Ultra-compact model for large-scale spatio-temporal data

Abstract

Disclosed herein is a method for time-series data forecasting. The method may include processing a time-series dataset through a convolutional aggregation module, transforming an output of the convolutional aggregation module into a frequency-domain representation, segmenting the frequency-domain representation into a plurality of subsequences, modeling intra-period dynamics of each of the plurality of subsequences, modeling inter-period dynamics, generating a time-series forecast. In this embodiment, modeling intra-period dynamics may include the use of a shape bank module. Also disclosed herein is a system for forecasting spatio-temporal data.

Description

Attorney Docket No. 250127PCT / 9975WO01ULTRA-COMPACT MODEL FOR LARGE-SCALE SPATIO-TEMPORAL DATACROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of and priority under 35 U. S. C. § 119(e) to U. S. Provisional Application Serial No. 63 / 748,054 filed January 22, 2025, entitled “ULTRA-COMPACT MODEL FOR LARGE-SCALE SPATIO-TEMPORAL DATA,” the contents of which is hereby incorporated by reference in its entirety herein.TECHNICAL FIELD

[0002] This disclosure pertains to forecasting spatio-temporal data. Specifically, it involves techniques that integrate ultra-compact shape bank components with a crossperiod sparse forecast component.BACKGROUND

[0003] Spatio-temporal data, prevalent in real-world applications such as traffic monitoring, financial transactions, and ride-share demands, represents a special case of multivariate time-series. This data type is characterized by two unique properties: high dimensionality and commensurability across spatial locations.

[0004] Time-series forecasting is a core task in many application domains, including energy systems, transportation, finance, and climate science. Modern forecasting problems are increasingly multivariate, where multiple related variables (or channels) are observed simultaneously over time. While multivariate information can improve predictive accuracy, it also introduces challenges related to scalability, noise propagation, and spurious inter-variable dependencies. As a result, a central question in recent forecasting research is how to efficiently exploit temporal and cross-variable information without incurring excessive model complexity or overfitting.

[0005] Early deep learning approaches to time-series forecasting typically relied on recurrent or convolutional architectures designed to model both temporal and crosschannel dependencies jointly. However, such architectures often suffer from high computational costs, including a large number of parameters and parameter fitting. Whereas recent advances have shown that strong forecasting performance can be achieved by focusing primarily on temporal dependencies rather than complex crosschannel interactions. In one example, a lightweight channel-independent forecasting model demonstrates that many multivariate forecasting benchmarks can beAttorney Docket No. 250127PCT / 9975WO01addressed using lightweight linear or near-linear temporal models augmented with sparsity-inducing mechanisms.

[0006] Channel-independent forecasting has been built on the observation that real-world time-series often exhibit temporal periodicity, where only a subset of historical time steps meaningfully contributes to future predictions. Instead of modeling full temporal histories densely, it is possible to rely on learnable sparse projections over the input time dimension. These projections selectively emphasize informative time points while suppressing irrelevant or noisy time points, resulting in improved generalization and computational efficiency. The channel-independent approaches emphasize temporal sparsity and parameter efficiency. When applied independently across channels with shared temporal projections, sparse models can capture common temporal patterns while avoiding overfitting to cross-channel noise.

[0007] Moreover, channel-independent sparse forecasting supports modular extensibility. Recently developed channel-independent sparse forecasting models underperform on spatio-temporal data compared to state-of-the-art methods due to limited ability to capture intra-period temporal dependencies.SUMMARY

[0008] A system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions.

