Dynamic surface prediction method based on spatiotemporal multi-expert network

Abstract

The application provides a dynamic surface prediction method based on a space-time multi-expert network, a multi-scale trend and fluctuation feature is extracted from a bottom driving sequence affecting surface evolution through a driving variable time sequence feature extraction module, and a decay perception attention mechanism is combined to capture a dynamic evolution law. A hybrid expert network based on prior constraints is constructed, a parameterized model meeting specific geometric shapes is embedded into the expert network as an activation function, the smoothness and rationality of an output surface are ensured from the structure, and a dynamic gating mechanism is adapted to the heterogeneity of different spatial regions. A surface space attention module is introduced, global attention mechanism is used to fuse sparse real-time observation data and a theoretical surface, and adaptive and accurate correction of the surface is realized. The application can simultaneously realize interpolation reconstruction of sparse data at the current time and prediction of the surface shape at the next time, while ensuring high precision, and effectively maintaining the structural rationality of the surface.

Description

Technical Field

[0001] This invention relates to the fields of data mining, machine learning, and spatiotemporal data analysis, specifically to a general modeling method for data interpolation and dynamic prediction of two-dimensional or multi-dimensional surfaces with spatiotemporal evolution characteristics. Background Technology

[0002] In numerous application fields such as scientific observation, industrial sensing, and geographic information systems, the research object often manifests as a dynamic surface defined on a specific spatial coordinate system (such as latitude and longitude, spatial location, or parametric plane). Due to limitations in observation methods or high data acquisition costs, the actual acquired data is usually discrete and sparse, and this data is often accompanied by noise. To obtain complete full-field information, surface interpolation and reconstruction are necessary; simultaneously, to grasp the development trend of the system, it is also necessary to predict the shape of the surface in the next moment based on historical data.

[0003] Interpolation Reconstruction and Temporal Series Prediction Task Description: In the modeling of dynamic surfaces, the core tasks are divided into two categories: restoring the surface based on current sparse data (interpolation reconstruction) and predicting the future shape based on historical information (temporal series prediction). Let the discrete observation data set acquired at time t be... , For a preset set of regular grid coordinates, If the underlying driving variable sequence is used, then the two tasks are formalized as follows:

[0004]

[0005]

[0006] in and These are the parameters that the model needs to learn.

[0007] Existing surface prediction methods mainly face the following challenges:

[0008] (1) Error accumulation problem in dynamic prediction: Traditional methods usually fit the complete surface at historical time points before making time-series predictions. However, in real-world scenarios, obtaining a complete and accurate historical surface often results in error accumulation. This "two-step" strategy is difficult to overcome the impact of historical fitting bias on subsequent dynamic predictions and cannot effectively capture the fundamental influence of underlying driving variables on the evolution of surface morphology.

[0009] (2) Structural constraints are difficult to guarantee: Real physical or natural surfaces usually need to satisfy specific structural prior knowledge, such as smoothness, monotonicity or specific geometric constraints. Existing data-driven models often apply soft constraints through loss functions, but in extreme cases where data is sparse or there is noise, they are very likely to produce structural errors that violate physical common sense (such as producing negative values, defective abrupt change points, etc.), resulting in unusable prediction results.

[0010] (3) Insufficient utilization of global spatial correlation and sparse observations: Data points on the surface are not isolated but have inherent global correlations. However, actual observation data is often sparse and unevenly distributed (high density in some areas, missing in others). Existing local interpolation methods or models that only focus on local neighborhood relationships cannot effectively propagate highly reliable local observation information to the global scale. They are also susceptible to local noise interference, resulting in a lack of overall consistency and robustness in the reconstructed or predicted surface.

[0011] Therefore, there is an urgent need for a general surface modeling method that can deeply integrate temporal dynamic information, strictly adhere to structural constraints, and effectively utilize sparse observation data. Summary of the Invention

[0012] This invention primarily addresses the problem of dynamic prediction error accumulation caused by reliance on historical fitted surfaces when performing surface prediction based on discrete sparse observation data in existing technologies; it also solves the problem that data-driven models cannot guarantee that the output surface conforms to specific geometric constraints; and it addresses the difficulty in achieving globally consistent surface reconstruction and prediction when observation data is sparse and unevenly distributed.

