined by a matrix on the vector, solves the scaling ratio when the transformed vector and the original vector remain unchanged in direction, and combines all scaling ratios and their corresponding unit vectors to obtain a covariance eigenvalue vector set; The principal component vector screening submodule: performs a numerical size comparison operation according to all scaling ratios in the covariance eigenvalue vector set, judges the largest scaling ratio, extracts the unit vector corresponding to the scaling ratio in the covariance eigenvalue vector set, takes the unit vector as the core direction, and generates a principal component direction vector group.

4. The AI prediction system for mathematical modeling in financial risk assessment according to claim 1, wherein: The compensation alignment execution module comprises a singular vector extraction submodule, a similarity matrix construction submodule, and a compensation direction calibration submodule: The singular vector extraction submodule obtains the time series of transaction frequency and price fluctuation in the target field market information data set, constructs a data matrix from the two groups of sequence data, performs singular value decomposition on the matrix, extracts the left singular vector matrix obtained after decomposition, and generates a left singular vector group of market information; The similarity matrix construction submodule calls the left singular vector group of market information and the principal component direction vector group, calculates the dot product of the corresponding vectors in the two vector groups column by column, divides each dot product result by the product of the lengths of the corresponding two vectors, and combines all the cosine similarity calculation results according to the original sequence to establish a cross-domain feature similarity matrix; The compensation direction calibration submodule performs eigenvalue decomposition on the cross-domain feature similarity matrix, compares the numerical values of all eigenvalues, selects the feature vector corresponding to the largest eigenvalue, and uses the feature vector as a compensation reference for dimension adjustment and transformation, to generate a feature space compensation matrix.

5. The mathematical modeling AI prediction system in financial risk assessment according to claim 1, wherein: The momentum regulation decision module includes a curvature ratio calculation submodule, a historical sequence construction submodule, and a decay parameter generation submodule: The curvature ratio calculation submodule calls the hidden layer weight parameter update record, calculates the second-order partial derivative matrix of the loss function with respect to the weight parameter, performs eigenvalue decomposition on the matrix, selects the maximum eigenvalue and the minimum eigenvalue of the matrix, divides the maximum eigenvalue by the minimum eigenvalue, and obtains the curvature ratio of the loss function; The historical sequence construction submodule stores the latest loss function curvature ratio in a queue structure according to a preset window length, determines whether the number of current queue data points exceeds the window length setting value, removes the earliest stored data point in the queue if it exceeds, and establishes a dynamic sequence of ratio changes; The decay parameter generation submodule calls the dynamic sequence of ratio changes, calculates the arithmetic mean of all data points in the sequence, extracts the loss function curvature ratio of the current iteration period, analyzes the standard deviation between the current ratio and the sequence arithmetic mean, normalizes the standard deviation, and generates a momentum decay rate regulation coefficient.

6. The mathematical modeling AI prediction system in financial risk assessment according to claim 2, wherein: The gradient direction optimization module includes a vector direction scalar submodule and an orthogonal projection execution submodule: The vector direction scalar submodule obtains the current gradient vector and the historical momentum vector, calculates the dot product value between the two vectors, and calculates the respective Euclidean norms, divides the dot product value by the product of the two norms, and takes the quotient as a quantitative indicator of direction consistency to obtain the vector direction cosine value; The orthogonal projection execution submodule calls the vector direction cosine value and the historical momentum vector, sets a direction deviation threshold, determines whether the vector direction cosine values of consecutive iteration periods are all lower than the threshold, and if so, calculates the dot product of the historical momentum vector and the current gradient vector, divides the dot product by the square of the gradient vector length, and multiplies the quotient by the current gradient vector to obtain a projection component and generate an optimized momentum vector.

7. The AI prediction system for mathematical modeling in financial risk assessment of claim 1, wherein: The risk assessment output module includes an input feature compensation submodule, a hidden layer activation output submodule, a forward propagation operation submodule, and a risk level calibration submodule: The input feature compensation submodule: obtain the standardized asset-liability ratio and cash flow volatility ratio data, integrate the two groups of data into an input vector, call the feature space compensation matrix, perform matrix multiplication operation on the input vector and the matrix, perform weighted summation on each element of the operation result, and obtain the compensated feature data stream; The hidden layer activation output submodule: call the compensated feature data stream as the input of the hidden layer neuron, apply the hyperbolic tangent function to each input data point for nonlinear transformation, calculate the difference between the natural logarithm index and the negative index divided by their sum, and recombine all the transformed values into a vector to establish a nonlinear activation vector; The forward propagation operator module: call the nonlinear activation vector, the optimized momentum vector, and the momentum decay rate control coefficient, perform weighted summation on the nonlinear activation vector and the output layer weight parameter, and linearly superimpose the sum value and the corresponding component of the optimized momentum vector, the superposition ratio is scaled by the momentum decay rate control coefficient, and the initial risk assessment value is obtained; The risk level calibration submodule: obtain the initial risk assessment value, collect the pre-set credit rating interval threshold, compare the initial risk assessment value with the upper and lower limits of each interval threshold, determine the specific rating classification to which it belongs, output the classification as the final evaluation conclusion, and generate the enterprise default risk level.

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