[0009] One general aspect includes a system for forecasting spatio-temporal data. The system may include one or more processor elements configured to obtain one or more spatially distinct time-series datasets and assign each of the one or more spatially distinct time-series datasets to at least one of the one or more processor elements. The one or more processors may be configured, for each of the one or more spatially distinct time-series datasets assigned to at least one of the one or more processor elements, to generate a time-series forecast for the assigned one or more spatially distinct time-series datasets. To generate the time-series forecast, the one or more processor elements may be configured to process each assigned spatially distinct time-series dataset through a convolutional aggregation module, transform anAttorney Docket No. 250127PCT / 9975WO01output of the convolutional aggregation module into a frequency-domain representation, segment the frequency-domain representation into a plurality of subsequences, model intra-period dynamics of each of the plurality of subsequences using a shape-bank module, model inter-period dynamics by applying a cross-period sparse forecasting module to the frequency-domain representation, generate a frequency-domain forecast by integrating the intra-period dynamics with the interperiod dynamics, and transform the frequency-domain forecast to a time-series forecast. The one or more processors may be further configured to assemble the timeseries forecasts generated for the one or more spatially distinct time-series datasets to generate a final forecast matching spatial and temporal dimensions of the one or more spatially distinct time-series datasets. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0010] Implementations may include one or more of the following features. The system where the shape bank module may be configured to: generate a query vector using a linear transformation; calculate an attention score between the query vector and a shape key of a shape bank database, where the shape bank database may include shape keys and corresponding shape values; and multiply the attention score and the corresponding shape value of the shape key, where the multiplying generates an intra-period dynamics output. Each subsequence of the plurality of subsequences corresponds to a period of length w; and where a convolutional filter has a size defined by w. The one or more processor elements may be further configured to: repeat the steps of modeling intra-period dynamics using a shape-bank module and modeling inter-period dynamics a number of times (nblock), where the number of times (nblock) is a learned hyperparameter. Calculating attention scores may include evaluating an ReLU activation function with respect to the query vectors and shape keys. The one or more processors may be further configured to: train weights associated with the shape bank database on a plurality of intra-period shape patterns, the intra-period shape patterns having a period length, w; and where the trained weights are associated with shape keys and corresponding shape values. The one or more processors may be further configured to: compare the final forecast with real-time measured time-series data; and retrain the shape bank database based on theAttorney Docket No. 250127PCT / 9975WO01comparison. The spatially distinct time-series datasets may be associated with measured indicators, and where the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands. The one or more processors may be further configured to: determine optimized hyper-parameters, where the optimized hyperparameters may include an optimal number of intra-period shape patterns and nblock, where determining may include determining associated error and complexity of optimized hyper-parameters. The one or more processor elements may be configured to operate in parallel. The one or more processor elements are one of compute processor units or graphical processing units. Two or more spatially distinct timeseries datasets are assigned to one of the one or more processor elements. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0011] One general aspect includes a method for time-series data forecasting may include processing a time-series dataset through a convolutional aggregation module, transforming an output of the convolutional aggregation module into a frequencydomain representation, segmenting the frequency-domain representation into a plurality of subsequences each corresponding to a period of length w, modeling intra-period dynamics of each of the plurality of subsequences, modeling inter-period dynamics by applying a cross-period sparse forecasting module to the frequencydomain representation, generating a frequency-domain forecast by integrating the intra-period dynamics with the inter-period dynamics, and transforming the frequencydomain forecast to a time-series forecast. In this embodiment, modeling intra-period dynamics may include generating a query vector using a linear transformation, calculating an attention score between the query vector and a shape key, and multiplying the attention score and the related shape value of the shape key such that the multiplying generates an intra-period dynamics output. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0012] Implementations may include one or more of the following features. The method where the time-series dataset may be segmented into subsequences corresponding to a period of length, w; and where the shape keys and correspondingAttorney Docket No. 250127PCT / 9975WO01shape values correspond to the period of length, w. The method may include: comparing the time-series forecast with real-time measured time-series data; and retraining the shape bank based on the comparison. The trained weights are associated with paired shape keys and corresponding shape values. The method may include: outputting a visual display of the time-series forecast; and based on the visual display, performing one or more actions affecting real-time measured time-series data. The time-series dataset is associated with measured indicators, and where the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands. The optimized hyper-parameters may include an optimal number of intra-period shape patterns and nblock, where determining may include determining associated error and complexity of optimized hyper-parameters. Calculating attention scores may include evaluating an ReLU activation function with respect to the query vectors and shape keys. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0013] One general aspect includes a non-transitory computer-readable medium having instructions stored thereon, that when executed by a processor, cause the processor to model intra-period dynamics of a time-series dataset. Modeling intra-period dynamics may include generating a query vector using a linear transformation, calculating an attention score between the query vector and a shape key, wherein the shape key corresponds to a related shape value, and multiplying the attention score and the related shape value of the shape key, wherein the multiplying generates an intra-period dynamics output. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0014] Implementations may include one or more of the following features. The instructions may provide for the shape keys and corresponding shape values to correspond to the period of length, w. The instructions may provide for comparing the intra-period dynamics with real-time measured time-series data; and retraining the shape bank based on the comparison. The trained weights are associated with paired shape keys and corresponding shape values. The time-series dataset is associated with measured indicators, and where the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission andAttorney Docket No. 250127PCT / 9975WO01distribution monitoring, and market demands. The optimized hyper-parameters may include an optimal number of intra-period shape patterns and nblock, where determining may include determining associated error and complexity of optimized hyperparameters. Calculating attention scores may include evaluating an ReLU activation function with respect to the query vectors and shape keys.

[0015] Implementations may include one or more of the following features. The non-transitory computer-readable medium where a shape bank mechanism adapts dynamically to input variations by updating key-value pairs during training. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In the description, for purposes of explanation and not limitation, specific details are set forth, such as particular embodiments, procedures, techniques, etc. to provide a thorough understanding of the present technology. However, it will be apparent to one skilled in the art that the present technology may be practiced in other embodiments that depart from these specific details.