[0013] To achieve the above objectives, this invention provides a dynamic surface prediction method based on a spatiotemporal multi-expert network, comprising the following steps:

[0014] Step S1: Data preprocessing: Map the discrete observation data to a preset spatiotemporal grid coordinate system, normalize the features, and use a random masking strategy to simulate the data sparsity scenario;

[0015] Step S2: Historical dynamic temporal dependency feature capture: such as Figure 1 As shown, multi-scale features are extracted from the sequence of underlying driving variables through the path dependency capture module (PD), and combined with the long short-term memory network and decay perception attention mechanism to generate a historical time-series feature vector containing evolutionary patterns.

[0016] Step S3: Multi-expert capture of historical normal distribution: such as Figure 1As shown in the Hybrid Multi-Expert Network Module (MoE), a hybrid multi-expert network containing parametric experts and general experts is constructed. The gating mechanism is used to fuse historical time series features and spatial coordinates to generate a basic prediction surface that meets geometric constraints.

[0017] Step S4: Dynamic fine-tuning of attention in curved space: such as Figure 1 As shown in the Spatial Attention Module (SPA), the global attention mechanism is used to calculate the deviation between sparse observation data and the base surface. The observation information is propagated to the entire grid through weighted fusion, and the final predicted or reconstructed surface is output.

[0018] Step S5: Model training loss function with structural prior: Construct a total loss function that includes data fitting loss and structural constraint loss, and train the model end-to-end to maintain the structural rationality of the surface while ensuring prediction accuracy.

[0019] The advantages of using the technical solution of this invention compared with the prior art are as follows:

[0020] 1. More accurate dynamic evolution modeling: By directly mining the temporal characteristics of the underlying driving variables, it avoids the dependence of traditional methods on historical fitted surfaces, effectively solves the problem of error accumulation, and improves the ability to predict the future shape of the surface.

[0021] 2. More robust structural constraints: By embedding the preset parametric constraint function into the activation function of the expert network, a "hard constraint" effect is achieved, ensuring that the generated surface conforms to physical or geometric common sense under any circumstances, and avoiding the occurrence of unusable results.

[0022] 3. Strong global consistency and noise resistance: By utilizing the global spatial attention mechanism, sparse but reliable observation information can be smoothly and reasonably propagated to the entire surface region, which not only maintains the global structural correlation of the surface, but also effectively suppresses the influence of local noise. Attached Figure Description

[0023] Figure 1 This is a diagram illustrating the overall structure of the dynamic surface prediction method based on a spatiotemporal multi-expert network of this invention.

[0024] Figure 2 This is a schematic diagram of the average "smile curve" under different time periods of the present invention. Detailed Implementation

[0025] To make the technical solutions, objectives, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0026] This embodiment uses options market data in the financial field as an example to illustrate how to use the method of this invention to reconstruct and predict three-dimensional dynamic implied volatility surfaces. In practical applications, this method is also applicable to other surface modeling scenarios with spatiotemporal evolution characteristics, such as meteorological monitoring and medical image analysis.

[0027] like Figure 1 As shown in the figure, this diagram illustrates the collaborative process of the three core modules of this invention:

[0028] (1) Path-dependent temporal capture module (PD): Input the sequence of underlying driving variables, extract features through multi-scale convolution and LSTM, and generate historical temporal feature vectors by fusing decaying attention.

[0029] (2) Hybrid Multi-Expert Network Module (MoE): As the core generator, it includes parametric experts and general experts with embedded parametric constraint activation functions; it uses a gated network to fuse temporal features and spatial coordinates to dynamically route and generate the basic prediction surface.

[0030] (3) Surface Spatial Attention Module (SPA): As a corrector, it receives sparse observation data, calculates the observation weights through a global attention mechanism, performs global bias fusion on the basic surface, and outputs the final prediction or reconstruction result.

[0031] This embodiment provides a dynamic surface prediction method based on a spatiotemporal multi-expert network. The specific implementation steps are as follows:

[0032] Step S1: Data Preprocessing: The discrete observation data is mapped to a preset spatiotemporal grid coordinate system, the features are normalized, and a random masking strategy is used to simulate a sparse data scenario. This aims to clean, extract features, and simulate missing data from the original options market data, providing high-quality input data for subsequent model training.

[0033] Specifically, this embodiment uses SSE 50 ETF option data as the data source. First, the implied volatility of each option contract is calculated by inverse solving the Black-Scholes-Merton model. The definition is constructed in the "value level". and "remaining term" A surface coordinate system on a two-dimensional plane, wherein: , The option strike price. Let be the current price of the underlying asset, and r be the risk-free interest rate. This represents the number of days remaining until the due date.

[0034] Data cleaning was performed to remove data samples with insufficient liquidity. The specific criteria were: remaining maturity. Transaction volume not within the 7-365 day range This is because data reflecting true market expectations in areas with scarce liquidity is considered noise data.

[0035] MinMax normalization maps eigenvalues ​​to a linear scaling factor. Interval. Specifically, for a certain feature, let the original value be x, and the minimum value of that feature be... The maximum value is The normalization formula is: The numerator is the offset of the current value relative to the minimum value, and the denominator is the range (range) of the feature values. This step eliminates dimensional differences and accelerates model convergence.

[0036] To enhance the model's robustness to scenarios with missing data, a random masking mechanism is introduced during the training phase. Specifically, for the real data matrix... Apply masking operation:

[0037]

[0038] The meanings of each symbol are as follows: This is the original observation data matrix. This represents the number of currently observable samples. For feature dimensions; Given a binary mask matrix, whose elements are independently and identically distributed with probability Values (This indicates that the data at this location is masked and considered missing), with probability. Values (This indicates that the original value will be retained); This represents the Hadamard product, which is the operator that multiplies the elements at corresponding positions of a vector. This is the masked data matrix, where the masked positions (corresponding to...) China The element was forcibly set to Simulating missing states forces the model to learn to infer missing values ​​using surrounding information, thereby achieving interpolation and reconstruction.

[0039] Step S2: Historical dynamic temporal dependency feature capture: such as Figure 1 The path-dependent temporal capture module (PD) in the middle section extracts multi-scale features from the underlying driving variable sequence. Combined with a long short-term memory network and a decay-aware attention mechanism, it generates a historical temporal feature vector containing evolutionary patterns. This step avoids directly using historical surface data with significant fitting bias by extracting features containing dynamic evolutionary patterns from the historical return sequence of the underlying asset. This step includes the following sub-steps:

[0040] Step S21: Multi-scale feature decomposition: corresponding to Figure 1 The Multi-Feature Module within the PD module aims to separate short-term and long-term volatility and trend characteristics from the underlying driving variables. Specifically, the input is a historical return series. A one-dimensional convolutional network with fixed weights is used for processing. To capture long-term trends and short-term fluctuations respectively, this embodiment designs four convolutional kernels with fixed and average weights, with kernel sizes of 10 and 5 respectively, to extract long-term and short-term trend features. and fluctuation characteristics .

[0041] The calculation formula is as follows:

[0042]

[0043] in, This represents the convolution operation. This represents a series of returns over T historical time points. This represents a sequence of absolute values ​​of returns. Calculating volatility using absolute values ​​is more efficient than using standard deviation, and it captures almost identical volatility dynamics, significantly reducing computational overhead.

[0044] Extracted features and With the original rate of return After performing concatenation and normalization by the input normalization layer, the input vector of the LSTM is obtained. :

[0045]

[0046] Step S22: Long and short-term time-series dependency capture: such as Figure 1 As shown in the LSTM unit within the PD module, this sub-step utilizes a Long Short-Term Memory (LSTM) network to encode multi-scale feature sequences, capturing long-short-term dependencies in the time series.

