Chain master industry chain collaborative platform self-adaptive frequency domain compression demand prediction method and system

Abstract

The present application belongs to the field of industrial chain coordination platform and time series prediction technology, and discloses a chain master industrial chain coordination platform adaptive frequency domain compression demand prediction method and system. Multi-source business time series data from the chain master enterprise industrial chain coordination platform is obtained; the multi-source business time series data is normalized and converted to the frequency domain through real fast Fourier transform; a compressed frequency domain representation is generated through a learnable complex frequency domain compression matrix; complex prediction is performed in the compressed frequency domain space to obtain the dominant frequency spectrum pattern of future demand; a residual compensation channel is constructed to compensate for the weakened local business fluctuations in the compression process; the main prediction spectrum and the residual compensation spectrum are fused, and the final demand prediction result is obtained through inverse real fast Fourier transform and inverse normalization. The present application reduces the model parameter quantity, inference delay and memory occupation while maintaining prediction accuracy, and is suitable as a lightweight demand prediction algorithm service in the chain master enterprise industrial chain coordination platform.

Description

Technical Field

[0001] This invention belongs to the field of industrial chain collaboration platform and time series prediction technology, and particularly relates to the adaptive frequency domain compression demand prediction method and system for the industrial chain collaboration platform of the chain leader. Background Technology

[0002] In the supply chain collaboration platform of the leading enterprise, business processes such as order coordination, inventory early warning, replenishment planning, production scheduling, logistics dispatching, and supplier fulfillment management typically rely on accurate forecasts of future demand changes. The data sources involved in these forecasting tasks are numerous, including order, sales, inventory, logistics status, production status, and supplier fulfillment data generated by enterprise resource planning systems, supply chain management systems, warehouse management systems, transportation management systems, and manufacturing execution systems. This type of data is typically characterized by multiple sources, multiple variables, multiple time granularities, and frequent business fluctuations. The forecasting services in the supply chain collaboration platform of the leading enterprise also need to be frequently invoked by multiple business processes; therefore, not only are high-accuracy forecast results required, but also models with low parameter count, low memory usage, and low inference latency.

[0003] Among existing long-term time-series forecasting methods, Transformer-based models have been widely applied to long-term time-series forecasting tasks. For example, some methods reduce the sequence length processed by the attention mechanism through patching, some apply the attention mechanism to the variable dimension to model the correlation between multiple variables, and some introduce trend decomposition, Fourier transform, or wavelet transform into the Transformer structure to enhance the ability to model long-period patterns. These methods can capture trends, cycles, and multivariate dependencies over long time spans to a certain extent, but they usually still contain attention structures, embedding layers, or multi-layer nonlinear networks, resulting in relatively high model parameter count, memory usage, and inference overhead. In chain-leader supply chain collaboration platforms, forecasting services often need to be called frequently by multiple business modules such as orders, inventory, replenishment, production scheduling, and logistics. The aforementioned computational and storage overhead limits the lightweight deployment and real-time invocation of models within the platform.

[0004] To reduce model complexity, existing technologies have proposed long-term time-series forecasting models that combine trend-seasonal decomposition with linear layers. These models decompose the input sequence into trend and seasonal terms, and then use linear mappings for prediction, enabling long-term time-series forecasting with lower computational overhead. However, supply chain business demand sequences are typically influenced by factors such as cyclical sales, promotional activities, abnormal orders, inventory adjustments, logistics delays, and changes in production plans, exhibiting complex cyclical, phase-varying, and localized abrupt changes. Simply relying on linear mappings or fixed decomposition structures is insufficient to fully characterize these complex business fluctuations, thus limiting their expressive power in complex, multi-source business demand forecasting scenarios.

[0005] Frequency-domain time-series prediction methods utilize tools such as Fourier transforms to convert time-domain sequences into frequency-domain representations, thereby modeling periodicity and global dependencies in the spectral space. Existing technologies similar to this approach include full-frequency-domain complex prediction methods and fixed-low-pass frequency-domain prediction methods. Full-frequency-domain complex prediction methods typically convert the input sequence into a complete spectrum and use a complex multilayer perceptron or similar network for prediction on that spectrum. While these methods leverage the global perspective of the frequency-domain representation, they model all frequency components, failing to explicitly utilize the characteristic that the spectral energy of most traffic time-series events is concentrated in a few dominant frequency components. Since weak-information frequency components and noise-dominant frequency components are also included in the prediction network, redundant computations are easily generated, potentially increasing the risk of the model fitting invalid spectral components.

[0006] Fixed low-pass frequency domain forecasting methods are typically based on the assumption that low-frequency components carry the main trend and cyclical information. They retain only frequency components within a preset cutoff frequency and then perform forecasting or interpolation on the retained spectrum. While this type of method can reduce the number of model parameters and computational load, its cutoff frequency is usually manually set or determined by fixed rules, making it difficult to adaptively adjust to different business objects, data sources, and spectral structures at different time granularities. In supply chain collaboration scenarios, promotional activities, abnormal orders, temporary replenishment, logistical disruptions, or production plan adjustments may cause local business fluctuations, which are not necessarily entirely within the preset low-frequency range. If only a fixed low-pass strategy is adopted, frequency components useful for predicting future demand may be discarded, resulting in forecasts that do not fully reflect local business changes.

[0007] Furthermore, even when existing frequency domain methods utilize the concentration of spectral energy to reduce modeling complexity, they typically lack compensation mechanisms for spectral information lost during compression or truncation. For multi-source business demand sequences within a blockchain-based supply chain collaboration platform, while the dominant cycle and long-term trends are important, local business fluctuations, abnormal order disturbances, and changes in supply chain fulfillment can also affect short-term demand forecasting results. If weakened or lost local spectral information is not compensated during frequency domain compression, forecasting accuracy may be sacrificed while reducing computational overhead.

[0008] Therefore, existing technologies have not yet provided a lightweight method suitable for predicting multi-source business demands in a blockchain-based supply chain collaboration platform. This method should be able to utilize the compressibility of the spectrum while adaptively learning compressed frequency domain representations based on the spectral structure of different business data, and compensate for the weakened local business fluctuations during compression. There is an urgent need for an adaptive frequency domain compression demand prediction method that can reduce the number of model parameters, inference latency, and memory usage while maintaining the ability to model dominant demand patterns and local business fluctuations, thereby meeting the prediction service requirements of high-frequency calls to multiple business processes in a blockchain-based supply chain collaboration platform.

[0009] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: (1) Long-term forecasting methods based on Transformers have high computational and storage overhead, making it difficult to meet the lightweight deployment requirements of forecasting services in the chain leader's supply chain collaboration platform due to their high frequency of calls. Existing methods such as PatchTST, iTransformer, and FEDformer can model trends, cycles, and multivariate dependencies over long time spans to a certain extent, but these methods usually still include attention mechanisms, embedding layers, or multi-layer nonlinear network structures. When attention mechanisms model correlations in the sequence or variable dimensions, they can lead to high computational load, memory usage, and inference latency as the historical window length, number of variables, or number of model layers increase. In the chain leader's supply chain collaboration platform, multiple business processes such as order collaboration, inventory warning, replenishment planning, production scheduling, and logistics scheduling may call demand forecasting services. If the above complex models are used, the deployment cost of the platform-side algorithm services will be high, making it difficult to meet the requirements of frequent calls from multiple business processes, low-latency response, and lightweight operation.

[0010] (2) While linear or simple decomposition-based forecasting methods are computationally efficient, they are insufficient in representing the complex fluctuations of demand sequences from multiple sources in the industrial chain. Existing methods such as DLinear use trend-seasonal decomposition combined with linear mapping for forecasting, which can reduce model complexity, but they mainly rely on linear transformations to characterize the correspondence between historical and future sequences. The demand sequences in the chain leader industrial chain collaboration platform are usually affected by factors such as cyclical sales, replenishment rhythms, promotional activities, abnormal orders, inventory adjustments, logistics delays, and changes in production plans, exhibiting characteristics such as complex cycles, phase changes, local mutations, and multi-source business disturbances. Simply relying on linear mapping or fixed decomposition structures makes it difficult to fully characterize the above-mentioned complex business patterns, especially to effectively model short-term local business fluctuations and the frequency domain variation characteristics between different business variables.

[0011] (3) Although existing frequency domain time series prediction methods utilize the global modeling capabilities of frequency domain representation, their utilization of spectral compressibility remains insufficient. Frequency domain prediction methods such as FreTS typically use complex MLP or similar structures for prediction on a complete N-dimensional spectrum after converting time series data to the frequency domain. This approach can utilize the amplitude and phase information in the frequency domain representation, but it models all frequency components without explicitly constructing a low-dimensional frequency domain subspace, nor does it adaptively compress the spectral representation according to the spectral structure of different data. Since the main energy in actual business time series is often concentrated in a small number of dominant frequency components, complete spectrum modeling will cause weak information frequency components or noise-dominant frequency components to participate in the prediction, resulting in redundant calculations and potentially increasing the risk of the model fitting invalid spectral components.

[0012] (4) Fixed low-pass frequency domain prediction methods lack adaptability to the spectral structure of different business scenarios. Methods such as FITS are usually based on the assumption that low-frequency components carry the main trend and periodic information, and use fixed low-pass filtering or preset cutoff frequencies to retain some low-frequency components in order to reduce model size and computational overhead. However, different business objects and different data sources in the chain master industry chain collaboration platform have differentiated spectral structures. For example, the periodicity, fluctuation intensity and abnormal disturbance characteristics of sequences such as store sales, material inventory, supplier fulfillment, logistics status and production status are not the same; local business changes such as promotional activities, temporary replenishment, abnormal orders, transportation delays or production plan adjustments may also correspond to effective spectral components in non-fixed low-frequency ranges. If the cutoff frequency is determined manually or by fixed rules, it is easy to discard frequency components that are useful for predicting future demand, resulting in insufficient adaptability of the model to different business scenarios.

[0013] (5) Existing frequency compression or frequency selection methods typically lack residual compensation mechanisms for compression losses, making it difficult to balance dominant demand patterns and local business fluctuations. Frequency compression can reduce modeling dimensionality, but compression, truncation, or filtering inevitably weakens some frequency information. For supply chain demand forecasting, dominant spectrum patterns usually reflect long-term trends, cyclical sales, and regular replenishment rhythms, while the local spectrum information weakened by compression may include short-term business fluctuations such as promotional disturbances, abnormal orders, inventory adjustments, logistics anomalies, or production changes. If existing methods only retain dominant frequency components and directly predict them, the lack of modeling and compensation for compression residual information may result in a loss of predictive ability for local business fluctuations while reducing computational load.

[0014] (6) Existing technologies have not yet formed a complete demand forecasting process for the main chain industry chain collaboration platform, consisting of "adaptive frequency domain compression - compressed domain prediction - residual compensation reconstruction". Existing Transformer-type methods focus on long-range dependency modeling, linear models focus on low-complexity prediction, FreTS and other methods focus on complete frequency domain complex prediction, and FITS and other methods focus on fixed low-pass frequency domain processing. However, none of the above technologies have constructed an end-to-end learnable complex frequency domain compression mapping for the multi-source business time-series data in the main chain industry chain collaboration platform, projecting the high-dimensional spectrum to a low-dimensional frequency domain subspace, predicting the dominant spectrum pattern of future demand in the compressed space, and further utilizing the frequency domain residual compensation channel to recover the local business fluctuations weakened during the compression process. Therefore, existing technologies are difficult to simultaneously meet the comprehensive requirements of multi-source business adaptation, prediction accuracy maintenance, lightweight model deployment, and high-frequency platform calls. Summary of the Invention

[0015] To overcome the problems existing in related technologies, the present invention discloses an adaptive frequency domain compression demand prediction method and system for a chain leader industry chain collaboration platform, the technical solution of which is as follows: This invention is implemented as follows: an adaptive frequency domain compression demand prediction method for a chain leader industry chain collaboration platform, comprising the following steps: S1. Obtain multi-source business time-series data from the supply chain collaboration platform of the chain leader enterprise; S2. Normalize the multi-source service time-series data and perform frequency domain transformation along the time dimension to obtain the corresponding frequency domain representation. ; S3. Learnable complex frequency domain compression matrix trained end-to-end For the frequency domain representation Different frequency components in the frequency domain are adaptively combined, and the frequency domain representation is projected onto a low-dimensional frequency domain subspace to obtain a compressed frequency domain representation. ; S4. In the low-dimensional frequency domain subspace, the complex prediction module is used to compress the frequency domain representation. To make predictions, we jointly model the dominant spectral patterns related to amplitude and phase in future demand sequences, and obtain compressed domain prediction results. ; S5. Based on the frequency domain representation With the compressed frequency domain representation The residual information is constructed by comparing the differences between the approximate reconstruction results. The residual compensation channel is used to compensate for the weakened local service fluctuations during the compression process, resulting in the residual compensation spectrum. ; S6. The main prediction spectrum corresponding to the compressed domain prediction result is fused with the residual compensation spectrum, and then subjected to inverse real fast Fourier transform. After inverse normalization, the final demand forecast result is output. .

[0016] In step S1, the multi-source business time series data includes at least two of the following: order data, sales data, inventory data, logistics data, and production status data obtained from ERP, SCM, WMS, TMS, and MES systems; the multi-source business time series data is a multivariate time series, and each variable corresponds to a business indicator under the dimensions of store, material, region, warehouse, or supplier.

[0017] In step S2, the multi-source service time-series data is normalized and frequency domain transformed along the time dimension. The normalization and frequency domain transformation include: The input multi-source business time-series data is represented as follows: ; In the formula, For the real number field, For batch size, For the length of the history window, This refers to the number of business variables or business channels. enter Normalized by reversible instances After performing instance-by-instance normalization, the normalized tensor is replaced with: ; In the formula, This is a normalized business sequence with time as the last dimension. Perform real fast Fourier transform along the time dimension The frequency domain representation is obtained as follows: ; In the formula, This is the frequency domain representation of the normalized service sequence. The length of the history window through The number of frequency points obtained afterwards For complex numbers; in, .

[0018] In step S3, the complex frequency domain compression matrix can be learned. include: set up For compression ratio, To compress the dimensionality, the number of historical frequency points is used. and compression ratio Determined; Parameterized learnable complex frequency domain compression matrix: ; In the formula, For use in Frequency domain representation compressed to Complex matrices in the low-dimensional frequency domain subspace. Let be the real part of the complex matrix. Let be the imaginary part of the complex matrix. The imaginary unit, Orthogonal initialization was used, and the combination relationship between each frequency component was adaptively learned through end-to-end supervised training. Frequency domain compression is achieved through complex matrix multiplication, yielding a compressed frequency domain representation: ; In the formula, To represent the frequency domain Compressed frequency domain representation after projection onto a low-dimensional frequency domain subspace; Will The real and imaginary parts are respectively denoted as and ,Will The real and imaginary parts are respectively denoted as and ,but and respectively by Calculated according to the rules of complex matrix multiplication; ; ; ; Orthogonal initialization is used to improve numerical stability in the early stages of training; this orthogonal initialization does not indicate Maintain strict orthogonality throughout the entire training process.

[0019] Furthermore, the compression ratio The value range is from 0.1 to 0.3.

[0020] In step S4, the complex prediction module is a complex MLP, each... The block consists of two layers of complex linear transformations; This indicates the dimension of the compressed frequency domain representation. Representing complex numbers The hidden dimension, the first layer of complex linear transformation Compressed frequency domain representation from Dimension mapping to Dimension, to obtain the intermediate complex number representation ; and They represent The real and imaginary parts; then the real and imaginary parts; and Apply nonlinear activation respectively With random inactivation And recombine them to obtain the intermediate representation of complex numbers. Second-level complex linear transformation Will from Dimension Mapping Back Dimension, to obtain the compression domain prediction result , Let be a complex tensor with the following dimensions: , representing the compressed domain spectral representation predicted in the low-dimensional frequency domain subspace; .

[0021] In step S5, compensating for the weakened local service fluctuations during the compression process through the residual compensation channel includes: Using the conjugate transpose of the learnable complex frequency domain compression matrix For the compressed frequency domain representation Perform approximate reconstruction And calculate the frequency domain representation. Residuals between the approximate reconstruction results It is used to characterize the residual information not retained in the main compression branch and to compensate for it during the reconstruction stage; in, For learnable complex frequency domain compression matrix The conjugate transpose of . This represents the frequency domain representation of the normalized traffic sequence obtained through the real-number fast Fourier transform. This represents a compressed frequency domain representation. This represents the frequency domain residual information not retained by the main compression branch. Indicates batch size. This indicates the number of business variables or business channels. This indicates the number of frequency points corresponding to the historical window. Indicates the compressed frequency domain dimension; Main projection With residual compensation projection This represents a complex-valued mapping implemented through a real-valued linear layer; it concatenates the real and imaginary parts of a complex tensor into a real vector, performs dimensionality transformation through a linear layer, and then splits the output into real and imaginary parts and recombines them into a complex form; it defines... , Represents the real part after splitting. Represents the imaginary part after splitting. Represents the imaginary unit; Predicted output Located in the compressed frequency domain space, dimensional matching is achieved through independent linear projection; its historical input frequency points are limited. Number of target frequency points corresponding to the prediction window Inconsistencies are resolved by matching dimensions using independent linear projections. The main channel is used to restore the low-dimensional compressed frequency domain prediction results to the target prediction spectral space: ; In the formula, Main predicted spectrum, and They represent The real and imaginary parts, This is a real vector formed by concatenating the real and imaginary parts. For from 2 Via A real-valued linear mapping of dimension, To predict the length, This indicates the number of target frequency points corresponding to the predicted length. The residual compensation channel is used to compensate for local business fluctuations that are not fully preserved in the main compression branch: ; In the formula, For residual compensation spectrum, Residuals The real and imaginary parts, To form a real vector by concatenating the real and imaginary parts of the residuals, From Via A real-valued linear mapping of dimension, This is the low-rank bottleneck dimension in the residual compensation channel. From Via A real-valued linear mapping of dimension.

[0022] In the residual compensation channel, complex residuals The real and imaginary parts are concatenated to form a dimension of The real vector, where N represents the number of frequency points corresponding to the historical window, and the coefficient 2 indicates that the complex spectrum contains both a real and an imaginary part; used to transfer the residual from In the real-valued linear layer that maps dimensionality to intermediate dimensions It is a low-rank bottleneck dimension, and Less than This is used to control the model size while preserving residual compensation capability; the output of the residual compensation channel corresponds to the target prediction spectrum, and the dimension of the concatenated real and imaginary parts is... ,in, This indicates the number of target frequency points corresponding to the predicted length.

[0023] In step S6, fusing the master prediction spectrum corresponding to the compressed domain prediction result with the residual compensation spectrum includes: The main prediction spectrum corresponding to the compressed domain prediction result is weighted and fused with the residual compensation spectrum to obtain the fused prediction spectrum. , This represents the main prediction spectrum obtained by mapping the compressed domain prediction results to the main channel. This represents the residual compensation spectrum output by the residual compensation channel, where α is the fusion coefficient used to control the impact of the residual compensation term on the final predicted spectrum. ; Using the inverse real fast Fourier transform The fused prediction spectrum Reconstructed to a length of The time-domain prediction sequence, where H represents the prediction length; then through The denormalization operation restores the original business volume dimensions, yielding the final prediction result. ,in, Indicates the future Multi-source business demand forecast results at each time step.

[0024] Another objective of this invention is to provide an adaptive frequency domain compression demand prediction system for a blockchain-based supply chain collaboration platform. This system is used to implement the aforementioned adaptive frequency domain compression demand prediction method for the blockchain-based supply chain collaboration platform. The system includes: The data acquisition module is used to acquire multi-source business time-series data from the supply chain collaboration platform of the chain leader enterprise; The frequency domain transformation module is used to normalize the multi-source service time-series data and perform frequency domain transformation along the time dimension to obtain the corresponding frequency domain representation. ; An adaptive frequency domain compression module is used to compress complex frequency domain matrices trained end-to-end. For the frequency domain representation Different frequency components in the frequency domain are adaptively combined, and the frequency domain representation is projected onto a low-dimensional frequency domain subspace to obtain a compressed frequency domain representation. ; The compressed domain prediction module is used to perform complex prediction on the compressed frequency domain representation in the low-dimensional frequency domain subspace. To make predictions, we jointly model the dominant spectral patterns related to amplitude and phase in future demand sequences, and obtain compressed domain prediction results. ; The residual compensation module is used to calculate the frequency domain representation. With the compressed frequency domain representation The residual information is constructed by comparing the differences between the approximate reconstruction results. The residual compensation channel is used to compensate for the weakened local service fluctuations during the compression process, resulting in the residual compensation spectrum. ; The fusion and reconstruction module is used to fuse the main prediction spectrum corresponding to the compressed domain prediction result with the residual compensation spectrum, and then perform an inverse real fast Fourier transform. After inverse normalization, the final demand forecast result is output. .

[0025] Combining all the above technical solutions, the beneficial effects of this invention are as follows: First, addressing the problem that existing long-time-series forecasting methods struggle to balance forecasting accuracy and deployment efficiency in demand forecasting scenarios within supply chain collaboration platforms, this invention achieves efficient demand forecasting in the low-dimensional frequency domain through a combined process of adaptive frequency domain compression, compressed domain complex prediction, and residual compensation reconstruction.

[0026] The business processes within a supply chain collaboration platform for leading enterprises, including order coordination, inventory alerts, replenishment planning, production scheduling, logistics dispatching, and supplier fulfillment management, all rely on accurate predictions of future demand changes. These prediction tasks typically involve multi-source time-series business data such as orders, sales volume, inventory, logistics status, production status, and supplier fulfillment, characterized by a large number of variables, long time spans, frequent business fluctuations, and high platform call frequency. While existing Transformer-based long-term time-series prediction models possess strong representational capabilities, their attention structures, embedding layers, and multi-layered nonlinear networks often result in high parameter counts, memory usage, and inference latency, making it difficult to meet the lightweight deployment requirements of high-frequency calls across multiple business processes in a supply chain collaboration platform. Linear or simple decomposition methods, while computationally less expensive, primarily rely on fixed decomposition and linear mapping, making it difficult to characterize complex cycles, replenishment rhythms, abnormal orders, inventory adjustments, and localized business fluctuations such as logistics disturbances.