[0017] The accompanying drawings, where like reference numerals refer to identical or functionally similar elements throughout the separate views, together with the detailed description below, are incorporated in and form part of the specification, and serve to further illustrate embodiments of concepts that include the claimed disclosure and explain various principles and advantages of those embodiments.

[0018] The apparatuses, systems, and methods disclosed herein have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the various embodiments of the present disclosure so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein.

[0019] FIG. 1 is a diagrammatic representation of a system for forecasting spatiotemporal data, according to at least one aspect of the present disclosure.

[0020] FIG. 2 is a diagrammatic representation of a time-series forecast module as part of a system for forecasting spatio-temporal data, according to at least one aspect of the present disclosure.Attorney Docket No. 250127PCT / 9975WO01

[0021] FIG. 3 is a flow diagram of the overall architecture design of a time-series forecast module, according to at least one aspect of the present disclosure.

[0022] FIG. 4 is a schematic representation of an aggregation operation and a cross-period sparse forecasting operation on spatio-temporal data, according to at least one aspect of the present disclosure.

[0023] FIG. 5 is a flow diagram of a shape bank module, according to at least one aspect of the present disclosure.

[0024] FIG. 6 is a flow diagram of a method for forecasting spatio-temporal data, according to at least one aspect of the present disclosure.

[0025] FIG. 7 is a block diagram of a computer apparatus with data processing subsystems or components, according to at least one aspect of the present disclosure.

[0026] FIG. 8 illustrates the effect of different hyper-parameter settings on model performance and size, according to at least one aspect of the present disclosure.

[0027] FIG. 9 presents results of methods that use less than 0.2% of the total parameter count compared to the second-best method on the California dataset in the LargeST benchmark, according to at least one aspect of the present disclosure.

[0028] FIG. 10 presents 64 learned shapes alongside their corresponding matches from the dataset, according to at least one aspect of the present disclosure.

[0029] FIG. 11 is a block diagram of a computer apparatus with data processing subsystems or components, according to at least one aspect of the present disclosure

[0030] FIG. 12 is a diagrammatic representation of an example computer system that includes a host machine within which a set of instructions to perform any one or more of the methodologies discussed herein may be executed, according to at least one aspect of the present disclosure.DESCRIPTION

[0031] The present specification describes a system and method for multivariate time-series forecasting based on univariate time-series modeling. The method integrates a sparse cross-period forecast with a shape bank component, leveraging the periodic nature of time-series data to achieve high efficiency and effectiveness. The shape bank component efficiently captures recurring patterns within time-series using an attention mechanism, enhancing the model’s capability to learn intra-period dynamics. The shape bank component provides a technical advantage in time-series forecasting by accounting for intra-period dynamics in univariate long time frame data.Attorney Docket No. 250127PCT / 9975WO01The combination of sparse temporal modeling and channel-independent processing represents a principled design choice grounded in both empirical evidence and theoretical considerations.

[0032] Achieving precise forecasts typically relies on powerful yet complex deep learning models, such as recurrent neural networks, temporal convolutional network, and Transformers. In recent years, there has been a growing interest in Longterm Time-series Forecasting (LTSF), which demands models to provide an extended predictive view for advanced planning. Although a longer predictive horizon offers convenience, it also introduces greater uncertainty. This demands models capable of extracting more extensive temporal dependencies from longer historical windows. Consequently, modeling becomes more complex to capture these long-term temporal dependencies. For instance, Transformer-based models often have millions or tens of millions of parameters, limiting their practical usability, especially in scenarios with restricted computational resources.

[0033] Recent advancements in the field of LTSF have seen a shift towards a Channel Independent (Cl) approach, especially when dealing with multivariate timeseries data. This strategy simplifies the forecasting process by focusing on individual univariate time-series within the dataset. Instead of the traditional approach, which utilizes the entire multivariate historical data to predict future outcomes, whereas Cl methodology utilizes a shared function for each univariate series. This approach provides a more targeted and simplified prediction model for each channel, reducing the complexity of accounting for inter-channel relationships. As a result, the main goal of state-of-the-art models in recent years has shifted towards effectively predict by modeling long-term dependencies, including periodicity and trends, in univariate sequences.

[0034] In one example of channel-independent forecasting, SparseTSF is a Sparse Softmax Tree Sampling Framework designed for machine learning and optimization tasks, particularly where efficient handling of sparse data structures is crucial. Sparse data structures, characterized by numerous zero or missing elements, render conventional dense storage and computation methods inefficient. A Softmax function is a mathematical function used in machine learning and statistics to transform a vector of numbers into a probability distribution.Attorney Docket No. 250127PCT / 9975WO01

[0035] SparseTSF employs algorithms optimized for sparse data [Lin et al., 2024], enabling efficient storage and computation by focusing resources on non-zero values and significant elements. SparseTSF enhances sampling efficiency by concentrating computational power on relevant branches rather than evaluating every possible path. Its scalability makes it suitable for large-scale machine learning tasks with sparse data, offering faster training and inference times compared to dense models. However, SparseTSF underperforms on spatio-temporal data due to its inability to capture intraperiod temporal dependencies.