[0047] LSTM adaptively adjusts its long-term and short-term memory through its unique gating mechanism (forget gate, input gate, output gate) to remember early key market conditions that have a lasting impact on current volatility predictions. The update formula for an LSTM cell is as follows:

[0048]

[0049] in, for The hidden state at all times The cell states represent current temporal characteristics and long-term memory information, respectively. for The hidden state at time -1 for Cell state at time -1.

[0050] Step S23: Dynamic fusion of historical features based on exponentially decaying perceptual attention: such as Figure 1 As shown in the decay-aware attention mechanism section within the PD module, this sub-step fuses the features from all time steps of the LSTM output into a fixed feature vector through an attention mechanism and introduces an exponential decay prior, common in the financial field. A key characteristic of financial markets is that the influence of historical information on current predictions typically decays exponentially over time. To inject this prior into the model, a decay-aware attention mechanism is designed. This mechanism uses a learnable decay parameter... Based on the time distance between the current moment and historical moments Adjust the attention weights. The specific calculation formula is as follows:

[0051]

[0052]

[0053] in, This represents the current moment, i.e., the total number of historical time steps involved in the integration; This serves as the index for the target historical moment in the current calculation of attention weights; The index variable is used to iterate through the historical moments in the summation term of the denominator, from 1 to... All historical time steps are used to calculate the global normalization factor; Is it LSTM at time? The output hidden state vector. It is a linear layer. The learnable decay rate parameter is used to control the attention weights over time. The exponential decay intensity. For the first Normalized attention weights for each time step. The path-dependent feature vector generated by the final fusion is used as the output of this sub-step.

[0054] Step S3: Multi-expert capture of historical normal distribution: such as Figure 1As shown in the middle section, the Hybrid Multi-Expert Network (MoE) module constructs a hybrid multi-expert network containing parametric experts and general experts. It utilizes a gating mechanism to fuse historical temporal features and spatial coordinates, generating a basic prediction surface that conforms to geometric constraints. This step constructs the Hybrid Multi-Expert Network (MoE) as the core generator of the surface. It introduces a parametric financial prior model as the activation function to structurally ensure the rationality of the output surface and uses a dynamic gating mechanism to adapt to the heterogeneity of different spatial regions.

[0055] Step S31: Coordinate Feature Upgrading: This sub-step will upgrade the spatial coordinates of the surface (in terms of value degree). and remaining term This is mapped to a high-dimensional feature space to enhance the network's expressive power. For each expert network... Using linear layers respectively and Upgrade to a higher dimension:

[0056]

[0057] in, For the index of the expert network, indicating the first... One expert; and The input spatial coordinates are usually one-dimensional scalar values, representing a certain spatial location or time offset. and For the first The learnable weight matrix of an expert, and For the corresponding learnable bias vector, The feature dimension after dimensionality upgrade. and They are respectively for and The feature vectors obtained after dimensionality increase. This dimensionality increase operation maps one-dimensional spatial coordinates to a higher-dimensional feature space, enabling subsequent activation functions to learn more complex nonlinear surface shapes on a higher-dimensional representation, thereby enhancing the expressive power of the expert network.

[0058] Step S32: Gating and fusing historical dynamic temporal dependency features: such as Figure 1 As shown in the gated routing module within the MoE module, this sub-step is used in the time series prediction task to process the path dependency features extracted in step S2. Injected into the spatial expert network. A Sigmoid gating mechanism was designed to balance historical path information with current timeline structural features:

[0059]

[0060]

[0061] in, and For the first The learnable weight matrix and bias terms of each expert. As a time-limited characteristic, Path dependency features extracted for the PD module It is the sigmoid activation function. The gating factor is within the range of between, This represents the Hadamard product, which is the element-wise multiplication operator of a vector. This gating mechanism adaptively balances historical path dependency information with current time-bound structural features. However, in the current time-bound interpolation prediction task, the PD module and the temporal fusion gating mechanism will be removed.

[0062] Step S33: Multi-parameter prior activation function embedding: To ensure that the generated implied volatility surface satisfies the financial constraint of "butterfly-free arbitrage," three types of SVI (Stochastic Volatility Inspired) models are embedded as activation functions into the parameterized expert network, as shown in Table 1, which contains the initialization parameters for the three types of SVI experts. Figure 2 As shown. Combined with Figure 2 The diagrams illustrating the "smile curve" under three maturity parameters show significant heterogeneity in the volatility surface shape across different remaining maturities in the actual market. For example, the short-term curve is noticeably sloping, while the long-term curve tends to be flatter. Using a single, fixed-parameter SVI activation function limits its expressive power, resulting in severely insufficient model generalization. Therefore, this invention introduces an SVI activation function with three parameter configurations. This avoids overfitting by purely data-driven approaches through an embedded no-arbitrage geometric prior, and overcomes the limitations of a single model. Thus, while accurately fitting heterogeneous patterns, it significantly improves the model's generalization ability. Its network-based unfolding is as follows:

[0063]

[0064]

[0065]

[0066]

[0067] In the above formula, Indicates the first An index of expert networks; and These represent the in-value feature vector and the remaining time feature vector, respectively, after dimensionality increase through a linear layer within the expert network. and These are the translation and scaling parameters of the SVI model, used to control the left and right translation of the center of the volatility smile curve and the smoothness of the inflection point region; These are the standardized intermediate feature variables; The horizontal displacement parameter determines the characteristics of the total variance. The baseline level; and These represent the parameters controlling the angle between the two wings and the parameter controlling the tilt in the SVI model, respectively, expressed through parametric relationships. and Transform into a curvature term coefficient vector and tilt control coefficient vector Used to jointly constrain total variance characteristics The conditions for butterfly-free arbitrage are met; The transpose of the reduced-dimensionality weight matrix within the expert network is... Used to map high-dimensional features to one-dimensional scalars; The remaining timeframe is a scalar; Sigmoid is the activation function. This represents the Hadamard product, which is the operator that multiplies the elements at corresponding positions of a vector. and These represent the implicit volatility eigenvalues ​​output by the parameterized SVI expert network and the general SoftPlus expert network, respectively. The on-value degree after dimensionality upgrade. After the SVI activation function, and then the duration feature... The Hadamard product operation is performed to fuse the features, and finally, the dimensionality reduction matrix within the expert network reduces the dimensionality of the features to obtain the final result. The expert's final implied volatility forecast output, using Unified representation and .

[0068] Table 1 Initialization parameters for the three types of SVI experts

[0069] Short 0.0011 0.0013 0.0037 0.0505 0.0882 Mid 0.0088 0.0026 0.0074 0.0464 0.1224 Long 0.0148 0.0058 0.0123 0.0607 0.1468

[0070] Step S34: Multi-Expert Dynamic Route Fusion Prediction: This sub-step utilizes a gating network to dynamically select the most suitable expert for prediction based on the input spatial coordinates, achieving heterogeneity modeling. First, the weights of each expert are calculated using a spatially aware gating network. :

[0071]

[0072]

[0073] in, For spatial coordinates and time offset A two-dimensional input vector formed by concatenation. These are the weight matrix and bias vector of the first linear transformation layer, respectively, used to map the two-dimensional input to a hidden space of a preset dimension; This is the intermediate feature vector output after ReLU activation of this layer. These are the weight matrix and bias vector of the second linear transformation layer, respectively, used to map the hidden features to the weight space corresponding to the number of experts; Here is the expert weight vector obtained after Softmax normalization, where Let be the total number of experts, and each component represent the probability weight of the corresponding expert being selected, satisfying the following condition: .

[0074] The final prediction value of the basic surface is the weighted sum of the outputs of each expert:

[0075]

[0076] in, The total number of experts, For expert indexing. The expert weight vector output by the gating network in step S34 The Each component satisfies , indicating the first An expert at the current spatial coordinates The probability weight of being selected. For the first The output value of an expert network, where the expert can be an SVI expert or a SoftPlus expert, corresponding to different types of implied volatility surface shape fitting functions, respectively. The final predicted value of the base surface obtained by fusion is represented in spatial coordinates. The implied volatility prediction results are obtained by dynamically weighting and combining the outputs of various experts.

[0077] Step S4: Dynamic fine-tuning of attention in curved space: such as Figure 1 As shown in the Surface Spatial Attention (SPA) module on the right, it uses a global attention mechanism to calculate the deviation between the sparse observation data and the base surface. Through weighted fusion, the observation information is propagated throughout the entire grid, outputting the final predicted or reconstructed surface. This step, through the Surface Spatial Attention (SPA) module, uses real-time sparse observation data to globally correct the generated base surface, ensuring it conforms to the latest distribution.

[0078] Step S41: Global Spatial Correlation Weight Capture: such as Figure 1 As shown, the curved space attention module receives the overall market observation data matrix. This matrix summarizes multidimensional information from all observation points. This sub-step aims to compute the relationship between each grid point to be predicted on the surface and... The correlation weights between various observation points are determined. In the specific calculation, the first... The feature vector corresponding to each observation point is denoted as . And construct a query vector based on this. and key vector :

[0079]

[0080]

[0081] In the formula for constructing the query vector, This represents the query vector for the current grid point to be predicted. This represents a two-dimensional spatial coordinate vector formed by concatenating the value of the grid point with the remaining time limit; and These are the learnable weight matrix and bias vector for the query branch, used to linearly project the low-dimensional coordinates to the high-dimensional latent space. In the formula for constructing the key vector, This represents the overall market matrix. The Middle The key vector of each observation point; It contains rich information about the observation point: spatial coordinates ( Indicates the degree of value. (Indicates remaining term), subject information () Indicates the price of the target. (Indicates the execution price) and liquidity information ( Indicates transaction volume. (Indicates open interest); and These are the learnable weight matrix and bias vector of the key branch, respectively, used to map the high-dimensional multi-source heterogeneous features of the market to a feature space of the same dimension as the query vector, so as to accurately capture spatial correlation through dot product operation in the future.

[0082] Calculate weights using scaled dot product attention:

[0083]

[0084] in, The query vector is obtained by linear projection of the spatial coordinates of the point to be predicted; For the first The key vector of each observation point is obtained by linear projection of the spatial coordinates of the observation point, the characteristics of the target, and the market liquidity characteristics. The dimensions of the query vector and key vector; This represents the total number of observation points; For the first The normalized attention weights corresponding to each observation point satisfy the following condition: Scaling factor Used to adjust the scale of the dot product result, avoiding issues caused by high dimensionality. Function gradient saturation.

[0085] Step S42: Calculation of the Deviation Between Historical Normal Surface and Latest Distribution: This sub-step calculates the deviation between the actually observed implied volatility and the predicted value of the basic surface, serving as a correction signal. First, the observation point is found through nearest neighbor search. On the basic surface Corresponding value on Then calculate the residuals. :

[0086]

[0087] in, Let be the implied volatility of the i-th market. This is the implied volatility predicted at this location by the basic normal surface.

[0088] Step S43: Global Spatial Attention Fusion Bias: This sub-step propagates the calculated bias to the entire mesh according to the attention weights, fine-tuning the base surface.

[0089]

[0090]

[0091] in, Represents spatial coordinates The final implied volatility prediction value after global correction is displayed. and These represent the on-value degree and remaining lifespan of the surface, respectively. This represents the underlying volatility forecast for the corresponding position generated by the preceding hybrid multi-expert network module; the summation symbol indicates that all available market observation points have been traversed. This represents the total number of observation points; This indicates the result calculated in step S41. Normalized attention weights of each observation point relative to the current grid point to be predicted; This indicates the calculation of the first step in step S42. The residual deviation between the actual observed implied volatility and the baseline predicted value at each observation point. Correction value for each grid point. All values ​​are derived from a weighted average of all observation points. This approach allows the model to adapt to changes in the latest market distribution while mitigating the impact of local noise through global information, thus maintaining the overall structural integrity of the surface.

[0092] Step S5: Model Training Loss Function with Structural Priors: Construct a total loss function that includes data fitting loss and structural constraint loss, and perform end-to-end training on the model to maintain the structural rationality of the surface while ensuring prediction accuracy. To further guarantee the arbitrage-free nature of the output surface, this invention introduces financial theory constraints into the loss function. , Let represent the first and second partial derivatives of implied volatility with respect to the degree of value m, respectively; , This represents the corresponding partial derivative with respect to the remaining timeframe (Note: Given that the IVS output is a discrete grid, all partial derivatives are solved using the finite difference method). The total loss function consists of three parts:

[0093]

[0094] in, , This is a hyperparameter used to balance the importance of various losses. The loss function is a monotonic constraint. This is the constraint loss function for butterfly arbitrage.

[0095] (1) Data fitting loss. To ensure prediction accuracy, a combination of mean squared error (MSE) and mean absolute percentage error (MAPE) is used:

[0096]

[0097] in, Indicates the number of samples. It is the implied volatility predicted by the model. This refers to the actually observed implied volatility. MSE is more sensitive to large deviations; when the market experiences significant volatility, it prompts the model to pay closer attention to these significant changes, thus ensuring the model's accuracy in capturing large market movements. MAPE focuses on measuring relative error, being more sensitive to low implied volatility deviations near at-the-money levels, while being relatively insensitive to high implied volatility in deep out-of-the-money areas. This characteristic allows the model to pay more attention to highly liquid options while avoiding overfitting to abnormal volatility in extreme areas such as deep out-of-the-money or in-the-money markets.

[0098] (2) Monotonicity constraint loss. Used to constrain implied volatility as the remaining maturity increases. The changes follow a monotonically decreasing pattern (short-term volatility is usually higher than long-term volatility), preventing the formation of calendar spread arbitrage patterns in options trading. The calculation formula is:

[0099]

[0100] (3) Butterfly arbitrage constraint. Used to constrain the volatility smile curve under the same period to be smooth and without abnormal bulges, so as to prevent butterfly arbitrage.

[0101]

[0102] By combining these three modules and using a constrained loss function, this invention effectively solves the three core challenges of traditional methods: difficulty in capturing time-series information, difficulty in guaranteeing the prior shape of no-arbitrage financial markets, and insufficient utilization of global spatial correlation. It provides an effective solution for modeling implicit volatility surfaces and successfully integrates theory and practice.

[0103] The above-described embodiments are merely one implementation of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.

Claims

1. A dynamic surface prediction method based on spatiotemporal multi-expert networks, characterized in that... Includes the following steps: Step S1: Data preprocessing: Map the discrete observation data to a preset spatiotemporal grid coordinate system, normalize the features, and use a random masking strategy to simulate the data sparsity scenario; Step S2: Historical dynamic temporal-series dependent feature capture: Multi-scale features are extracted from the underlying driving variable sequence through the path dependency capture module, and combined with the long short-term memory network and decay perception attention mechanism to generate a historical temporal feature vector containing evolutionary patterns; Step S3: Capture historical normal distribution using hybrid multi-expert network: Construct a hybrid multi-expert network that includes parametric experts and general experts, and use a gating mechanism to fuse historical time series features and spatial coordinates to generate a basic prediction surface that meets geometric constraints; Step S4: Dynamic fine-tuning of surface space attention: The deviation between sparse observation data and the base surface is calculated using a global attention mechanism. The observation information is then propagated to the entire grid through weighted fusion to output the final predicted or reconstructed surface. Step S5: Model training loss function with structural prior: Construct a total loss function that includes data fitting loss and structural constraint loss, and train the model end-to-end to maintain the structural rationality of the surface while ensuring prediction accuracy.

2. The method according to claim 1, characterized in that, The data preprocessing in step S1 includes feature normalization and random masking; the observed data is normalized to the [0,1] interval using MinMax; and a 5% random masking strategy is adopted during training.

3. The method according to claim 1, characterized in that, Step S2 includes multi-scale feature decomposition; a one-dimensional convolutional network with fixed weights is used to extract features, with kernel sizes of 10 and 5, respectively, to extract long-term and short-term trend features. and fluctuation characteristics ; Trend features are obtained by convolving the sequence, and fluctuation features are obtained by convolving the absolute value of the sequence, as shown in the following formulas: in, This represents the convolution operation. This represents the historical return series at time T. This represents a sequence of absolute values ​​of returns.

4. The method according to claim 1, characterized in that, Step S2 includes dynamic fusion of historical features based on exponentially decaying perceptual attention; based on the hidden states extracted by LSTM, an exponential decay factor related to time distance is introduced to calculate the attention weights, as shown in the following formula: in, This represents the current moment, i.e., the total number of historical time steps involved in the integration; Indexing historical moments; The index variable is used to iterate through the historical moments in the summation term of the denominator, from 1 to... All historical time steps are used to calculate the global normalization factor; Is it LSTM at time? The output hidden state vector; Linear layer; The learnable decay rate parameter is used to control the attention weights over time. The exponential decay intensity; For the first Normalized attention weights for each time step; The path-dependent feature vector generated by the final fusion is used as the output of this sub-step.

5. The method according to claim 1, characterized in that, Step S3 includes embedding a multi-parameter prior activation function; in the parameterization expert, a quadratic parameterization model satisfying a specific geometric shape is used as the activation function, as shown in the following formula: in, Indicates the first An index of expert networks; This represents the Hadamard product, which is the operator that multiplies the elements at corresponding positions of a vector. and These represent the in-value feature vector and the remaining time feature vector, respectively, after dimensionality increase through a linear layer within the expert network. and These are the translation and scaling parameters of the SVI model, used to control the left and right translation of the center of the volatility smile curve and the smoothness of the inflection point region; These are the standardized intermediate feature variables; The horizontal displacement parameter determines the characteristics of the total variance. The baseline level; and These represent the parameters controlling the angle between the two wings and the parameter controlling the tilt in the SVI model, respectively, expressed through parametric relationships. and Transform into a curvature term coefficient vector and tilt control coefficient vector Used to jointly constrain total variance characteristics The conditions for butterfly-free arbitrage are met; The transpose of the reduced-dimensionality weight matrix within the expert network is... Used to map high-dimensional features to one-dimensional scalars; The remaining timeframe is a scalar; Sigmoid is the activation function. and These represent the implicit volatility eigenvalues ​​output by the parameterized SVI expert network and the general SoftPlus expert network, respectively; the on-value degree after dimensionality upgrade. After the SVI activation function, and then the duration feature... The Hadamard product operation is performed to fuse the features, and finally, the dimensionality reduction matrix within the expert network reduces the dimensionality of the features to obtain the final result. The expert's final implied volatility forecast output, using Unified representation and .

6. The method according to claim 1, characterized in that, Step S3 includes gating fusion and dynamic route prediction; temporal features and coordinate features are fused through a spatiotemporal gating mechanism, and expert weights are dynamically allocated through a Softmax gating network.

7. The method according to claim 1, characterized in that, Step S4 includes dynamic fine-tuning of global spatial attention; calculating the deviation between the observation point and the base surface, obtaining global weights using scaled dot product attention and fusing the deviations, as shown in the following formula: in, For residuals; Implied volatility in the market; The implied volatility predicted by the underlying surface at this location; The query vector is obtained by linear projection of the spatial coordinates of the point to be predicted; For the first The key vector of each observation point is obtained by linearly projecting the spatial coordinates of the observation point and the market characteristics together. Grid coordinates; Includes the first The spatial coordinates, target information, and mobility information of each observation point; the spatial coordinates include information indicating the degree of value. and indicating the remaining term The target information includes information representing the target price. and representing the execution price The liquidity information includes representations of trading volume. And represents the position size. ; and It is the bias vector; Dimensions of the query vector and key vector; scaling factor Used to adjust the scale of the dot product result, avoiding issues caused by high dimensionality. Function gradient saturation; This represents the total number of observation points; For the first The normalized attention weights corresponding to each observation point satisfy the following condition: .

8. The method according to claim 1, characterized in that, Step S5 includes the model training loss function with structure prior; the total loss is obtained by weighted summation of the data fitting loss and the structure regularization loss, as shown in the following formula: in, , These are hyperparameters used to balance the importance of various losses; The loss function is a monotonic constraint. This is the constraint loss function for butterfly arbitrage.

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