[0027] This invention leverages the energy concentration and compressibility inherent in time-series business data in the frequency domain. It employs a real-number Fast Fourier Transform to convert the normalized business sequence into a frequency domain representation. Furthermore, it uses an end-to-end trained, learnable complex frequency domain compression matrix to project the high-dimensional spectrum onto a low-dimensional frequency domain subspace, resulting in a compressed frequency domain representation. Compared to full frequency domain modeling, this approach reduces redundant modeling of weak-information frequency components and noise-dominant frequency components. Compared to fixed low-pass filtering, this method can adaptively learn the combination relationships between different frequency components during supervised training, thereby better adapting to the spectral structures of different business objects, data sources, and time granularities.

[0028] Building upon the compressed frequency domain representation, this invention further employs a complex prediction module to perform predictions in a low-dimensional frequency domain subspace, jointly modeling the dominant spectral patterns related to amplitude and phase in future demand sequences. Since the real and imaginary parts of the spectral components jointly determine amplitude and phase, the complex prediction module is more suitable than simple real-valued mapping for describing frequency domain patterns such as periodic variations, replenishment rhythms, and demand fluctuations. Simultaneously, this invention constructs frequency domain residual information based on the difference between the approximate reconstruction results of the original and compressed frequency domain representations, and compensates for local business fluctuations weakened or not fully preserved by the main compression branch during the compression process through a residual compensation channel. Therefore, this invention can reduce the dimensionality of frequency domain modeling while preserving dominant demand patterns and compensating for local fluctuation information, avoiding a decrease in prediction accuracy due to simple compression or fixed truncation.

[0029] From a theoretical perspective, this invention uses Fourier transform, Parseval's theorem, optimal K-term approximation, and complex linear operations as the fundamental tools and theoretical explanations for frequency domain modeling. Parseval's theorem states that there is an equivalence between the energy of a time-domain signal and the energy of its frequency-domain coefficients; when spectral energy is concentrated, a small number of dominant frequency components can carry most of the signal energy. The optimal K-term approximation further demonstrates that, under sparse or near-sparse spectral conditions, the original spectrum can be effectively approximated by a low-dimensional frequency domain representation. It should be noted that the aforementioned mathematical tools themselves belong to the fundamental theory of frequency domain analysis. The technical improvement of this invention does not lie in proposing these mathematical conclusions in isolation, but rather in constructing a combined prediction process of "learnable frequency domain compression—compressed domain complex prediction—residual compensation reconstruction" for the multi-source business demand sequence of the industry chain collaborative platform. This enables the model to complete efficient prediction within a low-dimensional frequency domain subspace and mitigates the loss of detail caused by compression through residual compensation.

[0030] Second, from the perspective of experimental results and engineering deployment, the present invention has achieved positive technical effects in terms of prediction accuracy, computational efficiency, module collaboration and compression strategy adaptability.

[0031] Regarding prediction accuracy, this invention was validated on several publicly available long-term time-series prediction benchmark datasets. Experiments covered datasets such as Weather, Traffic, ECL (Electric Power), ETT (Electric Transformer Temperature), and Solar, and were compared with methods such as TimeMixer++, PatchTST, iTransformer, DLinear, FreTS, and TimesNet under different prediction step sizes. Experimental results show that this invention achieved the best mean squared error (MSE) in 26 out of 32 prediction settings across 8 datasets, accounting for approximately 81% of all settings. This result demonstrates that by compressing the high-dimensional spectrum to a low-dimensional frequency domain subspace, this invention does not significantly sacrifice prediction accuracy due to reduced modeling dimensionality; on the contrary, it improves the stability of prediction results by weakening the influence of weak information frequency components and noise frequency components.

[0032] In terms of computational efficiency, the main advantage of this invention comes from low-dimensional frequency domain subspace modeling. Since the main prediction operations are performed on the compressed dimension K, rather than on the full number of frequency points N, the number of model parameters, inference latency, and training memory usage are all reduced. In efficiency experiments on the ECL power dataset, when the historical window length, number of variables, and prediction length are the experimental settings, the model of this invention has approximately 0.5M parameters, a single inference latency of approximately 1.08ms, and training memory of approximately 37MB. In comparison, PatchTST has approximately 7.5M parameters, an inference latency of approximately 39.75ms, and training memory of approximately 2306MB; iTransformer has approximately 5.2M parameters, an inference latency of approximately 1.46ms, and training memory of approximately 137MB. Therefore, this invention can significantly reduce model deployment overhead while maintaining competitive prediction accuracy, making it more suitable as a lightweight prediction algorithm service frequently called by multiple business processes in the supply chain collaboration platform of a leading enterprise.

[0033] Regarding the synergistic effect of modules, ablation experiments show that frequency domain transformation, frequency domain compression, and residual compensation in this invention all contribute to the prediction performance. Removing frequency domain modeling increases the prediction error; removing the residual compensation channel reduces the model's ability to compensate for local service fluctuations; and removing the compression mechanism makes it difficult for the model to fully utilize the low-dimensional frequency domain representation to filter redundant frequency components. Related experimental results show that removing frequency domain transformation, residual compensation, and compression modules all lead to varying degrees of increase in the average prediction error, indicating that the technical effect of this invention is not generated by a single module, but rather by the synergistic effect of adaptive frequency domain compression, compressed domain complex prediction, and residual compensation reconstruction.

[0034] Regarding the adaptability of compression strategies, comparative experiments under the same compression dimension show that learnable frequency domain projection outperforms compression strategies such as fixed low-pass filtering, random projection, and high-pass filtering. Fixed low-pass filtering only retains low-frequency components based on a preset cutoff frequency, making it difficult to adapt to the spectral structure of different service sequences; while random projection can achieve dimensionality reduction, it cannot learn useful frequency combinations for the prediction task; and high-pass filtering easily ignores long-term trends and dominant cycles. This invention uses an end-to-end trained learnable complex frequency domain compression matrix to adaptively learn the combination relationships between different frequency components, making the compressed frequency domain representation more aligned with future prediction needs. Compression rate sensitivity experiments also show that a smaller compression rate on multiple datasets does not lead to a decrease in prediction performance; in fact, some datasets achieve lower errors under stronger compression, indicating that setting the compression rate in the range of 0.1 to 0.3 has experimental basis and practical feasibility.

[0035] Third, from the perspective of product application of the industrial chain collaboration platform, this invention can improve the deployment adaptability and business support capabilities of the prediction algorithm service.

[0036] This invention addresses multi-source business demand forecasting tasks within a supply chain collaboration platform for leading enterprises. It can access order, sales, inventory, logistics, and production status data from systems such as ERP, SCM, WMS, TMS, and MES, and output demand forecasts for multiple future time steps. Because the model performs primary forecast calculations in a low-dimensional frequency domain subspace, it reduces the computational resources required for a single forecast call. Furthermore, by introducing a residual compensation channel, it can retain local business fluctuation information such as promotional activities, abnormal orders, inventory adjustments, logistics delays, and production plan changes while compressing the model. Therefore, this invention is suitable for high-frequency forecasting scenarios in business modules such as order collaboration, inventory alerts, replenishment planning, production scheduling, logistics dispatching, and supplier collaboration. It helps reduce the deployment cost of platform algorithm services and improves the real-time performance and stability of forecasting services.

[0037] In summary, this invention does not simply combine mature tools such as Fourier transform, complex MLP, or low-pass compression. Instead, it addresses the challenge of simultaneously achieving "accuracy preservation, lightweight deployment, and local fluctuation compensation" in the multi-source business demand forecasting of the chain leader industry chain collaborative platform. It presents a complete technical solution combining learnable frequency domain compression, compressed domain complex prediction, residual compensation reconstruction, and inverse normalization output. This solution can reduce the number of model parameters, inference latency, and memory usage while maintaining prediction accuracy, and improves adaptability to different business spectral structures and local business fluctuations, demonstrating clear technical effectiveness and platform application value.

[0038] Fourth, this invention addresses multi-source business demand forecasting tasks within the supply chain collaboration platform of leading enterprises. It can serve as a foundational forecasting algorithm service for business modules such as order collaboration, inventory early warning, replenishment planning, production scheduling, logistics dispatching, and supplier fulfillment management. By mapping high-dimensional spectra to low-dimensional frequency domain subspaces and performing complex number predictions in a compressed space, this invention reduces the number of model parameters, inference latency, and GPU memory usage, thereby lowering platform deployment and operating costs. For leading enterprises requiring frequent calls to forecasting services, this method helps improve the response speed of forecasting services, reduces reliance on high-performance computing resources, and enhances the integration and adaptability of algorithm services within supply chain collaboration platforms, supply chain management systems, warehouse management systems, transportation management systems, and manufacturing execution systems.

[0039] At the business application level, this invention can provide predictive basis for setting inventory safety levels, generating replenishment plans, scheduling production resources, planning logistics and transportation, and making collaborative decisions with suppliers, which helps reduce inventory backlog, reduce stockout risks, and improve the timeliness of replenishment and production scheduling. Because this invention takes into account both dominant demand patterns and local business fluctuations, it can model cyclical demand changes as well as short-term changes such as promotions, abnormal orders, logistical disruptions, and production adjustments, thus possessing significant platform deployment value and commercial promotion potential.

[0040] Among existing long-term time-series forecasting methods, Transformer-based models focus on long-range dependency modeling, linear models focus on low-complexity forecasting, and existing frequency domain forecasting methods mainly include full spectrum modeling or fixed low-pass processing. Although the above methods have certain effects in terms of forecasting accuracy, computational efficiency, or frequency domain modeling, they have not yet formed a complete technical solution that combines learnable frequency domain compression, compressed domain complex prediction, and residual compensation reconstruction for the multi-source business demand forecasting scenarios in the supply chain collaboration platform of the chain leader enterprise.

[0041] This invention does not simply apply ordinary Fourier transform to demand forecasting. Instead, it leverages the spectral compressibility of multi-source business time-series data from the industry chain to construct an end-to-end trainable learnable complex frequency domain compression matrix. This matrix projects the frequency domain representation onto a low-dimensional frequency domain subspace, predicting the dominant spectral patterns of future demand within this lower-dimensional space. Simultaneously, it recovers local business fluctuations weakened during compression through a residual compensation channel. This technical solution provides a targeted supplement and improvement to existing frequency domain forecasting technologies for lightweight demand forecasting services for industry chain leader collaborative platforms.

[0042] In the field of long-term demand forecasting, there has long been a trade-off between forecast accuracy and deployment efficiency. Complex models can improve representation capabilities, but they typically introduce higher parameter counts, memory consumption, and inference latency; lightweight models, while easier to deploy, tend to weaken their ability to characterize complex cycles, phase changes, and local business fluctuations. Especially in chain-leader supply chain collaboration platforms, forecasting services need to be frequently invoked by multiple business processes such as orders, inventory, replenishment, production, and logistics. Therefore, the model not only needs to accurately predict future demand, but also needs to meet the requirements of low latency, low resource consumption, and sustainable service-oriented deployment.

[0043] This invention reduces the computational load of prediction by using low-dimensional frequency domain subspace modeling, jointly models spectral amplitude and phase through a complex prediction module, and compensates for weakened local service fluctuations during compression through a residual compensation channel. Thus, it balances prediction accuracy, computational efficiency, and local fluctuation compensation capabilities within the same technical process. Therefore, this invention provides an feasible technical solution to the problem of simultaneously achieving high-precision prediction, lightweight deployment, and local service fluctuation modeling in multi-source service demand forecasting across the industry chain.

[0044] Fifth, in existing technologies, one type of approach tends to believe that long-term time-series forecasting requires complex Transformer structures or full-frequency domain modeling to achieve strong predictive capabilities, thus leading to the use of large-scale models in high-dimensional, multivariate, and long-prediction-window scenarios. Another type of approach tends to believe that lightweight frequency-domain forecasting can be achieved by directly retaining low-frequency components through fixed low-pass filtering, thus assuming that low-frequency components are sufficient to represent the main demand patterns. However, in the multi-source business data of the industry chain collaboration platform, different business objects, different time granularities, and different business events will form differentiated spectral structures. Fixed low-pass strategies may discard non-low-frequency components useful for future demand forecasting, while full-frequency domain modeling introduces redundant computation.

[0045] This invention overcomes the aforementioned technical biases: on the one hand, it no longer relies on complete high-dimensional spectra or complex attention structures for prediction, but instead adaptively constructs a low-dimensional frequency domain subspace through a learnable complex frequency domain compression matrix; on the other hand, it does not simply discard frequency components using fixed low-pass rules, but instead learns the combination relationships between different frequency components through end-to-end training, and utilizes residual compensation channels to retain the local service fluctuations weakened during the compression process. This design demonstrates that, with appropriate learnable frequency domain compression and residual compensation mechanisms, the lightweight model can still maintain effective predictive capabilities in multi-source demand forecasting scenarios across the industry chain. Attached Figure Description

[0046] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the disclosure of this invention and, together with the description, serve to explain the principles of the disclosure of this invention. Figure 1 This is a flowchart of the adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform provided in this embodiment of the invention; Figure 2 This is the CRAFT overall architecture provided in the embodiments of the present invention; Figure 3 This is a schematic diagram of RevIN normalization and rFFT provided in an embodiment of the present invention; Figure 4 This is a learnable complex compression matrix provided in the embodiments of the present invention. Will 3D spectral projection to Schematic diagram of 3D subspace ( ); Figure 5 This is a schematic diagram of the complex MLP and Residual Predictor provided in the embodiments of the present invention; Figure 6 This is an efficiency comparison chart (ECL) provided in the embodiments of the present invention. , , ); Latency: batch 1, CUDA, 50 averages; Memory: training forward + backward, batch 1; where (a) is the inference latency graph; (b) is the training memory graph; Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0048] The innovation of this invention lies in: First, this invention addresses the multi-entity, multi-node, and multi-product demand forecasting scenario within a supply chain collaboration platform. It unifies demand, order, inventory, capacity, and delivery cycle data from various sources, including the supply chain leader, suppliers, distributors, warehousing nodes, production nodes, and sales terminals, into multivariate time series data. Compared to demand forecasting methods targeting only a single enterprise or product, this invention can characterize the demand transmission and collaborative response relationships between upstream and downstream nodes in the supply chain, thereby providing a forecasting basis for the supply chain leader to conduct procurement planning, production scheduling, inventory early warning, and supplier collaboration.

[0049] Secondly, this invention maps the normalized demand time series from the time domain to the frequency domain, obtaining a complex-valued spectral representation through Fourier transform. This allows the model to identify long-term trend components, cyclical fluctuation components, and short-term disturbance components in the demand data from a frequency domain perspective. Since supply chain demand data is typically influenced by factors such as production cycles, replenishment cycles, sales cycles, holiday cycles, promotional activities, and upstream and downstream delivery cycles, the frequency domain representation can more directly express the impact of different cyclical components on future demand changes, solving the problem that traditional time-domain forecasting models struggle to fully capture long-cycle dependencies and multi-cycle superposition characteristics.

[0050] Third, this invention constructs a learnable complex frequency domain compression matrix to adaptively mix and compress multiple frequency components in the frequency domain representation. The learnable complex frequency domain compression matrix includes real and imaginary parameters, enabling it to automatically learn the importance and correlation of each frequency component based on the changing demand patterns of different products, regions, and link nodes during model training. Compared to fixed low-frequency truncation, manual frequency selection, or fixed dimensionality reduction methods, this invention avoids the erroneous discarding of key frequency components and retains the main spectral information contributing to demand prediction while reducing the dimensionality of frequency domain features and computational complexity.

[0051] Fourth, after obtaining the compressed spectral representation, this invention further reconstructs an approximate spectrum based on the compressed spectral representation and calculates the residual spectral components between the original spectral representation and the reconstructed spectral representation. These residual spectral components are used to characterize high-frequency fluctuations, abnormal disturbances, sudden order changes, and local demand shifts that were not fully expressed during frequency domain compression. By setting a residual predictor to compensate for the residual spectral components, this invention can reduce the information loss caused by frequency domain compression while maintaining the model's lightweight nature, and improve the model's responsiveness to sudden demand changes and local fluctuations.

[0052] Fifth, this invention employs a complex multilayer perceptron to perform nonlinear mapping in a compressed complex spectral space, jointly modeling the amplitude and phase information in the complex-valued spectral data. Since the amplitude in the spectrum reflects the intensity of demand fluctuations, and the phase reflects the time shift of periodic changes, this invention uses a complex multilayer perceptron to simultaneously model the relationship between the two, enabling the prediction model to more accurately learn the coupling relationship between different demand cycles and improve the prediction accuracy of multivariate demand sequences.

[0053] Sixth, this invention fuses the compressed spectrum prediction result output by the complex multilayer perceptron with the residual spectrum prediction result output by the residual predictor, and restores the fused frequency domain prediction result to the time domain through inverse Fourier transform, and then obtains the final demand prediction result through inverse normalization. This method can take into account long-term trend prediction, cyclical fluctuation prediction, and short-term disturbance compensation, making the prediction results more applicable to specific business scenarios such as procurement decisions, production planning, inventory control, supplier collaboration, and logistics scheduling in the chain leader industry chain collaboration platform.

[0054] Example 1: The adaptive frequency domain compression demand prediction processing flow of the chain leader industry chain collaboration platform provided in this embodiment of the invention includes data normalization, frequency domain transformation, adaptive frequency domain compression, compression space prediction, residual compensation reconstruction, and prediction result inverse normalization output.

[0055] In the supply chain collaboration platform, demand-related data generated by different business systems are characterized by dispersed sources, inconsistent dimensions, different periodic characteristics, and frequent sudden disturbances. For example, order volume and sales volume in the ERP system can reflect changes in market demand; supplier delivery cycle in the SCM system can reflect upstream supply responsiveness; inventory and inbound / outbound volume in the WMS system can reflect the supply and demand status on the warehousing side; transportation timeliness in the TMS system can reflect logistics fulfillment fluctuations; and production plan volume and capacity status in the MES system can reflect manufacturing supply capacity. If a common time-domain forecasting model is directly used to uniformly model the above multi-source data, problems such as insufficient capture of long-term dependencies, mixed forecasting characteristics of different business objects, smoothing of short-term abnormal fluctuations, and high model computational overhead are likely to occur.

[0056] To address the aforementioned issues, this embodiment reduces the distribution offset between different business objects through normalization processing, extracts periodic change features in orders, inventory, logistics, and production status through frequency domain transformation, adaptively selects and mixes frequency components that contribute to future demand forecasting through a learnable complex frequency domain compression matrix, jointly models amplitude and phase changes in the compressed frequency domain space through complex MLP, and compensates for weakened local business fluctuations during the compression process through a residual compensation channel, thereby achieving efficient forecasting of multi-source demand sequences in the main chain industry chain.

[0057] The following formulas describe one implementation method for each step, where normalization, Fourier transform, and complex linear operations are basic computational tools. The main technical improvements of this invention are reflected in: a combined process of learnable frequency domain compression for multi-source demand sequences in the industrial chain, compressed spatial complex prediction, and residual compensation reconstruction. The overall architecture of CRAFT is as follows: Figure 2 As shown, the input, after RevIN normalization, is transformed to the frequency domain via rFFT, allowing the learning of a complex compression matrix. Will 3D spectral projection to The complex MLP performs nonlinear prediction in the compressed space, and the residual compensates for the lost high-frequency details. Finally, the temporal prediction sequence is reconstructed by irFFT.

[0058] like Figure 1 As shown, the specific process of adaptive frequency domain compression demand prediction for the chain leader industry chain collaboration platform provided in this embodiment of the invention can be divided into six steps: S1. Obtain multi-source business time-series data from the supply chain collaboration platform of the chain leader enterprise; Multi-source business time-series data from systems such as ERP, SCM, WMS, TMS, and MES are acquired and aligned according to the prediction object, time granularity, and business node to form a multivariate business time series. Specifically, ERP system data includes historical order volume, sales volume, purchase requisition volume, and customer demand plans, reflecting changes in downstream market demand; SCM system data includes supplier delivery cycles, procurement arrival status, and supplier inventory status, reflecting upstream supply responsiveness; WMS system data includes inventory levels, inbound volume, outbound volume, and safety stock thresholds, reflecting warehouse-side inventory fluctuations; TMS system data includes transportation timeliness, in-transit quantity, and arrival delay information, reflecting logistics fulfillment disruptions; and MES system data includes production plan volume, capacity utilization rate, production cycle time, and work order completion status, reflecting manufacturing-side supply capacity. By unifying the above data into an input time series tensor, the model can simultaneously utilize multi-dimensional information such as order demand, inventory changes, supply delivery, logistics fulfillment, and production capacity to predict future demand.

[0059] S2. Normalize the multi-source service time-series data and perform frequency domain transformation along the time dimension to obtain the corresponding frequency domain representation. ; The business sequence is normalized and converted to the frequency domain using Fast Fourier Transform (rFFT) to reduce the dimensional differences and distribution shifts between different products, regions, business nodes and business indicators, and to extract periodic variation features such as sales cycle, replenishment cycle, production cycle and logistics cycle.

[0060] S3. Learnable complex frequency domain compression matrix trained end-to-end For the frequency domain representation Different frequency components in the frequency domain are adaptively combined, and the frequency domain representation is projected onto a low-dimensional frequency domain subspace to obtain a compressed frequency domain representation. ; By generating compressed frequency domain representations through learnable complex frequency domain compression matrices, the model can adaptively select and mix frequency components that contribute to future demand predictions based on the spectral distribution of different business objects, avoiding redundant calculations caused by full spectrum modeling and the loss of key information caused by fixed low-pass truncation.

[0061] S4. In the low-dimensional frequency domain subspace, the complex prediction module is used to compress the frequency domain representation. To make predictions, we jointly model the dominant spectral patterns related to amplitude and phase in future demand sequences, and obtain compressed domain prediction results. ; Complex forecasting is performed in the compressed frequency domain to obtain the dominant spectral patterns of future demand. This step uses complex MLP to jointly model amplitude and phase variations in the spectrum, thereby preserving information relevant to future forecasts, such as order volatility, cycle shifts, replenishment rhythms, and demand trends.

[0062] S5. Based on the frequency domain representation With the compressed frequency domain representation The residual information is constructed by comparing the differences between the approximate reconstruction results. The residual compensation channel is used to compensate for the weakened local service fluctuations during the compression process, resulting in the residual compensation spectrum. ; A residual compensation channel is constructed to compensate for localized business fluctuations weakened during the compression process. These localized business fluctuations include short-term demand surges caused by promotional activities, abnormal order disturbances, localized changes caused by inventory adjustments, logistics delays, and short-term fluctuations caused by changes in production plans.

[0063] S6. The main prediction spectrum corresponding to the compressed domain prediction result is fused with the residual compensation spectrum, and then subjected to inverse real fast Fourier transform. After inverse normalization, the final demand forecast result is output. ; The main forecast spectrum and the residual compensation spectrum are integrated, and the final demand forecast result is obtained by inverse real fast Fourier transform (irFFT) and inverse normalization. This restores the output result to the original business volume dimension, so that it can be called by business modules such as procurement planning, inventory warning, production scheduling, supplier collaboration and logistics scheduling in the chain master industry chain collaboration platform.

[0064] Through the processing in steps S1 to S6 above, this embodiment can form a complete processing link in the chain-main supply chain collaboration platform, from multi-source business data acquisition, frequency domain feature extraction, adaptive frequency domain compression, compressed space prediction, residual disturbance compensation to business dimension prediction output. Specifically, normalization is used to reduce data distribution differences between different business systems and different business objects; frequency domain transformation is used to extract periodic variation features such as sales cycles, replenishment cycles, production cycles, and logistics cycles; the learnable complex frequency domain compression matrix is ​​used to retain the dominant spectral patterns related to future demand forecasting in the low-dimensional frequency domain space; complex MLP is used to jointly model spectral amplitude and phase changes in the compressed frequency domain space; and the residual compensation channel is used to compensate for local disturbance information such as short-term promotions, abnormal orders, inventory adjustments, logistics delays, and production plan changes. Therefore, this embodiment can solve the technical problems of traditional demand forecasting methods in multi-source data scenarios within the supply chain, such as insufficient long-cycle feature capture, poor adaptability of fixed frequency truncation, inaccurate prediction of sudden business fluctuations, and high computational overhead from repeated model calls.

[0065] like Figure 3 As shown, in step S2, the multi-source service time-series data is normalized and frequency-domain transformed along the time dimension. The normalization and frequency-domain transformation include: The input multi-source business time-series data is represented as follows: ; In the formula, For the real number field, For batch size, For the length of the history window, This refers to the number of business variables or business channels. enter Normalized by reversible instances After performing instance-by-instance normalization, the normalized tensor is replaced with: ; In the formula, This is a normalized business sequence with time as the last dimension. Perform real fast Fourier transform along the time dimension The frequency domain representation is obtained as follows: ; In the formula, This is the frequency domain representation of the normalized service sequence. The length of the history window through The number of frequency points obtained afterwards For complex numbers; in, .

[0066] According to Parseval's theorem, the sum of squares of a time-domain signal is equivalent to the sum of squares of the magnitudes of the frequency-domain coefficients, which provides a basis for subsequent frequency-domain compression modeling.

[0067] Learnable frequency domain compression specifically includes: Existing frequency domain prediction methods typically suffer from two types of shortcomings in frequency compression strategies: one type of method is in complete... Modeling on the spectrum without explicitly utilizing the frequency domain compressibility of demand sequences can easily lead to redundant computations. Another approach uses a fixed low-pass cutoff, directly discarding frequency components outside the cutoff frequency, which is difficult to adapt to the differences in sales cycles, replenishment rhythms, and local fluctuations among different business entities. To address these issues, this invention employs an end-to-end learnable complex frequency domain compression matrix to adaptively compress the spectral representation of multi-source business sequences in the industry chain.

[0068] In step S3, the complex frequency domain compression matrix can be learned. include: set up For compression ratio, To compress the dimensionality, the number of historical frequency points is used. and compression ratio Determined; Parameterized learnable complex frequency domain compression matrix: ; In the formula, For use in Frequency domain representation compressed to Complex matrices in the low-dimensional frequency domain subspace. Let be the real part of the complex matrix. Let be the imaginary part of the complex matrix. The imaginary unit, Orthogonal initialization is used in all cases to improve numerical stability during the early stages of training. It should be noted that orthogonal initialization is only a training implementation method and does not represent... Maintain strict orthogonality throughout the entire training process.

[0069] Frequency domain compression is achieved through complex matrix multiplication, yielding a compressed frequency domain representation: ; In the formula, To represent the frequency domain Compressed frequency domain representation after projection onto a low-dimensional frequency domain subspace; Will The real and imaginary parts are respectively denoted as and ,Will The real and imaginary parts are respectively denoted as and ,but and respectively by Calculated according to the rules of complex matrix multiplication; ; ; ; Orthogonal initialization is used to improve numerical stability in the early stages of training; this orthogonal initialization does not indicate Maintain strict orthogonality throughout the entire training process.

[0070] Unlike fixed low-pass filters that retain only preset low-frequency components, matrix filters... It can adaptively learn the combination relationship between different frequency components during supervised training, and convert the original 3D spectrum compression 3D compressed frequency domain representation. For multi-source business sequences such as orders, sales volume, inventory, logistics, and production status in a supply chain collaboration platform, this compressed mapping can retain the dominant cycles, replenishment rhythms, and business fluctuation patterns related to future demand forecasts in a low-dimensional space, while reducing redundant modeling of weak information or noisy frequency components. Learnable complex compressed matrix Will 3D spectral projection to dimensional subspace ( The overall architecture is as follows: Figure 4 As shown.

[0071] Compression inevitably results in the loss of some frequency information. Therefore, this invention utilizes... An approximate reconstruction is performed on the compressed representation, and the residual is defined. It is used to characterize the residual information not retained in the main compression branch and to compensate for it in the subsequent reconstruction stage.

[0072] The reasons why learnable compression is effective include: Let the spectrum vector Arrange its frequency components in descending order of amplitude as follows: If only the (K) frequency components with the largest amplitudes are retained, then the optimal (K) approximation error satisfies: ; This relationship illustrates that when spectral energy is concentrated in a small number of dominant frequency components, a smaller (K) can retain most of the signal energy, thus indicating that the frequency domain representation of the demand sequence is compressible. It should be noted that the above-mentioned optimal (K) approximation relationship serves only as the theoretical basis for frequency domain compression modeling and is not a separate technical improvement of this invention. The improvement of this invention does not lie in adopting this mathematical conclusion itself, but in constructing a learnable complex frequency domain compression mapping for multi-source business sequences such as supply chain orders, inventory, logistics, and production status. This allows the model to retain the dominant cycles, replenishment rhythms, and business fluctuation patterns related to future demand forecasting in a low-dimensional frequency domain space.

[0073] Unlike simply truncating on the original frequency coordinates, the compression matrix... It implements a general linear projection, capable of combining multiple frequency components within a compressed dimension. From the perspective of average reconstruction error, the optimal rank- Projection corresponds to the principal subspace of the data, thus promising to characterize the statistical correlations between frequencies, rather than being limited to individual frequency components. Therefore, projective learning offers stronger representational power compared to fixed truncation.

[0074] In this invention, Furthermore, it is jointly trained end-to-end with subsequent predictors under supervised loss, thus aiming not only to preserve reconstructable information but also to retain frequency patterns as useful as possible for future predictions. This further illustrates the potential advantages of learnable frequency domain compression compared to fixed low-pass truncation.

[0075] Furthermore, compressed space prediction: complex MLP specifically includes: Encoding stage 3D compressed frequency domain representation Then, the model predicts the dominant spectral pattern of future demand sequences within this low-dimensional frequency domain. For the spectral components... The real and imaginary parts are jointly related to the amplitude and phase. If the real and imaginary parts are input separately into a regular real-valued MLP, the coupling between them is easily weakened. Therefore, this invention uses a complex-parameterized MLP to predict the compressed frequency domain representation. Specifically, for complex inputs... With complex weights The linear transformation of complex numbers adopts the following conventional complex multiplication expansion form: ; It should be noted that the above complex linear transformation formula itself is a basic implementation method in complex feature processing. The improvement of this invention is that the complex mapping is limited to the low-dimensional frequency domain subspace obtained by adaptive frequency domain compression, so that the model can jointly model the amplitude and phase changes in business sequences such as orders, sales, inventory, logistics and production status with a lower number of parameters, thereby preserving frequency domain patterns related to future demand forecasting, such as sales cycle, replenishment rhythm and order fluctuation.

[0076] Each ComplexMLP block consists of two layers of complex linear transformations, with nonlinear activation and random deactivation applied to the real and imaginary parts respectively: ; The two layers of complex mapping, GELU, and Dropout mentioned above are standard network components in the model implementation, their role being to perform nonlinear predictions in the compressed frequency domain representation. Since all prediction operations are performed in a (K)-dimensional compressed space, the main computational cost of a single ComplexMLP block is two complex linear mappings, with a complexity of approximately O(K^2), thus reducing the computational overhead when model services are repeatedly invoked in the industry chain collaboration platform. Complex MLP and the Residual Predictor are as follows... Figure 5 As shown.

[0077] Furthermore, spectral projection and residual compensation specifically include: in, and This represents a complex-valued mapping implemented through a real-valued linear layer. Specifically, the real and imaginary parts of the complex tensor are first concatenated into a real vector, then the dimension is transformed using a linear layer. Finally, the output is split back into its real and imaginary parts and reassembled into a complex form. Definition Predicted output It still resides in the compressed frequency domain space. Due to the number of historical input frequency points ( ) and the number of target frequency points corresponding to the prediction window ( The dimensions are usually inconsistent and require independent linear projection to achieve dimension matching.

[0078] ; In the formula, Main predicted spectrum, and They represent The real and imaginary parts, This is a real vector formed by concatenating the real and imaginary parts. For from 2 Via A real-valued linear mapping of dimension, To predict the length, This indicates the number of target frequency points corresponding to the predicted length. This main channel is used to restore the low-dimensional compressed frequency domain prediction results to the target prediction spectrum space, mainly preserving the stable frequency domain patterns in the supply chain demand sequence, such as periodic sales changes, regular replenishment rhythms, long-term demand trends, and dominant change components shared among different business objects.

[0079] ; In the formula, For residual compensation spectrum, Residuals The real and imaginary parts, To form a real vector by concatenating the real and imaginary parts of the residuals, From Via A real-valued linear mapping of dimension, This is the low-rank bottleneck dimension in the residual compensation channel. From Via A real-valued linear mapping of dimension.

[0080] This residual compensation channel is used to compensate for local business fluctuations that are not fully preserved by the main compression branch, such as short-term demand surges caused by promotional activities, abnormal order disturbances, local changes caused by inventory adjustments, and short-term fluctuations caused by changes in logistics or production plans. The low-rank bottleneck design can control the model size while retaining compensation capabilities, making it suitable for scenarios in supply chain collaboration platforms where forecasting services are repeatedly called by multiple business processes.

[0081] ; ; Using the inverse real fast Fourier transform The fused prediction spectrum Reconstructed to a length of The time-domain prediction sequence, where H represents the prediction length; then through The denormalization operation restores the original business volume dimensions, yielding the final prediction result. ,in, Indicates the future Multi-source business demand forecast results at each time step. A fixed fusion coefficient is used to control the impact of the residual compensation term on the final predicted spectrum. Subsequently, through... The fused predicted spectrum is reconstructed into a time-domain predicted sequence, and then... By restoring the original business volume dimensions, the final forecast result can be obtained. .

[0082] Example 2: The adaptive frequency domain compression demand prediction system for the chain leader industry chain collaboration platform provided in this embodiment of the invention includes: The data acquisition module is used to acquire multi-source business time-series data from the supply chain collaboration platform of the chain leader enterprise; The frequency domain transformation module is used to normalize the multi-source service time-series data and perform frequency domain transformation along the time dimension to obtain the corresponding frequency domain representation. ; An adaptive frequency domain compression module is used to compress complex frequency domain matrices trained end-to-end. For the frequency domain representation Different frequency components in the frequency domain are adaptively combined, and the frequency domain representation is projected onto a low-dimensional frequency domain subspace to obtain a compressed frequency domain representation. ; The compressed domain prediction module is used to perform complex prediction on the compressed frequency domain representation in the low-dimensional frequency domain subspace. To make predictions, we jointly model the dominant spectral patterns related to amplitude and phase in future demand sequences, and obtain compressed domain prediction results. ; The residual compensation module is used to calculate the frequency domain representation. With the compressed frequency domain representation The residual information is constructed by comparing the differences between the approximate reconstruction results. The residual compensation channel is used to compensate for the weakened local service fluctuations during the compression process, resulting in the residual compensation spectrum. ; The fusion and reconstruction module is used to fuse the main prediction spectrum corresponding to the compressed domain prediction result with the residual compensation spectrum, and then perform an inverse real fast Fourier transform. After inverse normalization, the final demand forecast result is output. To further demonstrate the positive effects of the above embodiments, the present invention conducts the following experiments based on the above technical solutions.

[0083] 1. To further demonstrate the positive effects of the embodiments of the present invention in terms of prediction accuracy, computational efficiency, module synergy, and compression strategy adaptability, the present invention conducted comparative experiments on publicly available datasets, efficiency tests, component ablation experiments, and compression rate sensitivity experiments based on the above technical solutions. These experiments were used to verify the effectiveness of the present invention in demand prediction in a low-dimensional frequency domain subspace, and the technical effects resulting from the combination of learnable frequency domain compression, compressed domain complex prediction, and residual compensation reconstruction.

[0084] It should be noted that although the publicly available long-term time-series prediction dataset used in the following experiments is not entirely equivalent to the actual order, inventory, logistics, and production status data in the chain leader supply chain collaboration platform, it also possesses time-series characteristics such as multivariability, long time span, periodicity, trend, and local fluctuations. It can be used to verify the general predictive capability and lightweight deployment capability of this invention for multi-source business time-series data. For the actual business data in the chain leader supply chain collaboration platform, data from systems such as ERP, SCM, WMS, TMS, and MES can be accessed as described in Example 1, and the same model structure and training process can be used for prediction service deployment.

[0085] This experiment evaluates the invention on eight commonly used long-term time series (LTSF) benchmark datasets, including four ETT variant datasets, the Weather dataset, the Electricity dataset, the Solar dataset, and the Traffic dataset. These datasets cover multivariate time series scenarios with different variable scales, periodic variations, and noise levels, and can be used to verify the predictive capabilities of this invention under different spectral structures.

[0086] The comparison methods included TimeMixer++, PatchTST, iTransformer, DLinear, FreTS, and TimesNet. Results for each method were derived from publicly available papers or reproduced according to the authors' publicly available configurations. To ensure experimental comparability, all models were compared using the same data partitioning method, the same prediction step size, and the same evaluation metrics.

[0087] 2. Implementation details and main configurations; CRAFT is implemented in PyTorch and trained using the Adam optimizer and a cosine annealing learning rate adjustment strategy. The training epochs are set to 50, the early stopping parameter (patience) is set to 10, and the mean squared error (MSE) is used as the loss function. Prediction strides are set to 96, 192, 336, and 720 to cover short-term, medium-term, and long-term prediction scenarios. Dropout is set to 0.3 to 0.5, compression ratio (r) to 0.1 to 0.30, and batch size to 16 to 128, adjusted according to different dataset sizes. All experiments are run on a single NVIDIA RTX 4090 24GB graphics card, and the evaluation metrics are mean squared error (MSE) and mean absolute error (MAE).

[0088] 3. Main results; Table 1 reports the results for 8 datasets and 32 settings. Table 1 presents the MSE and MAE results of the CRAFT model of this invention compared to various existing prediction methods under 8 datasets and 32 prediction settings. Lower MSE and MAE values ​​indicate smaller prediction errors and better prediction performance. This experiment verifies whether the present invention can maintain prediction accuracy after reducing the modeling dimensionality.

[0089] Table 1 shows the multivariate long-term prediction results based on eight benchmark datasets. Lower MSE and MAE indicate better performance.

[0090]

[0091] As shown in Table 1, CRAFT achieved the best MSE results in 26 out of 32 prediction settings with fewer than 500K parameters, accounting for approximately 81% of all prediction settings. Compared to PatchTST and iTransformer, which have higher parameter counts, CRAFT maintained lower prediction errors in most prediction settings, indicating that the present invention, after projecting the high-dimensional spectrum to the low-dimensional frequency domain subspace using a learnable complex frequency domain compression matrix, did not significantly sacrifice prediction accuracy due to compression processing.

[0092] On high-dimensional multivariate datasets such as ECL and Traffic, CRAFT's advantages are even more pronounced. These datasets have a large number of variables, and the spectra exhibit strong shared periods and dominant frequency patterns. This invention reduces redundant modeling of weak-information and noise frequency components through frequency domain compression, and extracts shared patterns that contribute to prediction in a low-dimensional frequency domain subspace. On small-to-medium-sized datasets such as ETTm1 and ETTm2, CRAFT also maintains competitive prediction performance, indicating that this invention is not only applicable to high-dimensional multivariate scenarios but also has good versatility.

[0093] 4. Efficiency analysis; Table 2 compares the results of different models in terms of parameter count, inference latency, and training memory usage. All latency measurements were performed on the ECL dataset using a single NVIDIA RTX 4090 graphics card with a batch size of 1, and averaged over 50 iterations, with the first 20 iterations used as warm-up. Training memory statistics include memory usage during forward and backward propagation. Figure 6 The efficiency comparison results on the ECL dataset are shown.

[0094] Table 2 Comparison of inference latency, training memory, and parameter count

[0095] From Table 2 and Figure 6 It can be seen that CRAFT has advantages in terms of parameter count, inference latency, and training memory usage. All results are lower than the comparison models. Compared to PatchTST, CRAFT inference speed is improved by approximately 36.8 times, and training memory usage is reduced to about 1 / 62 of its speed; compared to TimeMixer, CRAFT inference speed is improved by approximately 13.1 times, and training memory usage is reduced to about 1 / 20 of its speed; compared to iTransformer, CRAFT inference latency is similar, but training memory usage is only about 1 / 3.7 of its speed. These results demonstrate that this invention can reduce model deployment overhead while maintaining competitive prediction accuracy, making it more suitable as a lightweight prediction service frequently invoked by multiple business modules such as order coordination, inventory alerts, replenishment planning, production scheduling, and logistics dispatching in a chain leader supply chain collaboration platform.

[0096] CRAFT's efficiency advantage stems from its adaptive frequency domain compression mechanism. Since the primary prediction computations are performed in the low-dimensional frequency domain subspace corresponding to the compressed dimension K, rather than in the full spectrum space corresponding to the number of complete frequency points N, the computational load and parameter count of the complex prediction module are reduced. This result demonstrates that the frequency domain compression of this invention is not merely a mathematical dimensionality reduction, but directly brings engineering benefits in terms of inference latency, memory usage, and deployment costs.

[0097] 5. Ablation test; 5.1 Component Ablation; To verify whether each module of the present invention contributes to the technical effect, component ablation experiments were conducted. Table 3 shows the impact of removing each module one by one (on three representative datasets, covering small-scale ETTm1, medium-scale Weather, and high-dimensional ECL).

[0098] Table 3 shows the impact of removing each module one by one.

[0099] Component ablation (MSE). The average degradation rate relative to the complete model.

[0100] Table 3 shows that the average error degrades most significantly after removing the frequency domain transformation, indicating that frequency domain modeling plays a crucial role in extracting long-period and dominant spectral modes. The error increases after removing residual compensation, indicating that the residual compensation channel can compensate for the weakened local fluctuation information during compression. The error also increases after removing the compression module, demonstrating that the compression mechanism not only reduces computational load but also filters redundant frequency components and suppresses noise. These results prove that the positive effects of this invention are not generated by a single module, but rather by the synergistic effect of frequency domain transformation, learnable frequency domain compression, compressed space complex prediction, and residual compensation reconstruction.

[0101] 5.2 Comparison of Compression Strategies; Table 4 shows the compression strategies at the same compression dimension. The following compares four strategies.

[0102] Table 4 Same Compression Dimension Comparison of the following four strategies

[0103] Comparison of compression strategies (MSE). All strategies use the same compression dimension. .

[0104] As shown in Table 4, under the same compression dimension, learnable projection achieves the best results in all three representative settings. While fixed low-pass filtering can preserve trend and some periodic information, it struggles to adapt to non-low-frequency effective components in different business objects; random projection, although capable of dimensionality reduction, lacks frequency combination learning relevant to the prediction target; high-pass filtering exhibits the most significant degradation, indicating that retaining only high-frequency components cannot effectively express long-term trends and dominant cycles. This invention employs an end-to-end trained learnable complex frequency domain compression matrix, which can adaptively learn the combination relationships between different frequency components based on training data. Therefore, it possesses stronger spectral adaptability compared to fixed low-pass, random projection, and high-pass filtering.

[0105] 5.3 Compression ratio sensitivity; Table 5 shows the compression ratio sensitivity. From 0.1 to 1.0 ( (Indicates no compressed baseline).

[0106] Table 5 Comparison of Compression Sensitivity

[0107] Compression ratio Sensitivity (MSE). Corr: Pearson correlation coefficient with MSE (positive value indicates...) MSE tends to increase as it increases.

[0108] The results show that datasets with more concentrated spectral energy generally benefit more from stronger compression. ETTm1 (Corr = +0.83) and Weather (+0.79) perform better at lower compression rates, suggesting that a more compact frequency domain representation may help filter out redundant or noisy components; ECL has weaker correlation (+0.18). The overall variation within the range is relatively small. In practice, datasets with more concentrated spectral energy can prioritize a lower compression ratio, such as 0.1 to 0.2; datasets with more dispersed spectra can appropriately relax this to 0.2 to 0.3. This result provides experimental basis for the compression ratio range of 0.1 to 0.3 in this invention.

[0109] 6. Demand forecasting applications and supplementary experiments for industrial supply chain collaboration platforms; 6.1 Application Motivation; In the supply chain collaboration platform managed by the leading enterprise, supply chain demand forecasting is not an isolated time-series task, but rather a prerequisite capability for business processes such as order coordination, inventory alerts, replenishment planning, production scheduling, and resource allocation. The leading enterprise needs to continuously acquire order, sales, inventory, logistics, production, and supplier status data from industrial software systems such as ERP, SCM, WMS, TMS, and MES, and feed the forecast results back to the process engine, rule engine, and scheduling optimization module, forming a closed loop of "data access – model prediction – business decision-making – process execution." Therefore, the forecasting model not only needs high accuracy but also low inference overhead, service-oriented deployment, and the ability to be repeatedly invoked by the platform.

[0110] Compared to general benchmarks such as ETT, ECL, and Weather, order / demand time-series data in industrial supply chains typically exhibit a more defined business structure: first, stable cycles driven by sales, replenishment, production planning, and holidays; second, similar change patterns among business objects such as stores, departments, materials, or regions; and third, clear aggregation constraints between total volume and sub-channels. For these series, models not only need to fit local fluctuations but also extract stable common change patterns from multi-channel demand series.

[0111] CRAFT's advantage lies not in simply using longer histories, but in leveraging the compressible spectral structure of sequences to compress the main signal energy and stable, predictable patterns into a low-dimensional frequency domain subspace, and then recovering local details that may have been lost during compression through residual paths. Therefore, the core question addressed in this section is: can CRAFT serve as a lightweight demand forecasting algorithm service in the supply chain collaboration platform of leading enterprises, consistently achieving advantages on order / demand sequences with supply chain business implications, and striking a better trade-off between forecasting accuracy and deployment efficiency?

[0112] 6.2 Task Definition and Data Construction; This invention abstracts industrial supply chain demand forecasting into a multivariate long-term forecasting task. Given a historical observation sequence: ; Predicting the future Multivariate sequences at time steps: ; in, For the length of the history window, To predict the length, The number of variables. Each variable can correspond to a store, department, material, region, warehouse, or other business aggregation channel.

[0113] Because real-world industrial supply chain data typically involves sensitive information such as enterprise orders, inventory, suppliers, logistics, and costs, which is difficult to obtain publicly, this invention selects publicly available retail / order demand data as proxy verification data for the industrial supply chain demand forecasting stage. Although this data does not cover the entire industrial supply chain process, it contains daily or weekly order demand, hierarchical aggregation structures, and total quantity constraints, which can be used to verify the effectiveness of CRAFT as a demand forecasting algorithm service. It should be noted that this invention experimentally verifies the demand forecasting stage within an industrial supply chain collaboration platform, rather than a complete optimization process covering supplier fulfillment, production execution, logistics, and inventory control. The forecast results can be used as input for subsequent inventory optimization, production scheduling, and logistics dispatching modules.

[0114] To avoid duplicate scoring of multiple approximate views within the same family, this invention retains a representative view in each data family for main result statistics and uniformly summarizes results at different prediction lengths: M5: Data is sourced from Walmart M5 Forecasting daily retail sales data. The raw data records long-term sales sequences at the finest granularity of product-store, with state, store, category, and department levels. This invention will categorize the raw sales data according to… dept_id Aggregated into departmental daily series, resulting in 7 departmental channels plus 1 total channel, used to characterize departmental demand changes; forecast length set to... .

[0115] Demand: Data is sourced from publicly available retail demand forecast data. The original table records the daily relationships between products, stores, and sales volume. This invention aggregates the original sales volume by store, constructing a daily multivariate sequence with 10 store channels and 1 total volume channel to characterize store-level demand fluctuations and replenishment rhythms; the forecast length is set to... .

[0116] Walmart: Data is sourced from weekly sales data from Walmart Recruiting-Store Sales Forecasting. The raw data includes store, department, and some exogenous economic features. This invention retains its global demand perspective, further aggregating all store / department sales by date to construct a weekly overall sales sequence and associated aggregated features, used to evaluate the predictive ability of overall demand trends over shorter weekly historical periods; the prediction length is set to... .

[0117] All results were split into training, validation, and test sets in chronological order to avoid future information leakage. All models used the same data partitioning, prediction length, and evaluation metrics. CRAFT employed the same frequency domain compression settings as the main experiment, while PatchTST, iTransformer, and TimeMixer used common configurations found in their public implementations. The overall channel was obtained only by aggregating sub-channels at the same time step, serving as a business aggregation metric in the multivariate input and containing no future information.

[0118] 6.3 Main results and data fit; Table 6 summarizes the family-level results for three representative supply chain / retail demand datasets across multiple forecast lengths. To avoid the randomness inherent in a single forecast length, the table also reports the average MSE and average MAE for each model across the corresponding data family. The average value measures the overall performance of the model across different forecast lengths within the same data family. This statistical approach is not used for cross-dataset comparisons of difficulty, but rather for comparing the relative merits of different models within the same data family across multiple forecast lengths.

[0119] Table 6. Family-level results for three representative supply chain / retail demand datasets across multiple forecast lengths.

[0120] Family-level results are aggregated on a representative supply chain / retail demand dataset. Each cell reports the average across all forecast lengths.

[0121] As can be seen from Table 6, CRAFT achieved the best average MSE and average MAE on all three representative data families, indicating that its advantage does not come from accidental results on a single dataset or a single prediction length, but rather from stable performance across different time granularities and different business aggregation levels.

[0122] On the M5 dataset, CRAFT reduced the average MSE to It is significantly better than TimeMixer. And PatchTST, iTransformer This demonstrates that in departmental demand forecasting, CRAFT can preserve the main periodic structure and overall demand change trends in a frequency domain compressed representation.

[0123] On the Demand dataset, CRAFT's advantage is even more pronounced, with average MSE / MAE of [missing data]. Significantly lower than TimeMixer This indicates that for store-level daily demand sequences, CRAFT is able to capture synchronous fluctuations, cyclical demand, and replenishment rhythms in store demand effectively, thus maintaining a stable advantage in multi-horizon forecasting.

[0124] On the Walmart dataset, despite its weekly overall sales sequence and relatively short historical length, CRAFT still achieved the lowest average MSE and MAE. This indicates that after further aggregation of sales from multiple stores and departments, the global trend and cyclical structure in the sequence become clearer, and frequency domain compression modeling can effectively extract the main change patterns.

[0125] From an industrial supply chain application perspective, reducing demand forecasting errors can further impact inventory warning thresholds, replenishment plan generation, capacity pre-allocation, and logistics resource preparation. Therefore, CRAFT's stable performance across multiple demand data families indicates that it can serve as a foundational forecasting model in the platform's intelligent algorithm library, providing more reliable demand input for subsequent inventory optimization, production scheduling, supplier collaboration, and logistics dispatching algorithms.

[0126] The analysis of the three data families reveals that CRAFT consistently achieves optimal performance across multiple forecast lengths when the supply chain demand sequence possesses a clear aggregated view, a stable cyclical structure, and strong spectral compressibility. This indicates that CRAFT is not only applicable to standard long-term time-series forecasting benchmarks but can also serve as a lightweight demand forecasting model in industrial supply chain collaboration platforms.

[0127] 6.4 Spectral compressibility analysis; To further explain the advantages of CRAFT in supply chain demand data, this invention analyzes the energy concentration of representative sequences in the frequency domain. Specifically, as shown in Table 7, this invention performs rFFT on standardized historical sequences, sorts them by frequency component energy from high to low, and calculates the percentage of frequency components required to reach 80%, 90%, and 95% of the total energy. The lower the percentage, the fewer frequency domain components the main signal energy can be expressed by, and the more suitable the sequence is for frequency domain compression modeling.

[0128] Table 7. Ranking results of different datasets by frequency component energy.

[0129] Spectral energy concentration analysis of supply chain / retail demand sequences. The numerical value represents the proportion of frequency components required to reach the corresponding cumulative energy; the lower the value, the easier it is to compress.

[0130] Table 7 shows that all three representative demand sequences exhibit a clear concentration of spectral energy. Among them, the spectral energy of Demand is the most concentrated, requiring only... The frequency components can cover 90% of the total energy, and the required proportion to reach 95% of the total energy is only [amount missing]. Both the M5 and Walmart exhibit strong spectral compressibility: the frequency component percentages required to reach 90% of the total energy for both are respectively... and The proportions required to reach 95% of the total energy are as follows: and This indicates that the main signal energy in these retail / order demand sequences can be expressed by a relatively small number of frequency components, making them suitable for frequency domain compression modeling.

[0131] This result is consistent with the conclusions of the main experiment: when the demand sequence has a clear periodic pattern, a stable business aggregation structure, and strong spectral compressibility, CRAFT can preserve the main signal structure in the low-dimensional frequency domain subspace and achieve good predictive performance. In other words, CRAFT's advantage in supply chain demand data does not come solely from model size or training techniques, but rather from its match with the spectral structure of this type of data itself.

[0132] 6.5 Efficiency Analysis; The main results of this experiment show that CRAFT can achieve a stable advantage on representative retail / demand sequences, but when deploying it for industrial platforms, model complexity and inference overhead still need to be considered simultaneously. Since the main nonlinear prediction process of CRAFT occurs in the compressed frequency domain subspace, its deployment value is reflected not only in prediction accuracy, but also in its lower parameter count, memory usage, and inference latency.

[0133] Table 8 presents the efficiency evaluation results on Demand. This dataset has a large number of channels, making it suitable for evaluating the inference cost of the model in fine-grained demand prediction scenarios. The results show that CRAFT has only a small number of parameters. M, single-batch inference time is ms, peak memory usage MB. Compared to PatchTST and TimeMixer, CRAFT has significant advantages in both inference time and memory usage; compared to iTransformer, CRAFT also maintains a lower number of parameters and slightly lower inference overhead. This demonstrates that frequency domain compression is not only an effective prediction mechanism but also a practically deployable computational simplification method.

[0134] Table 8 Efficiency Evaluation Results on Demand

[0135] Performance benchmark results on Demand. Time and memory usage are based on a single-GPU, single-batch forward benchmark with a batch size of 16.

[0136] In industrial supply chain collaboration platforms, predictive models are typically invoked repeatedly by multiple business modules, including order coordination, inventory alerts, replenishment planning, production scheduling, and resource allocation. High model inference costs hinder their deployment as platform algorithm services. CRAFT, by performing primary predictive calculations in a low-dimensional frequency domain subspace, reduces service invocation costs while maintaining strong predictive performance. Therefore, it is better suited for encapsulation as a lightweight predictive service to support leading enterprises in anticipating changes in demand, inventory trends, and replenishment rhythms.

[0137] 6.6 Service integration for the collaborative platform of chain leader enterprises; Based on the above results, the applicability of CRAFT in supply chain scenarios can be more precisely described as follows: It is suitable for order / demand forecasting in industrial supply chains, and applicable to multivariate time series with stable cyclical structures, multi-channel spectral similarity, and clear aggregation constraints. Within this scope, frequency domain compression modeling not only helps extract dominant demand patterns but also makes it easier to achieve a better accuracy-efficiency tradeoff.

[0138] Within the chain-leader enterprise collaboration platform, CRAFT can be registered, deployed, invoked, and monitored as a predictive algorithm service within the intelligent algorithm library. Its typical service-oriented process includes: First, the platform obtains historical order, sales, inventory, logistics, and production status data from systems such as ERP, SCM, WMS, TMS, and MES through standardized interfaces; second, the data governance component aligns the data according to business objects such as products, materials, stores, warehouses, regions, or suppliers, and constructs multivariate demand sequences; subsequently, CRAFT predicts future demand trends; finally, the prediction results are invoked by the process engine, rule engine, and scheduling optimization module to support inventory alerts, replenishment plans, production scheduling, supplier collaboration, and resource allocation.

[0139] Unlike forecasting modules embedded in single business systems, CRAFT operates as a model service within this platform, enabling it to be reused across multiple collaborative processes. For order collaboration processes, model forecasts can be used to anticipate demand fluctuations; for inventory alert processes, forecasted demand can be combined with safety stock rules to trigger replenishment suggestions or inventory warnings; for production scheduling processes, forecasted demand can serve as input for APS or scheduling optimization algorithms; and for logistics collaboration processes, forecasts can be used to assess transportation resource needs in advance. Thus, CRAFT not only provides single-point forecasting capabilities but also becomes a platform-based algorithmic resource connecting "data-model-process-decision."

[0140] Furthermore, since CRAFT's main computations occur in the compressed frequency domain subspace, its parameter count and inference overhead are relatively low, making it suitable for flexible deployment between the central cloud and edge nodes. The central cloud can perform global demand forecasting across regions and product lines; the edge can perform local demand forecasting and inventory trend alerts for warehouses, factories, or regional nodes, thereby reducing data backhaul pressure and improving business response speed. Therefore, the supplementary experiments in this section not only verify CRAFT's predictive performance on publicly available supply chain demand data but also demonstrate its potential as a lightweight forecasting service for supply chain collaboration platforms for leading enterprises.

[0141] 7. Conclusion; This invention proposes an adaptive frequency-domain compressed demand forecasting method for supply chain collaboration platforms of leading enterprises. This method targets multi-source business sequences such as orders, sales volume, inventory, logistics, and production status. First, it obtains a spectral representation through frequency domain transformation. Then, it generates a compressed frequency domain representation using a learnable complex frequency domain compression matrix and performs complex prediction within the compressed space. Simultaneously, it recovers weakened local business fluctuations during compression through a residual compensation channel. Finally, it fuses the main prediction spectrum and the residual compensation spectrum to obtain the future demand forecast result. The Fourier transform, Parseval's theorem, optimal K-term approximation, complex linear transformation, and inverse real fast Fourier transform (irFFT) used in this invention are all fundamental computations or theoretical explanations. The main technical improvement of this invention lies in the combined process of adaptive frequency domain compression, compressed space prediction, and residual compensation reconstruction for multi-source demand sequences in the supply chain. This method can serve as a lightweight forecasting algorithm service in supply chain collaboration platforms, providing demand input for inventory early warning, replenishment planning, production scheduling, supplier collaboration, and logistics scheduling.

[0142] The core inspiration of this invention is not limited to Fourier transform: finding the low-dimensional structure of the prediction problem in a suitable transform domain and modeling it in that space may provide new ideas for other structured prediction tasks.

[0143] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for adaptive frequency domain compression demand forecasting in a chain-leader industry chain collaborative platform, characterized in that, The method includes the following steps: S1. Obtain multi-source business time-series data from the supply chain collaboration platform of the chain leader enterprise; S2. Normalize the multi-source service time-series data and perform frequency domain transformation along the time dimension to obtain the corresponding frequency domain representation. ; S3. Learnable complex frequency domain compression matrix trained end-to-end For the frequency domain representation Different frequency components in the frequency domain are adaptively combined, and the frequency domain representation is projected onto a low-dimensional frequency domain subspace to obtain a compressed frequency domain representation. ; S4. In the low-dimensional frequency domain subspace, the complex prediction module is used to compress the frequency domain representation. To make predictions, we jointly model the dominant spectral patterns related to amplitude and phase in future demand sequences, and obtain compressed domain prediction results. ; S5. Based on the frequency domain representation With the compressed frequency domain representation The residual information is constructed by comparing the differences between the approximate reconstruction results. The residual compensation channel is used to compensate for the weakened local service fluctuations during the compression process, resulting in the residual compensation spectrum. ; S6. The main prediction spectrum corresponding to the compressed domain prediction result is fused with the residual compensation spectrum, and then subjected to inverse real fast Fourier transform. After inverse normalization, the final demand forecast result is output. .

2. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 1, characterized in that, In step S1, the multi-source business time series data includes at least two of the following: order data, sales data, inventory data, logistics data, and production status data obtained from ERP, SCM, WMS, TMS, and MES systems; the multi-source business time series data is a multivariate time series, and each variable corresponds to a business indicator under the dimensions of store, material, region, warehouse, or supplier.

3. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 1, characterized in that, In step S2, the multi-source service time-series data is normalized and frequency domain transformed along the time dimension. The normalization and frequency domain transformation include: The input multi-source business time-series data is represented as follows: ； In the formula, For the real number field, For batch size, For the length of the history window, This refers to the number of business variables or business channels. enter Normalized by reversible instances After performing instance-by-instance normalization, the normalized tensor is replaced with: ； In the formula, This is a normalized business sequence with time as the last dimension. Perform real fast Fourier transform along the time dimension The frequency domain representation is obtained as follows: ； In the formula, This is the frequency domain representation of the normalized service sequence. The length of the history window through The number of frequency points obtained afterwards For complex numbers; in, 。 4. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 1, characterized in that, In step S3, the complex frequency domain compression matrix can be learned. include: set up For compression ratio, To compress the dimensionality, the number of historical frequency points is used. and compression ratio Determined; Parameterized learnable complex frequency domain compression matrix: ； In the formula, For use in Frequency domain representation compressed to Complex matrices in the low-dimensional frequency domain subspace. Let be the real part of the complex matrix. Let be the imaginary part of the complex matrix. The imaginary unit, Orthogonal initialization was used, and the combination relationship between each frequency component was adaptively learned through end-to-end supervised training. Frequency domain compression is achieved through complex matrix multiplication, yielding a compressed frequency domain representation: ； In the formula, To represent the frequency domain Compressed frequency domain representation after projection onto a low-dimensional frequency domain subspace; Will The real and imaginary parts are respectively denoted as and ,Will The real and imaginary parts are respectively denoted as and ,but and respectively by Calculated according to the rules of complex matrix multiplication; ； ； ； Orthogonal initialization is used to improve numerical stability in the early stages of training; this orthogonal initialization does not indicate Maintain strict orthogonality throughout the entire training process.

5. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 4, characterized in that, The compression ratio The value range is from 0.1 to 0.

3.

6. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 1, characterized in that, In step S4, the complex prediction module is a complex MLP, each... The block consists of two layers of complex linear transformations; This indicates the dimension of the compressed frequency domain representation. Representing complex numbers The hidden dimension, the first layer of complex linear transformation Compressed frequency domain representation from Dimension mapping to Dimension, to obtain the intermediate complex number representation ; and They represent The real and imaginary parts; then the real and imaginary parts; and Apply nonlinear activation respectively With random inactivation And recombine them to obtain the intermediate representation of complex numbers. Second-level complex linear transformation Will from Dimension Mapping Back Dimension, to obtain the compression domain prediction result , Let be a complex tensor with the following dimensions: , representing the compressed domain spectral representation predicted in the low-dimensional frequency domain subspace; 。 7. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 1, characterized in that, In step S5, compensating for the weakened local service fluctuations during the compression process through the residual compensation channel includes: Using the conjugate transpose of the learnable complex frequency domain compression matrix For the compressed frequency domain representation Perform approximate reconstruction And calculate the frequency domain representation. Residuals between the approximate reconstruction results It is used to characterize the residual information not retained in the main compression branch and to compensate for it during the reconstruction stage; in, For learnable complex frequency domain compression matrix The conjugate transpose of . This represents the frequency domain representation of the normalized traffic sequence obtained through the real-number fast Fourier transform. This represents a compressed frequency domain representation. This represents the frequency domain residual information not retained in the main compression branch. Indicates batch size. This indicates the number of business variables or business channels. This indicates the number of frequency points corresponding to the historical window. Indicates the compressed frequency domain dimension; Main projection With residual compensation projection This represents a complex-valued mapping implemented through a real-valued linear layer; it concatenates the real and imaginary parts of a complex tensor into a real vector, performs dimensionality transformation through a linear layer, and then splits the output into real and imaginary parts and recombines them into a complex form; it defines... , Represents the real part after splitting. Represents the imaginary part after splitting. Represents the imaginary unit; Predicted output Located in the compressed frequency domain space, dimensional matching is achieved through independent linear projection; its historical input frequency points are limited. Number of target frequency points corresponding to the prediction window Inconsistencies are resolved by matching dimensions using independent linear projections. The main channel is used to restore the low-dimensional compressed frequency domain prediction results to the target prediction spectral space: ； In the formula, Main predicted spectrum, and They represent The real and imaginary parts, This is a real vector formed by concatenating the real and imaginary parts. For from 2 Via A real-valued linear mapping of dimension, To predict the length, This indicates the number of target frequency points corresponding to the predicted length. The residual compensation channel is used to compensate for local business fluctuations that are not fully preserved in the main compression branch: ； In the formula, For residual compensation spectrum, Residuals The real and imaginary parts, To form a real vector by concatenating the real and imaginary parts of the residuals, From Via A real-valued linear mapping of dimension, This refers to the low-rank bottleneck dimension in the residual compensation channel. From Via A real-valued linear mapping of dimension.

8. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 7, characterized in that, In the residual compensation channel, complex residuals The real and imaginary parts are concatenated to form a dimension of The real vector, where N represents the number of frequency points corresponding to the historical window, and the coefficient 2 indicates that the complex spectrum contains both a real and an imaginary part; used to transfer the residual from In the real-valued linear layer that maps dimensionality to intermediate dimensions It is a low-rank bottleneck dimension, and Less than This is used to control the model size while preserving residual compensation capability; the output of the residual compensation channel corresponds to the target prediction spectrum, and the dimension of the concatenated real and imaginary parts is... ,in, This indicates the number of target frequency points corresponding to the predicted length.

9. The adaptive frequency domain compression demand prediction method for the chain leader industry chain collaboration platform according to claim 1, characterized in that, In step S6, fusing the master prediction spectrum corresponding to the compressed domain prediction result with the residual compensation spectrum includes: The main prediction spectrum corresponding to the compressed domain prediction result is weighted and fused with the residual compensation spectrum to obtain the fused prediction spectrum. , This represents the main prediction spectrum obtained by mapping the compressed domain prediction results to the main channel. This represents the residual compensation spectrum output by the residual compensation channel, where α is the fusion coefficient used to control the impact of the residual compensation term on the final predicted spectrum. ； Using the inverse real fast Fourier transform The fused prediction spectrum Reconstructed to a length of The time-domain prediction sequence, where H represents the prediction length; then through The denormalization operation restores the original business volume dimensions, yielding the final prediction result. ,in, Indicates the future Multi-source business demand forecast results at each time step.

10. An adaptive frequency domain compression demand forecasting system for a chain leader industry chain collaborative platform, characterized in that, This system is used to implement the adaptive frequency domain compression demand forecasting method for the chain leader industry chain collaboration platform as described in any one of claims 1 to 9. The system includes: The data acquisition module is used to acquire multi-source business time-series data from the supply chain collaboration platform of the chain leader enterprise; The frequency domain transformation module is used to normalize the multi-source service time-series data and perform frequency domain transformation along the time dimension to obtain the corresponding frequency domain representation. ; An adaptive frequency domain compression module is used to compress complex frequency domain matrices trained end-to-end. For the frequency domain representation Different frequency components in the frequency domain are adaptively combined, and the frequency domain representation is projected onto a low-dimensional frequency domain subspace to obtain a compressed frequency domain representation. ; The compressed domain prediction module is used to perform complex prediction on the compressed frequency domain representation in the low-dimensional frequency domain subspace. To make predictions, we jointly model the dominant spectral patterns related to amplitude and phase in future demand sequences, and obtain compressed domain prediction results. ; The residual compensation module is used to calculate the frequency domain representation. With the compressed frequency domain representation The residual information is constructed by comparing the differences between the approximate reconstruction results. The residual compensation channel is used to compensate for the weakened local service fluctuations during the compression process, resulting in the residual compensation spectrum. ; The fusion and reconstruction module is used to fuse the main prediction spectrum corresponding to the compressed domain prediction result with the residual compensation spectrum, and then perform an inverse real fast Fourier transform. After inverse normalization, the final demand forecast result is output. .

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