[0036] The present disclosure improves on the SparseTSF by introducing a shape bank module to capture recurring patterns within time-series to the sparse time-series forecast model, enhancing the learning of intra-period dynamics. The disclosed method processes input time-series through a convolutional aggregation module, transforming it for the shape bank and cross-period sparse forecast modules. The shape bank module uses a linear layer and an efficient attention layer to model intra-period trends, complementing the cross-period sparse forecast module.

[0037] The present disclosure describes a shape bank component that is capable to model intra-period relationships in channel independent, sparse forecasting systems. The shape bank learns a set of patterns of length w, each represented as a key-value pair, and employs an attention mechanism to compute the output based on the input subsequence (query). This lightweight attention module is applied independently to each subsequence, focusing on modeling intra-period dynamics, which complements the cross-period sparse forecasting component in capturing temporal relationships.

[0038] FIG. 1 illustrates the system 100 for spatio-temporal forecasting. The system may include a computer apparatus as shown and described in FIG. 11 and / or computer system as shown and described in FIG. 12. It is contemplated that the arrangement of computing processor elements and device storage are configured as shown and described in FIG. 1. The system 100 is configured to receive input of spatially distinct [(x1), (x2), …, (xn)] time-series datasets 110 by an input layer 120. The spatially distinct time-series datasets 110 may be input as distinct inputs or as a multivariate input. It is contemplated that the input layer 120 is capable of handling any such input format. The system 100 includes control logic 130 configured to assign each time-series dataset 110 to a processor element 150 [P1, P2, …, Pn]. EachAttorney Docket No. 250127PCT / 9975WO01processor element 150 includes at least a time-series forecast module 160 and may additionally include a final forecast module 170. The output layer 140 is configured to output a final forecast 180. In some embodiments, the control logic 130 assigns one or more time-series datasets 110 to one or more processor elements 150. In one embodiment, the control logic 130 assigns one time-series dataset 110 to one processor element 150. In another embodiment, the control logic 130 assigns two or more time-series datasets 110 to one processor element 150.

[0039] In one embodiment, as shown in FIG. 2, the time-series forecast module 160 includes a convolutional aggregation module 161, a transform module 162, a segmentation module 163, a shape bank module 164, and a cross-period sparse forecast module 165. The time-series forecast module 160 being implemented on each of the processor elements 150 of the system 100.

[0040] In one embodiment, FIG. 3 illustrates the overall architecture 300 of the times series forecast module. A time-series dataset is input with a size of n × tinto the convolutional aggregation module. Given a spatio-temporal time-series with length tinand n dimensions / spatial locations, the input time-series is first processed with the convolutional aggregation module. The convolutional aggregation module computes the weighted sum along the time dimension at each time step for each spatial location. This module can be implemented with a convolutional layer with a filter size of w and a skip connection where w is the period length.

[0041] After the convolutional aggregation module, the input time-series is reshaped in the transformer module from n × tinto n × w × kinwhere tin:= w × kin. This operation converts the time-series to the frequency domain for both the shape bank mechanism and the cross-period sparse forecast mechanism. The frequencydomain dataset is segmented at each dimension of the input time-series into kinsubsequences of length w. Next, the frequency-domain dataset is fed into a sequence of core blocks (nblock). Within each block, the frequency-domain subsequence is first processed by the shape bank module and then the cross-period sparse forecast module. The output of the sequence of core blocks is reshaped from the frequencydomain back to the time-domain ( tout:= kout× w ) resulting in the time-series forecast output.Attorney Docket No. 250127PCT / 9975WO01

[0042] Of note, throughout this disclosure n, tin, w, d, and toutare used to denote the number of spatial locations, input time steps, period length, number of learned shapes, and output time steps, respectively.

[0043] Referring to FIG. 4, the computation of the weighted sum 400 using the convolutional aggregation module is shown schematically. There are two reasons behind the module design. First, it prevents the loss of information, as each time step after the convolutional aggregation module now has the contextual information from other time steps within the same period. Second, the aggregation module mitigates the impact of outliers.

[0044] In some embodiments, the cross-period sparse forecasting module includes a linear function 450 applied to each kinsubsequence to derive kout, as shown in FIG. 4.

[0045] FIG. 5 illustrates the ultra-compact shape bank component that consists of a linear layer that projects the input to the query / key space, and an efficient attention layer that computes the output. The ultra-compact shape bank component shown in FIG. 5 operates on each kinsubsequence independently with the weights shared across all subsequences.

[0046] Referring still to FIG. 5, given a subsequence, a linear layer is used first to obtain the query vector. Assuming the number of d shapes is specified in the shape bank; the query vector is multiplied with the key associated with each shape in the shape bank to obtain the attention scores. In some embodiments, the attention score is determined using a Rectified Linear Unit (ReLU) activation function or by a Softmax function. The ReLU activation function is a commonly used activation function in neural networks, particularly in deep learning. It is a simple yet effective non-linear function that introduces sparsity and helps neural networks learn complex patterns. Finally, the attention score is multiplied by the shape value in the shape bank to produce the output.

[0047] In one embodiment, the system disclosed herein may be a system for forecasting spatio-temporal data. The system may include one or more processor elements configured to obtain one or more spatially distinct time-series datasets and assign each of the one or more spatially distinct time-series datasets to at least one of the one or more processor elements. The one or more processors may be configured, for each of the one or more spatially distinct time-series datasets assigned to at leastAttorney Docket No. 250127PCT / 9975WO01one of the one or more processor elements, to generate a time-series forecast for the assigned one or more spatially distinct time-series datasets. To generate the timeseries forecast, the one or more processor elements may be configured to: process each assigned spatially distinct time-series dataset through a convolutional aggregation module, transform an output of the convolutional aggregation module into a frequency-domain representation, segment the frequency-domain representation into a plurality of subsequences, model intra-period dynamics of each of the plurality of subsequences using a shape-bank module, model inter-period dynamics by applying a cross-period sparse forecasting module to the frequency-domain representation, generate a frequency-domain forecast by integrating the intra-period dynamics with the inter-period dynamics, and transform the frequency-domain forecast to a time-series forecast. The one or more processors may be further configured to assemble the time-series forecasts generated for the one or more spatially distinct time-series datasets to generate a final forecast matching spatial and temporal dimensions of the one or more spatially distinct time-series datasets.

[0048] In some embodiments of the system, the shape bank module provides instructions to a processor element to: generate a query vector using a linear transformation, calculate an attention score between the query vector and a shape key of a shape bank database, and multiply the attention score and the corresponding shape value of the shape key to generate an intra-period dynamics output. The shape bank module may include a shape bank database where the shape bank database includes shape keys and corresponding shape values.

[0049] In some embodiments of the system, each subsequences of the plurality of subsequences to model intra-period dynamics corresponds to a period of length w. In some embodiments, the convolutional filter has a filter size defined by w.

[0050] In some embodiments of the system, the one or more processor elements are configured to repeat the modeling of intra-period dynamics and modeling interperiod dynamics as a number of core blocks to be repeated of core blocks (nblock) times. In some embodiments, the number of core blocks (nblock) is a learned hyperparameter.

[0051] In some embodiments of the system, calculating attention scores includes evaluating an ReLU activation function with respect to the query vectors and shape keys.Attorney Docket No. 250127PCT / 9975WO01

[0052] In some embodiments of the system, the one or more processor elements are further configured to train weights associated with the shape bank database on a plurality of intra-period shape patterns, the intra-period shape patterns having a period length, w. In some embodiments, the trained weights are associated with shape keys and corresponding shape values. In some embodiments, the one or more processors are further configured to compare the final forecast with real-time measured timeseries data; and retrain the shape bank database based on the comparison.

[0053] In some embodiments of the system, the system further includes an output device communicatively coupled to the one or more processor elements, the one or more processor elements configured to output a visual display of the final forecast, and based on the visual display, performing one or more actions affecting real-time measured time-series data.

[0054] In some embodiments of the system, the spatially distinct time-series datasets are associated with measured indicators, and wherein the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands.

[0055] In some embodiments of the system, the one or more processor elements are configured to determine optimized hyper-parameters, wherein the optimized hyper-parameters include an optimal number of intra-period shape patterns and nblock. In some embodiments, the one or more processor elements are configured to determine an associated error and complexity of optimized hyper-parameters.

[0056] In one embodiment of the system, the one or more processor elements are configured to operate in parallel. In some embodiments, the one or more processor elements are one of computing processor units or graphical processing units. In another embodiment of the system, two or more spatially distinct time-series datasets are assigned to one of the one or more processor elements.

[0057] Referring now to FIG. 6, illustrated herein is a method for time-series data forecasting. The method 600 may include processing 610 a time-series dataset through a convolutional aggregation module, transforming 620 an output of the convolutional aggregation module into a frequency-domain representation, segmenting 630 the frequency-domain representation into a plurality of subsequences each corresponding to a period of length w, modeling intra-period dynamics 640 of each of the plurality of subsequences by a shape bank module, modeling inter-periodAttorney Docket No. 250127PCT / 9975WO01dynamics 650 by applying a cross-period sparse forecasting module to the frequencydomain representation; generating a frequency-domain forecast 660 by integrating the intra-period dynamics with the inter-period dynamics; and transforming 670 the frequency-domain forecast to a time-series forecast.

[0058] In some embodiments, modeling intra-period dynamics may include the steps as shown in FIG. 7. A method of modeling intra-period dynamics may include generating a query vector 710 using a linear transformation, calculating an attention score 720 between the query vector and a shape key, and multiplying 730 the attention score and the related shape value of the shape key such that the multiplying generates an intra-period dynamics output. In some embodiments, the shape key corresponds to a related shape value as stored in a shape bank database.

[0059] In some embodiments, a method for time-series data forecasting may include processing a time-series dataset through a convolutional aggregation module, transforming an output of the convolutional aggregation module into a frequencydomain representation, segmenting the frequency-domain representation into a plurality of subsequences each corresponding to a period of length w, modeling intra-period dynamics of each of the plurality of subsequences, modeling inter-period dynamics by applying a cross-period sparse forecasting module to the frequencydomain representation; generating a frequency-domain forecast by integrating the intra-period dynamics with the inter-period dynamics, and transforming the frequencydomain forecast to a time-series forecast. In this embodiment, modeling intra-period dynamics may include generating a query vector using a linear transformation, calculating an attention score between the query vector and a shape key, and multiplying the attention score and the related shape value of the shape key such that the multiplying generates an intra-period dynamics output.

[0060] In some embodiments of the method, the time-series dataset is segmented into subsequences corresponding to a period of length, w. In some embodiments, the shape keys and corresponding shape values correspond to the period of length, w.

[0061] In some embodiments, calculating attention scores may include evaluating an ReLU activation function with respect to the query vectors and shape keys.

[0062] In some embodiments, the method may further include training shape keys and the related shape values on a plurality of intra-period shape patterns, wherein trained weights are associated with paired shape keys and related shape values.Attorney Docket No. 250127PCT / 9975WO01

[0063] In some embodiments, the method may further include comparing the timeseries forecast with real-time measured time-series data and retraining the retraining the shape keys and the related shapes based on the comparison.

[0064] In some embodiments, the method may further include outputting a visual display of the time-series forecast and based on the visual display, performing one or more actions affecting real-time measured time-series data.

[0065] In some embodiments of the method, the time-series dataset is associated with measured indicators. In some embodiments, the measured indicators may be related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands.

[0066] In some embodiments, the method may further include determining optimized hyper-parameters where the optimized hyper-parameters may include an optimal number of intra-period shape patterns and nblock. In some embodiments of the method, determining may include determining associated error and complexity of optimized hyper-parameters.

[0067] In some embodiments, disclosed herein is a non-transitory computer-readable medium having instructions stored thereon, that when executed by a processor, cause the processor to model intra-period dynamics of a time-series dataset. The instructions may include features and modules as depicted in FIG. 5, for example. Modeling intra-period dynamics may include generating a query vector using a linear transformation, calculating an attention score between the query vector and a shape key, wherein the shape key corresponds to a related shape value, and multiplying the attention score and the related shape value of the shape key, wherein the multiplying generates an intra-period dynamics output.

[0068] In some embodiments, the non-transitory computer-readable medium is used in coordination and in addition to one or more long time-series forecasting models. The long time-series forecasting model may be, for example, Diffusion Convolutional Recurrent Neural Network (DCRNN), Spatio-Temporal Graph Convolutional Networks (STGCN), Attribute-augmented Spatio-Temporal Graph Convolutional Network (AST-GCN), Adaptive Graph Convolutional Recurrent Network (AGCRN), Spatial-Temporal Graph Ordinary Differential Equation Networks (STGODE), Decoupled Spatial-Temporal Graph Neural Network (DST-GNN), Dynamic Graph Convolutional Recurrent Network (DGCRN), Sparse Time-SeriesAttorney Docket No. 250127PCT / 9975WO01Forecasting (SparseTSF), Dynamic Spatial-Temporal Aware Graph Neural Network (DSTAGNN), all-Multi-Layer Perceptron (all-MLP) time-series forecasting architecture (RPMixer), or any suitable model known in the art.

[0069] Implementations may include one or more of the following features. The instructions may provide for the shape keys and corresponding shape values to correspond to the period of length, w. The instructions may provide for comparing the intra-period dynamics with real-time measured time-series data; and retraining the shape bank based on the comparison. The trained weights are associated with paired shape keys and corresponding shape values. The time-series dataset is associated with measured indicators, and where the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands. The optimized hyper-parameters may include an optimal number of intra-period shape patterns and nblock, where determining may include determining associated error and complexity of optimized hyperparameters. Calculating attention scores may include evaluating an ReLU activation function with respect to the query vectors and shape keys.

[0070] FIG. 8 illustrates the effect of different hyper-parameter settings on model performance (e.g., average MAE) and size. The MAE has been shown on both the test and validation partitions of the SD dataset. The SD dataset is used to study the effect of different hyper-parameters on the model architecture disclosed in this specification. The focus is on three key hyper-parameters: the number of core blocks nblockthe number of shapes (d) in the shape bank, and the period (w). The analysis described in this specification examines these hyper-parameters’ impact on both forecasting accuracy (measured by average MAE) and model size. The experimental results for this hyper-parameter study are presented in FIG. 8. The average MAE is reported on both test and validation partitions to assess the generalizability of the hyper-parameters across dataset partitions.

[0071] The number of core blocks nblockdemonstrates a linear relationship with the model size, consistent with the analysis described above. As the number of core blocks were increased, a reduction in MAE is observed. However, the improvement in MAE becomes minimal between nblock+ 4 and nblock+ 6 for both validation and test sets. Consequently, nblock+ 4 is used in all of the subsequent experiments to balance performance and model complexity. The number of shapes d in the shape bank alsoAttorney Docket No. 250127PCT / 9975WO01exhibits a linear relationship with model size, aligning with the analysis described previously. Regarding MAE, setting d = 16 was found to yield the best performance across both validation and test sets. Therefore, d = 16 is adopted for all other experiments disclosed in this specification. The relationship between the period w and model size is more complex. Among the six w settings tested, w = 24 produces the smallest model, with size increasing for both smaller and larger values. Considering MAE, it is observed that w = 12 leads to the best performance on both test and validation sets. As a result, set w = 12 in all other experiments.

[0072] The model disclosed in this specification, with the hyper-parameters found previously, learns 64 shapes through its shape bank components. To validate the relevance of these patterns, an analysis was conducted using the SD dataset. The 64 shapes were extracted from the trained SD model and searched for their closest matches within the SD dataset using Matrix Profile. FIG. 10 presents these 64 learned shapes alongside their corresponding matches from the dataset. Visual inspection confirms that each shape indeed represents a genuine pattern found in the original data, demonstrating the model’s ability to capture meaningful temporal structures. FIG.10 illustrates the shapes learned by the model can be found in the dataset.Computational Efficiency and Comparative Results

[0073] Spatio-temporal forecasting methods typically combine graph modeling architectures, such as graph convolutional networks (GCNs) or graph attention networks (GATs), with sequential modeling architectures like recurrent neural networks (RNNs), temporal convolutional networks (TCNs), or transformers. Graph modeling components process spatial relationships from the input graph data, while sequential modeling components capture temporal dependencies in time-series data.

[0074] Recent models in this domain, including DCRNN, STGCN, ASTGCN, AGCRN, STGODE, D2STGNN, and DGCRN, exemplify this integration of spatial and temporal modeling. However, an alternative direction explored by methods such as DSTAGNN and RPMixer bypasses reliance on predefined spatial graphs. Instead, these methods infer relationships between locations directly from time-series data. Despite their differences, many of these approaches learn the dependencies between different locations, resulting in model complexities of at least O(n) with respect to the number of locations. Whereas linear models employing the independent channel strategy have shown competitive performance, particularly in comparison to moreAttorney Docket No. 250127PCT / 9975WO01complex transformer-based solutions. Compact architectures, such as SparseTSF, further push the boundaries of efficiency while maintaining strong predictive performance, and the disclosed model, referred to as SuperSparseTSF, enhances the predictive performance of SparseTSF by including linear components to model intraperiod features.

[0075] The effectiveness of the cross-period sparse forecast component is based on the periodicity assumption, as shown herein. Given a univariate time-series X and its period w, X can be decomposed into the periodic component P and trend component T whereX = P + T (1)P i] = P[i + w] (2)

[0076] Assume the length of X is tin+ toutwhere the first tintime steps are the input and the last touttime steps are the prediction target. Given that kin=kout= w—, Xin= X [0: tin], and Xout= X [tin: tout], for any i ∈ [0, ..., kout] and l ∈[0,...,w] the cross-period sparse forecast component can be formulated with Eq. (3) where fiis the sparse forecast function for the ith output subsequence.Xout[iw + l] = fi(Xin[l], Xin[w + l], ... , Xin[(kin− 1)w + l]) (3)

[0077] For simplicity, Eq. (3) is denoted asXout[iw + l] = fi(Xin[jw + l]), j = 0, ... , kin(4)

[0078] If Eq. (1) is plugged into Eq. (4), Eq. (5) is obtained.Pout[iw + l] + Tout[iw + l] = fi(Pin[jw + l] + Tin[jw + l]) (5)

[0079] Due to the periodicity described in Eq. (2), Eq. (5) can be simplified to Eq. (6).P[l] + Tout[iw + l] = fi(P[l] + Tin[jw + l]) (6)

[0080] Given that P[l] is a fixed value for a given I and is present in both the input and output of the forecasting function, the parameters of the cross-period sparse forecast component focus on learning the trends of the time-series.

[0081] This analysis highlights both the type of information captured by the crossperiod sparse forecast component and the information that is not captured by it. Since the function ft is fixed regardless of Z, it cannot learn the correct relationship between Toutand Tinwhen the mapping between them varies with respect to Z, regardless ofAttorney Docket No. 250127PCT / 9975WO01the architecture used for fi. The ultra-compact shape bank component addresses this issue.

[0082] The same univariate time-series X can be used to analyze the effectiveness of the shape bank component. This time, the function f is used to represent the shape bank component. For any i ∈ [0, w, 2w, ... , koutw], the output is computed with Eq. (7).Xout[i : i + w] = f(Xin[i − tin: i − tin+ w]) (7)

[0083] If Eq. (1) is also plugged into Eq. (7), Eq. (8) is obtained.Pout[i : i + w] + Tout[i : i + w] = f(Pin[i − tin: i − tin+ w] + Tin[i − tin: i − tin+ w]) (8)

[0084] Given that tinis a multiple of w, Eq. (8) can be simplified into Eq. (9) with Eq. (2).P[0 : w] + Tout[i : i + w] = f(P[0 : w] + Tin[i − tin: i − tin+ w]) (9)

[0085] Since P[0 : w] is a fixed vector in both the input and output of, the shape bank component is once again focused on modeling the trend of the time-series. However, by comparing Eq. (9) with Eq. (6), it can be observed that the shape bank component focuses on modeling the trend variation within a period, while the sparse forecasting component focuses on the cross-period trend. Together, the shape bank component and the sparse forecasting component complement each other.

[0086] The above complexity analysis shows that the disclosed method maintains similar time and space complexities to SparseTSF, with a slightly higher parameter count due to the shape bank component. Experiments using the LargeST datasets demonstrate SuperSparseTSF's superior performance and efficiency compared to more than a dozen other baseline methods. The model is capable of generalization, showing minimal performance differences across different regions. A hyper-parameter study on the SD dataset identified optimal settings for core blocks, shapes in the shape bank, and period length, as shown in FIG. 8. Visualization of the shape bank, as shown in FIG. 10, confirms that the learned shapes represent genuine patterns in the data, validating the model's ability to capture meaningful temporal structures.

[0087] FIG. 9 illustrates the disclosed method, SuperSparseTSF, uses less than 0.2% of the total parameter count compared to the second-best method on the CA dataset in the LargeST benchmark. However, as illustrated in FIG. 9, applying SparseTSF to spatio-temporal data via the channel independent strategy revealsAttorney Docket No. 250127PCT / 9975WO01notable performance limitations. SparseTSF and its variants underperform on such data, likely due to limited learning capabilities. Specifically, SparseTSF’s compactness stems from segmenting the input time-series into subsequences based on a user-specified period w, focusing solely on modeling cross-period relationships while neglecting intra-period temporal dependencies.

[0088] The complexity of the disclosed method, SuperSparseTSF, is analyzed in terms of time complexity, space complexity, and number of model parameters. Table 1 summarizes the results of the complexity analysis for the SuperSparseTSF method alongside the complexities of the baseline variant of SparseTSF. Notably, despite the superior performance demonstrated in FIG. 9, SuperSparseTSF maintains identical time and space complexities to the baseline variant of SparseTSF, with only a marginally higher parameter count to account for the shape bank and multi-layer design.Table 1. Complexity analysisSuperSparseTSF SparseTSF Time O(nt2in) O(nt2in) Space O(ntin) O(ntin)⌊w / 2⌋ + 1 + (nblock− 1)(w2+ 2wd + t2in / w2)LZ J yParameter+ (w2+ 2wd + tintout / w2)⌊w / 2⌋ + 1 + (tintout / w2)

[0089] The time complexity of the model disclosed in this specification can be analyzed by examining each process illustrated in FIG. 3. The convolutional layer’s time complexity is O(ntin). For the shape bank component, the linear layer has a time complexity of O(nw2kin) = O(nwtin). Since w is a constant, this simplifies to O(ntin). Both multiplications in the shape bank component have a time complexity of O(nwdkin) = O(ntin). As d is also a constant, this again simplifies to O(ntin). The cross-period sparse forecast component’s time complexity is either O(nwk2in) = O(nt / w2) = O(ntin) or O(nwkinkout) = O(ntt / w2) = O(ntintout). For spatio-temporal datasets, the typical relationship between n, tin, and toutis n > tin≥ tout. Therefore, the overall time complexity of the method disclosed in this specification is O(nt2in). This complexity is comparable to that of SparseTSF, which also has a time complexity of O(nt2in), indicating that the method is suitable for large-scale datasets.Attorney Docket No. 250127PCT / 9975WO01

[0090] The space complexity of the method disclosed in this specification can be derived from FIG. 5. Begin by examining the sizes of the input, intermediate, and output tensors. