Data interpolation and fitting analysis system

Abstract

The invention relates to the technical field of numerical calculation and data analysis, in particular to a data interpolation and fitting analysis system which comprises a data processing module, a depth generation interpolation module, an uncertainty quantification module, an interpretability optimization module, a multi-source heterogeneous data processing module and a hybrid calculation acceleration module. In the prior art, a traditional interpolation method is easy to generate over-fitting or under-fitting in a complex data distribution and high noise scene, and a single deep learning model is insufficient in generalization ability in a small sample or data sparse region; through the dynamic fusion architecture of the depth generation interpolation module, the advantages of a traditional numerical method and deep learning are combined, the weight is automatically adjusted based on data characteristics, the prediction error under noise data is remarkably reduced, the adaptability to complex distribution is improved, and the stability of a data sparse region is enhanced; the problems of insufficient precision and weak generalization ability of a single model of a traditional method are effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical calculation and data analysis, and in particular to a data interpolation and fitting analysis system. Background Art

[0002] With the development of artificial intelligence (AI), demand for data interpolation and fitting analysis has surged in fields such as industrial inspection, medical imaging, and weather forecasting. While traditional interpolation methods such as linear and spline interpolation offer high computational efficiency, they struggle to handle complex data distributions, high-dimensional heterogeneous data, and massive data volumes. They are sensitive to missing values ​​and noise, and lack multimodal semantic understanding, resulting in insufficient interpolation accuracy and reliability. Deep learning techniques, particularly generative adversarial networks (GANs) and spatiotemporal transformers, have improved interpolation capabilities but still face the risk of overfitting, particularly when data is sparse, resulting in poor generalization. Furthermore, the "black box" nature of these models lacks transparency in the decision-making process, making it difficult to meet the interpretability requirements of high-risk sectors such as healthcare and finance. Furthermore, traditional architectures suffer from low computational efficiency and high graphics memory usage, making them unable to meet real-time requirements and becoming a bottleneck for large-scale applications.

[0003] The demand for cross-modal data processing is increasingly urgent. Scenarios such as the Industrial Internet of Things and intelligent transportation require the fusion of heterogeneous information from multiple sources, including sensor data, text reports, and images. However, traditional methods offer only simple concatenation or weighted averaging, failing to address the spatial and temporal differences and semantic gaps between modalities. This leads to information loss and semantic bias. Existing systems lack the ability to deeply mine multimodal associations, making it difficult to achieve knowledge-driven semantic-level feature fusion, limiting their effectiveness in complex scenarios.

[0004] When it comes to uncertainty quantification, traditional interpolation systems only provide a single result, lacking credibility assessment and risk warning mechanisms. This can lead to serious consequences in high-stakes decision-making. While Bayesian neural networks and Monte Carlo sampling offer new approaches, their high computational complexity and integration difficulties hinder their large-scale application.

[0005] In addition, traditional computing architectures are unable to meet the computing power requirements of deep learning. Problems such as insufficient GPU video memory and low computing efficiency restrict the processing capabilities of large-scale interpolation tasks. Existing optimization solutions often require complex system adjustments, and edge deployment capabilities are limited, which cannot meet the real-time requirements of the Industrial Internet of Things. In response to these technical bottlenecks, the present invention proposes a data interpolation and fitting analysis system. Through innovative technologies such as deep generative interpolation, multimodal fusion, uncertainty quantification, interpretable optimization, and hybrid computing acceleration, an efficient and accurate intelligent interpolation platform is constructed, breaking through the limitations of existing technologies and promoting the in-depth application of data interpolation technology in multiple fields. Summary of the Invention

[0006] In order to overcome the problems raised in the above background technology, the present invention proposes a data interpolation and fitting analysis system.

[0007] The technical solution of the present invention is: a data interpolation and fitting analysis system, comprising:

[0008] Data processing module, used to normalize input data, remove outliers, mark missing values ​​and perform block processing;

[0009] A deep generative interpolation module, which implements adaptive interpolation through spatiotemporal Transformers and generative adversarial networks, and dynamically integrates traditional numerical methods;

[0010] Uncertainty quantification module, used to generate risk warning confidence intervals based on the credibility of Bayesian neural network and Monte Carlo sampling quantification interpolation results;

[0011] The explainability optimization module combines gradient significance analysis with causal reasoning techniques to provide transparent logical traceability and counterfactual explanations of interpolation decisions.

[0012] Multi-source heterogeneous data processing module, used to achieve spatiotemporal alignment of multiple cross-modal data and feature fusion driven by knowledge graphs;

[0013] The hybrid computing acceleration module is used to achieve parallel computing acceleration of large-scale interpolation tasks through GPU-CPU heterogeneous architecture optimization and intelligent scheduling of video memory.

[0014] Preferably, the data processing module normalizes the input data, removes outliers, marks missing values, and performs block processing, specifically including:

[0015] S11: Data input, receiving raw data in various formats;

[0016] S12: Data cleaning: outlier detection and elimination based on the 3σ criterion, and missing values ​​are marked;

[0017] S13: Data preprocessing: normalize the cleaned data, scale the data to the range of [-1, 1], and divide the data into blocks according to the set size, where the size of each block after division is less than 1GB.

[0018] As a preferred method, the deep generative interpolation module implements adaptive interpolation through the spatiotemporal Transformer and the generative adversarial network, and dynamically integrates traditional numerical methods, specifically including:

[0019] S21: Feature extraction: extract features from data using the spatiotemporal Transformer model and semantic model, and use a dynamic attention mechanism to perform weighted fusion of features from different modalities to generate fused features;

[0020] S22: Generative interpolation core calculation, receiving fused features, generating candidate interpolation points through a deep learning-based generator, capturing complex data distribution, and running traditional numerical methods in parallel, and finally automatically adjusting the weights of the deep learning and traditional methods based on the data characteristics;

[0021] S23: Adaptive Optimization and Feedback: This integrates adversarial loss, reconstruction error, and smoothness constraints through a multi-objective loss function, automatically adjusts the core parameters of traditional methods using Bayesian optimization, and optimizes the generator network weights through gradient backpropagation.

[0022] S24: Output post-processing and verification: Based on the output of the discriminator in the generative adversarial network, the credibility of each interpolation point is quantified, and low-confidence areas are marked for manual review. Anisotropic diffusion filtering technology is applied to eliminate local mutations. Finally, a 3D spatiotemporal interpolation surface and uncertainty heat map are generated, and compared with domain knowledge to verify the rationality of the results.

[0023] Preferably, when receiving fusion features and generating candidate interpolation points through a deep learning-based generator to capture complex data distribution, the specific architecture of the deep learning-based generator is as follows:

[0024] A11: Multimodal encoder, including spatiotemporal data branch, image branch, and text branch. The spatiotemporal data branch includes a multi-head self-attention layer and position encoding. The image branch uses a U-Net encoder to extract multi-scale features of image data. The text branch uses the BERT fine-tuned model to generate semantic embedding vectors. The multimodal encoder uses a cross-modal attention gating mechanism to dynamically calculate inter-modal attention weights and perform adaptive feature fusion. The principle formula of the cross-modal attention gating mechanism is:

[0025]

[0026] Among them, Q is the spatiotemporal feature matrix, K is the other modal feature matrix, and W q To query the projection matrix, W k is the key projection matrix;

[0027] A12: Conditional generative encoder, consisting of cascaded residual blocks and a traditional method reference area. Each residual block in the cascaded residual blocks contains a spatiotemporal convolution layer, instance-based normalization, and a LeakyReLU activation function. The traditional method reference area is used to calculate the results of the traditional interpolation algorithm.

[0028] A13: Adversarial training head, used to improve generation quality through adversarial training, using a multi-scale discriminator and spectral normalization constraints to stabilize the adversarial training process.

[0029] As a preference, when automatically adjusting the weights of the results of deep learning and traditional methods based on data characteristics, the rules used include:

[0030] A21: For high-noise and washed-out data, traditional interpolation algorithms are preferred;

[0031] A22: For dense data and complex distributed data, focus on deep learning;

[0032] A23: Automatically switches the dominant algorithm based on a preset threshold.

[0033] Preferably, the uncertainty quantification module generates a risk warning confidence interval based on the credibility of the Bayesian neural network and Monte Carlo sampling quantization interpolation results, specifically including:

[0034] S31: Data input and preprocessing, aligning the interpolation results with the original data coordinate system, marking missing areas and estimating noise distribution;

[0035] S32: Bayesian neural network inference, obtaining multiple prediction results through Monte Carlo sampling, separating the sources of model and data uncertainty;

[0036] S33: Confidence interval generation, calculation of predicted mean and total variance, generation of 95% confidence interval and risk heat map;

[0037] S34: Risk warning and feedback, triggering threshold alarms and pushing manual review, and dynamically adjusting interpolation strategies for high-risk areas;

[0038] S35: Module collaboration and output, linked interpolation and interpretable module optimization results, output of structured reports and real-time warning signals.

[0039] Preferably, when obtaining multiple prediction results through Monte Carlo sampling and separating the sources of model and data uncertainty, the following are specifically included:

[0040] S41: Monte Carlo sampling, sampling the network weights T times, each sampling generates a set of weight instances;

[0041] S42: Multiple forward propagations, for each weight instance, input interpolation area data to obtain T groups of prediction results;

[0042] S43: Uncertainty decomposition, including model uncertainty and data uncertainty. Model uncertainty is obtained by calculating the variance of the prediction results, and data uncertainty is obtained by calculating the noise distribution parameters. The calculation principle formula of model uncertainty is:

[0043]

[0044] Among them, Var modelis the model uncertainty, T is the number of samplings, y (t) is the prediction result of group t, is the average value of the prediction results of group T.

[0045] As a preferred option, the explainability optimization module combines gradient significance analysis and causal reasoning technology to provide transparent logical traceability and counterfactual explanations of interpolation decisions, specifically including:

[0046] S51: Input preparation, receiving interpolation results and original data;

[0047] S52: Gradient significance analysis, by calculating the gradient of the interpolation result to the input data, generating a heat map to show the key impact areas;

[0048] S53: Causal inference modeling, building structural causal models, and identifying causal chains of missing data and interpolation bias;

[0049] S54: Generate counterfactual explanations, simulate variable interventions, and output comparative reports to reveal changes in interpolation results;

[0050] S55: Rule extraction and feedback, converting deep learning logic into readable rules and pushing them to the interpolation module to optimize the generation strategy.

[0051] Preferably, the multi-source heterogeneous data processing module specifically includes the following steps when realizing the spatiotemporal alignment of multiple cross-modal data and feature fusion driven by knowledge graphs:

[0052] S61: Input dispatch and preprocessing, automatically identifying input types and performing data cleaning;

[0053] S63: Knowledge graph driven fusion, extracting entities and reasoning about implicit relationships, dynamically weighting modality importance;

[0054] S64: Unify feature representation, concatenate symbolic knowledge and neural network features, and output a 512-dimensional fusion vector.

[0055] As a preferred option, the hybrid computing acceleration module implements parallel computing acceleration of large-scale interpolation tasks through GPU-CPU heterogeneous architecture optimization and intelligent video memory scheduling, specifically including:

[0056] S71: Data segmentation and transmission optimization, dynamically dividing data into blocks adapted to GPU memory, and reducing latency through page-locked memory and asynchronous transmission;

[0057] S72: Distributed task scheduling and load balancing, using MPI to split global tasks, dynamically assigning subtasks based on node computing power, monitoring load in real time, and migrating overloaded tasks;

[0058] S73: GPU-CPU heterogeneous computing collaboration, GPU executes CUDA optimized kernel functions and kernel fusion, CPU schedules I / O and preprocessing;

[0059] S74: Intelligent memory scheduling and reuse, pre-allocated memory pool and cross-GPU sharing mechanism, combined with TensorRT computational graph optimization;

[0060] S75: Edge adaptation and deployment, deploying lightweight models + Triton dynamic batch processing;

[0061] S76: Merge and output the results, aggregate the distributed results through MPI, check the consistency of sub-block boundaries, and compress the output using Zstandard.

[0062] Beneficial effects of the present invention:

[0063] 1. Compared with the traditional interpolation methods in the prior art, which are prone to overfitting or underfitting in complex data distributions and high-noise scenarios, and the generalization ability of single deep learning models is insufficient in small sample sizes or data-sparse areas, this invention uses a dynamic fusion architecture of deep generation interpolation modules, combines the advantages of traditional numerical methods and deep learning, and automatically adjusts weights based on data characteristics. This significantly reduces prediction errors under noisy data, improves adaptability to complex distributions, and enhances stability in data-sparse areas, effectively solving the problems of insufficient accuracy of traditional methods and weak generalization ability of single models.

[0064] 2. Compared with existing technologies that cannot resolve spatiotemporal benchmark differences and semantic gaps when processing multi-source heterogeneous data, and the interpolation process lacks transparency, making it difficult to meet compliance requirements; this invention uses a knowledge graph-driven fusion engine and a gradient significance-causal reasoning dual-path interpretation mechanism to achieve cross-modal spatiotemporal alignment and decision traceability. It significantly improves the semantic fusion accuracy of multimodal data, provides visual logical traceability and counterfactual explanations, enhances decision transparency, and meets the strict compliance and traceability requirements of medical and financial fields.

[0065] 3. Compared with the traditional interpolation system in the existing technology, which is inefficient in processing large-scale high-dimensional data, has high memory usage, and is difficult to meet real-time requirements; the present invention achieves efficient utilization of computing resources through heterogeneous architecture optimization and intelligent memory scheduling technology, combined with lightweight edge deployment; significantly improves computing speed, reduces resource consumption, supports real-time processing of large-scale data and low-power deployment at the edge, and overcomes the problems of insufficient efficiency and hardware resource limitations of traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Shown is a schematic diagram of the structure of the data interpolation and fitting analysis system of the present invention;

[0067] Figure 2What is shown is a schematic diagram of the workflow of the depth generation interpolation module in the data interpolation and fitting analysis system of the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below with reference to the accompanying drawings and examples.

[0069] See also Figure 1-Figure 2 The present invention provides an embodiment: a data interpolation and fitting analysis system, comprising:

[0070] Data processing module, used to normalize input data, remove outliers, mark missing values ​​and perform block processing;

[0071] A deep generative interpolation module, which implements adaptive interpolation through spatiotemporal Transformers and generative adversarial networks, and dynamically integrates traditional numerical methods;

[0072] Uncertainty quantification module, used to generate risk warning confidence intervals based on the credibility of Bayesian neural network and Monte Carlo sampling quantification interpolation results;

[0073] The explainability optimization module combines gradient significance analysis with causal reasoning techniques to provide transparent logical traceability and counterfactual explanations of interpolation decisions.

[0074] Multi-source heterogeneous data processing module, used to achieve spatiotemporal alignment of multiple cross-modal data and feature fusion driven by knowledge graphs;

[0075] The hybrid computing acceleration module is used to achieve parallel computing acceleration of large-scale interpolation tasks through GPU-CPU heterogeneous architecture optimization and intelligent scheduling of video memory.

[0076] As described above, the present invention has achieved significant technological breakthroughs through multi-module collaborative optimization: in terms of accuracy and robustness, the deep generative interpolation module integrates the spatiotemporal Transformer and traditional numerical methods, and dynamically adjusts the weights based on data characteristics, effectively improving the interpolation accuracy in complex scenarios; in terms of interpretability and compliance, the interpretability optimization module combines gradient significance analysis and causal reasoning technology to provide transparent logical traceability and counterfactual explanations to meet compliance requirements in medical, financial and other fields; in terms of cross-modal data processing, the multi-source heterogeneous data processing module solves the spatiotemporal benchmark differences and semantic gap problems of multi-source data through semantic association mining and feature fusion driven by knowledge graphs; in terms of computational efficiency, the hybrid computing acceleration module adopts GPU-CPU heterogeneous architecture and video memory intelligent scheduling technology to break through the computing power bottleneck of traditional architecture, realize real-time processing of large-scale data and low-power deployment on the edge, significantly reduce resource consumption and improve system throughput, and finally form a set of intelligent interpolation analysis solutions that take into account accuracy, interpretability, generalization capability and operational efficiency.

[0077] Preferably, the data processing module normalizes the input data, removes outliers, marks missing values, and performs block processing, specifically including:

[0078] S11: Data input, receiving raw data in various formats;

[0079] S12: Data cleaning: outlier detection and elimination based on the 3σ criterion, and missing values ​​are marked;

[0080] S13: Data preprocessing: normalize the cleaned data, scale the data to the range of [-1, 1], and divide the data into blocks according to the set size, where the size of each block after division is less than 1GB.

[0081] As described above, the present invention achieves efficient data preprocessing through multi-step collaborative optimization: in the data input stage, it is compatible with raw data in various formats to ensure the system's wide adaptability to heterogeneous data sources; in the data cleaning stage, the 3σ criterion is used to accurately detect and eliminate outliers, and missing values ​​are marked at the same time, effectively improving data quality and reducing subsequent calculation noise interference; in the data preprocessing stage, the data is uniformly scaled to the range of [-1,1] through normalization to eliminate the impact of dimensional differences on model training, and processed in blocks of a set size (each block is less than 1GB), which not only avoids video memory overflow but also adapts to GPU parallel computing requirements, thereby significantly improving data quality and computing efficiency, and providing a high-quality, structured input foundation for subsequent deep generation interpolation and uncertainty quantification.

[0082] As a preferred method, the deep generative interpolation module implements adaptive interpolation through the spatiotemporal Transformer and the generative adversarial network, and dynamically integrates traditional numerical methods, specifically including:

[0083] S21: Feature extraction: extract features from data using the spatiotemporal Transformer model and semantic model, and use a dynamic attention mechanism to perform weighted fusion of features from different modalities to generate fused features;

[0084] S22: Generative interpolation core calculation, receiving fused features, generating candidate interpolation points through a deep learning-based generator, capturing complex data distribution, and running traditional numerical methods in parallel, and finally automatically adjusting the weights of the deep learning and traditional methods based on the data characteristics;

[0085] S23: Adaptive Optimization and Feedback: This integrates adversarial loss, reconstruction error, and smoothness constraints through a multi-objective loss function, automatically adjusts the core parameters of traditional methods using Bayesian optimization, and optimizes the generator network weights through gradient backpropagation.

[0086] S24: Output post-processing and verification: Based on the output of the discriminator in the generative adversarial network, the credibility of each interpolation point is quantified, and low-confidence areas are marked for manual review. Anisotropic diffusion filtering technology is applied to eliminate local mutations. Finally, a 3D spatiotemporal interpolation surface and uncertainty heat map are generated, and compared with domain knowledge to verify the rationality of the results.

[0087] As described above, the present invention achieves high-precision, adaptive interpolation calculations through multi-stage collaborative optimization: in the feature extraction stage, the spatiotemporal Transformer and the semantic model are combined with a dynamic attention mechanism to accurately capture the temporal-spatial correlation and semantic features of multimodal data, generating high-quality fusion features. In the core computation link, a deep learning-based generator and parallel traditional numerical methods form a complementary mechanism. Through dynamic weight adjustment driven by data characteristics, the advantages of deep learning are brought into play in complex distribution areas and the stability of traditional methods is enhanced in noise-sensitive areas. In the adaptive optimization stage, a multi-objective loss function and Bayesian optimization strategy are adopted to simultaneously improve the generation quality and the parameter accuracy of traditional methods, and a closed-loop feedback is formed through gradient backpropagation. In the output stage, an adversarial training discriminator and anisotropic diffusion filtering technology are combined to not only quantify the interpolation credibility and mark low-confidence areas for manual review, but also eliminate local mutations through post-processing. Ultimately, a 3D spatiotemporal interpolation surface and uncertainty heat map that conforms to domain knowledge are generated, significantly improving the accuracy, robustness, and interpretability of the interpolation results, providing reliable support for scientific computing and industrial applications in complex scenarios.

[0088] Preferably, when receiving fusion features and generating candidate interpolation points through a deep learning-based generator to capture complex data distribution, the specific architecture of the deep learning-based generator is as follows:

[0089] A11: Multimodal encoder, including spatiotemporal data branch, image branch, and text branch. The spatiotemporal data branch includes a multi-head self-attention layer and position encoding. The image branch uses a U-Net encoder to extract multi-scale features of image data. The text branch uses the BERT fine-tuned model to generate semantic embedding vectors. The multimodal encoder uses a cross-modal attention gating mechanism to dynamically calculate inter-modal attention weights and perform adaptive feature fusion. The principle formula of the cross-modal attention gating mechanism is:

[0090]

[0091] Among them, Q is the spatiotemporal feature matrix, K is the other modal feature matrix, and W q To query the projection matrix, W k is the key projection matrix;

[0092] A12: Conditional generative encoder, consisting of cascaded residual blocks and a traditional method reference area. Each residual block in the cascaded residual blocks contains a spatiotemporal convolution layer, instance-based normalization, and a LeakyReLU activation function. The traditional method reference area is used to calculate the results of the traditional interpolation algorithm.

[0093] A13: Adversarial training head, used to improve generation quality through adversarial training, using a multi-scale discriminator and spectral normalization constraints to stabilize the adversarial training process.

[0094] As described above, the present invention significantly improves the modeling capability of complex data distribution through a multimodal collaborative architecture: the multimodal encoder adopts a three-modal fusion structure of spatiotemporal data branch (multi-head self-attention + position encoding), image branch (U-Net multi-scale feature extraction) and text branch (BERT semantic embedding), and dynamically calculates the inter-modal attention weights through a cross-modal attention gating mechanism to achieve precise alignment and adaptive fusion of heterogeneous data features; the conditional generation encoder constructs a deep layer by cascading residual blocks (including spatiotemporal convolution, instance normalization and LeakyReLU activation) Feature expression, while introducing the reference area of ​​traditional methods to form a knowledge transfer channel, so that the generation process has both the expressive power of deep learning and the stability of traditional methods; the adversarial training head adopts multi-scale discriminator and spectral normalization technology to enhance the robustness of the model while improving the generation quality, and finally forms a three-stage collaborative mechanism of "multimodal fusion encoding-conditional generation enhancement-adversarial optimization stabilization", which can not only capture the subtle features of complex data distribution, but also suppress noise interference through the reference area of ​​traditional methods, significantly improving the accuracy and reliability of the interpolation results, and providing core technical support for the intelligent processing of high-dimensional heterogeneous data.

[0095] As a preference, when automatically adjusting the weights of the results of deep learning and traditional methods based on data characteristics, the rules used include:

[0096] A21: For high-noise and washed-out data, traditional interpolation algorithms are preferred;

[0097] A22: For dense data and complex distributed data, focus on deep learning;

[0098] A23: Automatically switches the dominant algorithm based on a preset threshold.

[0099] As described above, the present invention realizes intelligent optimization of interpolation strategies through data characteristic perception: for high noise and sparse data scenarios, the system automatically prefers traditional interpolation algorithms (such as RBF), using its mathematical stability to suppress noise interference and ensure the smoothness of the basic surface; in the face of dense data and complex distribution scenarios, the system dynamically improves the deep learning weights, gives full play to the powerful fitting ability of the generative adversarial network for nonlinear relationships, and accurately captures the inherent laws of the data; by pre-setting threshold parameters such as noise level and data density, the algorithm dominance is automatically switched, forming an adaptive strategy of "traditional priority in noise-sensitive areas, deep dominance in complex areas", which significantly improves the interpolation accuracy while ensuring computational efficiency, effectively solves the problem of insufficient adaptability of traditional fixed weight methods in changing scenarios, and provides dynamic optimization technical guarantee for multimodal data fusion.

[0100] Preferably, the uncertainty quantification module generates a risk warning confidence interval based on the credibility of the Bayesian neural network and Monte Carlo sampling quantization interpolation results, specifically including:

[0101] S31: Data input and preprocessing, aligning the interpolation results with the original data coordinate system, marking missing areas and estimating noise distribution;

[0102] S32: Bayesian neural network inference, obtaining multiple prediction results through Monte Carlo sampling, separating the sources of model and data uncertainty;

[0103] S33: Confidence interval generation, calculation of predicted mean and total variance, generation of 95% confidence interval and risk heat map;

[0104] S34: Risk warning and feedback, triggering threshold alarms and pushing manual review, and dynamically adjusting interpolation strategies for high-risk areas;

[0105] S35: Module collaboration and output, linked interpolation and interpretable module optimization results, output of structured reports and real-time warning signals.

[0106] As described above, the present invention achieves the quantification of the credibility of interpolation results and risk warning through the Bayesian deep learning framework: in the data preprocessing stage, a high-quality input foundation is constructed through coordinate system alignment and noise distribution estimation; the Bayesian neural network combined with Monte Carlo sampling technology not only obtains multiple sets of prediction results, but also innovatively separates model uncertainty (weight distribution differences) and data uncertainty (noise influence), providing refined decomposition for subsequent analysis; the confidence interval generation link constructs a 95% confidence interval and a heat map through mean and variance calculation, intuitively presenting the spatial distribution of prediction reliability; the risk warning system sets a dynamic threshold trigger mechanism, automatically pushes manual review to high-risk areas and adjusts the interpolation strategy, forming a "quantification-warning-feedback" closed-loop optimization; finally, by collaborating with the interpolation and interpretable modules, structured reports and real-time warning signals are output, significantly improving the system's reliability and risk management capabilities in complex scenarios, and providing quantifiable decision support guarantees for high-risk fields such as medical diagnosis and financial risk control.

[0107] Preferably, when obtaining multiple prediction results through Monte Carlo sampling and separating the sources of model and data uncertainty, the following are specifically included:

[0108] S41: Monte Carlo sampling, sampling the network weights T times, each sampling generates a set of weight instances;

[0109] S42: Multiple forward propagations, for each weight instance, input interpolation area data to obtain T groups of prediction results;

[0110] S43: Uncertainty decomposition, including model uncertainty and data uncertainty. Model uncertainty is obtained by calculating the variance of the prediction results, and data uncertainty is obtained by calculating the noise distribution parameters. The calculation principle formula of model uncertainty is:

[0111]

[0112] Among them, Var model is the model uncertainty, T is the number of samplings, y (t) is the prediction result of group t, is the average value of the prediction results of group T.

[0113] As described above, the present invention achieves accurate quantification of the credibility of interpolation results through Monte Carlo sampling and uncertainty decomposition mechanism: by generating diversified prediction results through T-times network weight sampling, it not only captures the uncertainty caused by the randomness of model parameters (model uncertainty), but also separates the uncertainty caused by input data noise (data uncertainty). The model uncertainty is calculated using the prediction variance, which effectively reflects the degree of influence of the network weight distribution on the result; this technology expands the traditional single uncertainty estimation into a two-dimensional decomposition, enabling the system to accurately identify different risk sources of "model itself instability" and "poor data quality", providing a differentiated processing basis for subsequent risk warnings. In medical diagnosis, it can distinguish between different scenarios of "inaccurate model prediction of rare diseases" and "sensor measurement noise interference", and in financial forecasting, it can identify different risk levels of "market model failure" and "sudden event impact", significantly improving the technical depth and application value of uncertainty quantification.

[0114] As a preferred option, the explainability optimization module combines gradient significance analysis and causal reasoning technology to provide transparent logical traceability and counterfactual explanations of interpolation decisions, specifically including:

[0115] S51: Input preparation, receiving interpolation results and original data;

[0116] S52: Gradient significance analysis, by calculating the gradient of the interpolation result to the input data, generating a heat map to show the key impact areas;

[0117] S53: Causal inference modeling, building structural causal models, and identifying causal chains of missing data and interpolation bias;

[0118] S54: Generate counterfactual explanations, simulate variable interventions, and output comparative reports to reveal changes in interpolation results;

[0119] S55: Rule extraction and feedback, converting deep learning logic into readable rules and pushing them to the interpolation module to optimize the generation strategy.

[0120] As described above, the present invention achieves transparency and logical traceability in the interpolation decision-making process through the deep integration of gradient significance analysis and causal reasoning technology. Gradient significance analysis calculates the gradient change of the interpolation result with respect to the input data, accurately locates the key areas that affect the interpolation result, and visualizes it in the form of a heat map, helping users intuitively understand the degree of influence of data features. Causal reasoning modeling constructs a structural causal model to systematically identify the causal chain between data missing and interpolation deviation, overcoming the limitations of traditional correlation analysis. The counterfactual explanation generation module simulates variable interventions, quantifies the impact of different factors on the interpolation result, and outputs a comparative report, revealing the underlying logic of "how the result changes if certain conditions are changed." The rule extraction and feedback mechanism transforms the complex decision-making process of deep neural networks into readable rules and reversely optimizes the interpolation algorithm parameters, forming a closed-loop improvement system of "analysis-interpretation-optimization". In medical diagnosis, it can explain "why the prediction confidence of a certain area is low" and in financial forecasting, it can explain "the specific impact path of policy changes on the volatility surface", significantly improving the credibility and compliance of the system and providing traceable technical support for high-risk decision-making scenarios.

[0121] Preferably, the multi-source heterogeneous data processing module specifically includes the following steps when realizing the spatiotemporal alignment of multiple cross-modal data and feature fusion driven by knowledge graphs:

[0122] S61: Input dispatch and preprocessing, automatically identifying input types and performing data cleaning;

[0123] S63: Knowledge graph driven fusion, extracting entities and reasoning about implicit relationships, dynamically weighting modality importance;

[0124] S64: Unify feature representation, concatenate symbolic knowledge and neural network features, and output a 512-dimensional fusion vector.

[0125] As described above, the present invention achieves efficient integration and semantic-level understanding of cross-modal data through a fusion architecture enhanced by a knowledge graph: the input dispatch and preprocessing stages automatically identify data types and complete cleaning, laying the foundation for subsequent processing; the knowledge graph-driven fusion module constructs a cross-modal semantic association network through entity extraction and relationship reasoning, dynamically adjusts the weight coefficients of different modalities, and effectively solves the problem of data heterogeneity; the unified feature representation layer deeply integrates symbolic knowledge (such as equipment numbers, medical terms) with deep learning features to generate a 512-dimensional compact vector representation, which not only retains explicit semantic information but also integrates implicit pattern features, realizes the association reasoning of multi-source sensor data and equipment knowledge base in industrial equipment fault diagnosis, and completes the collaborative analysis of satellite images, traffic flow data and weather information in intelligent transportation systems, significantly improving the system's semantic understanding ability and cross-modal association mining ability for complex scenes, and providing a standardized processing paradigm for multi-domain data fusion.

[0126] As a preferred option, the hybrid computing acceleration module implements parallel computing acceleration of large-scale interpolation tasks through GPU-CPU heterogeneous architecture optimization and intelligent video memory scheduling, specifically including:

[0127] S71: Data segmentation and transmission optimization, dynamically dividing data into blocks adapted to GPU memory, and reducing latency through page-locked memory and asynchronous transmission;

[0128] S72: Distributed task scheduling and load balancing, using MPI to split global tasks, dynamically assigning subtasks based on node computing power, monitoring load in real time, and migrating overloaded tasks;

[0129] S73: GPU-CPU heterogeneous computing collaboration, GPU executes CUDA optimized kernel functions and kernel fusion, CPU schedules I / O and preprocessing;

[0130] S74: Intelligent memory scheduling and reuse, pre-allocated memory pool and cross-GPU sharing mechanism, combined with TensorRT computational graph optimization;

[0131] S75: Edge adaptation and deployment, deploying lightweight models + Triton dynamic batch processing;

[0132] S76: Merge and output the results, aggregate the distributed results through MPI, check the consistency of sub-block boundaries, and compress the output using Zstandard.

[0133] As described above, the present invention realizes efficient parallel processing of large-scale interpolation tasks through heterogeneous architecture and intelligent scheduling technology: data block and transmission optimization adopt dynamic block strategy and locked page memory technology, which significantly reduces CPU-GPU data transmission delay and improves video memory utilization; distributed task scheduling combines MPI to achieve global task balanced distribution and dynamic load balancing, ensuring efficient utilization of multi-node computing resources; GPU-CPU heterogeneous computing collaboration mechanism maximizes GPU parallel computing capability through customized CUDA kernel function and kernel fusion technology, while using CPU to process I / O and preprocessing tasks to complement each other; video memory intelligent scheduling adopts pre-allocated pool and The cross-GPU sharing mechanism, combined with TensorRT computational graph optimization technology, effectively reduces video memory usage and improves data reuse rate; the edge adaptation module achieves low-power real-time inference through lightweight models and dynamic batch processing technology; the result merging link adopts MPI aggregation and consistency verification mechanism to ensure the accuracy of distributed computing results, and reduces storage and transmission overhead through Zstandard compression algorithm. It supports real-time processing of millions of sensor data in industrial Internet of Things scenarios and realizes rapid reconstruction of TB-level high-dimensional data in medical image analysis, significantly improving system computing efficiency and resource utilization, and providing high-performance computing solutions for large-scale data interpolation.

[0134] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge of those skilled in the art without departing from the spirit of the present invention.

Claims

1. A data interpolation and fitting analysis system; characterized in that: include: Data processing module, used to normalize input data, remove outliers, mark missing values ​​and perform block processing; A deep generative interpolation module, which implements adaptive interpolation through spatiotemporal Transformers and generative adversarial networks, and dynamically integrates traditional numerical methods; Uncertainty quantification module, used to generate risk warning confidence intervals based on the credibility of Bayesian neural network and Monte Carlo sampling quantification interpolation results; The explainability optimization module combines gradient significance analysis with causal reasoning techniques to provide transparent logical traceability and counterfactual explanations of interpolation decisions. Multi-source heterogeneous data processing module, used to achieve spatiotemporal alignment of multiple cross-modal data and feature fusion driven by knowledge graphs; The hybrid computing acceleration module is used to achieve parallel computing acceleration of large-scale interpolation tasks through GPU-CPU heterogeneous architecture optimization and intelligent scheduling of video memory.

2. A data interpolation and fitting analysis system according to claim 1, characterized in that: The data processing module normalizes the input data, removes outliers, marks missing values, and performs block processing, specifically including: S11: Data input, receiving raw data in various formats; S12: Data cleaning: outlier detection and elimination based on the 3σ criterion, and missing values ​​are marked; S13: Data preprocessing: normalize the cleaned data, scale the data to the range of [-1, 1], and divide the data into blocks according to the set size, where the size of each block after division is less than 1GB.

3. A data interpolation and fitting analysis system according to claim 2, characterized in that: The deep generative interpolation module implements adaptive interpolation through the spatiotemporal Transformer and the generative adversarial network, and dynamically integrates traditional numerical methods. Specifically, it includes: S21: Feature extraction: extract features from data using the spatiotemporal Transformer model and semantic model, and use a dynamic attention mechanism to perform weighted fusion of features from different modalities to generate fused features; S22: Generative interpolation core calculation, receiving fused features, generating candidate interpolation points through a deep learning-based generator, capturing complex data distribution, and running traditional numerical methods in parallel, and finally automatically adjusting the weights of the deep learning and traditional methods based on the data characteristics; S23: Adaptive Optimization and Feedback: This integrates adversarial loss, reconstruction error, and smoothness constraints through a multi-objective loss function, automatically adjusts the core parameters of traditional methods using Bayesian optimization, and optimizes the generator network weights through gradient backpropagation. S24: Output post-processing and verification: Based on the output of the discriminator in the generative adversarial network, the credibility of each interpolation point is quantified, and low-confidence areas are marked for manual review. Anisotropic diffusion filtering technology is applied to eliminate local mutations. Finally, a 3D spatiotemporal interpolation surface and uncertainty heat map are generated, and compared with domain knowledge to verify the rationality of the results.

4. A data interpolation and fitting analysis system according to claim 3, characterized in that: When receiving fused features and generating candidate interpolation points through a deep learning-based generator to capture complex data distribution, the specific architecture of the deep learning-based generator is as follows: A11: Multimodal encoder, including spatiotemporal data branch, image branch, and text branch. The spatiotemporal data branch includes a multi-head self-attention layer and position encoding. The image branch uses a U-Net encoder to extract multi-scale features of image data. The text branch uses the BERT fine-tuned model to generate semantic embedding vectors. The multimodal encoder uses a cross-modal attention gating mechanism to dynamically calculate inter-modal attention weights for adaptive feature fusion. A12: Conditional generative encoder, consisting of cascaded residual blocks and a traditional method reference area. Each residual block in the cascaded residual blocks contains a spatiotemporal convolution layer, instance-based normalization, and a LeakyReLU activation function. The traditional method reference area is used to calculate the results of the traditional interpolation algorithm. A13: Adversarial training head, used to improve generation quality through adversarial training, using a multi-scale discriminator and spectral normalization constraints to stabilize the adversarial training process.

5. A data interpolation and fitting analysis system according to claim 4, characterized in that: When automatically adjusting the weights of deep learning and traditional methods based on data characteristics, the rules used include: A21: For high-noise and washed-out data, traditional interpolation algorithms are preferred; A22: For dense data and complex distributed data, focus on deep learning; A23: Automatically switches the dominant algorithm based on a preset threshold.

6. A data interpolation and fitting analysis system according to claim 5, characterized in that: The uncertainty quantification module generates risk warning confidence intervals based on the credibility of the Bayesian neural network and Monte Carlo sampling quantization interpolation results, specifically including: S31: Data input and preprocessing, aligning the interpolation results with the original data coordinate system, marking missing areas and estimating noise distribution; S32: Bayesian neural network inference, obtaining multiple prediction results through Monte Carlo sampling, separating the sources of model and data uncertainty; S33: Confidence interval generation, calculation of predicted mean and total variance, generation of 95% confidence interval and risk heat map; S34: Risk warning and feedback, triggering threshold alarms and pushing manual review, and dynamically adjusting interpolation strategies for high-risk areas; S35: Module collaboration and output, linked interpolation and interpretable module optimization results, output of structured reports and real-time warning signals.

7. A data interpolation and fitting analysis system according to claim 6, characterized in that: When obtaining multiple prediction results through Monte Carlo sampling, separating the sources of model and data uncertainty, specifically including: S41: Monte Carlo sampling, sampling the network weights T times, each sampling generates a set of weight instances; S42: Multiple forward propagations, for each weight instance, input interpolation area data to obtain T groups of prediction results; S43: Uncertainty decomposition, including model uncertainty and data uncertainty. Model uncertainty is obtained by calculating the variance of the prediction results, and data uncertainty is obtained by calculating the noise distribution parameters.

8. A data interpolation and fitting analysis system according to claim 7, characterized in that: The explainability optimization module combines gradient significance analysis with causal reasoning techniques to provide transparent logical traceability and counterfactual explanations of interpolation decisions. Specifically, it includes: S51: Input preparation, receiving interpolation results and original data; S52: Gradient significance analysis, by calculating the gradient of the interpolation result to the input data, generating a heat map to show the key impact areas; S53: Causal inference modeling, building structural causal models, and identifying causal chains of missing data and interpolation bias; S54: Generate counterfactual explanations, simulate variable interventions, and output comparative reports to reveal changes in interpolation results; S55: Rule extraction and feedback, converting deep learning logic into readable rules and pushing them to the interpolation module to optimize the generation strategy.

9. A data interpolation and fitting analysis system according to claim 8, characterized in that: The multi-source heterogeneous data processing module implements the spatiotemporal alignment of multiple cross-modal data and the feature fusion driven by the knowledge graph, specifically including: S61: Input dispatch and preprocessing, automatically identifying input types and performing data cleaning; S63: Knowledge graph driven fusion, extracting entities and reasoning about implicit relationships, dynamically weighting modality importance; S64: Unify feature representation, concatenate symbolic knowledge and neural network features, and output a 512-dimensional fusion vector.

10. The data interpolation and fitting analysis system according to claim 9, characterized in that: The hybrid computing acceleration module achieves parallel computing acceleration for large-scale interpolation tasks through GPU-CPU heterogeneous architecture optimization and intelligent video memory scheduling. Specifically, it includes: S71: Data segmentation and transmission optimization, dynamically dividing data into blocks adapted to GPU memory, and reducing latency through page-locked memory and asynchronous transmission; S72: Distributed task scheduling and load balancing, using MPI to split global tasks, dynamically assigning subtasks based on node computing power, monitoring load in real time, and migrating overloaded tasks; S73: GPU-CPU heterogeneous computing collaboration, GPU executes CUDA optimized kernel functions and kernel fusion, CPU schedules I / O and preprocessing; S74: Intelligent memory scheduling and reuse, pre-allocated memory pool and cross-GPU sharing mechanism, combined with TensorRT computational graph optimization; S75: Edge adaptation and deployment, deploying lightweight models + Triton dynamic batch processing; S76: Merge and output the results, aggregate the distributed results through MPI, check the consistency of sub-block boundaries, and compress the output using Zstandard.

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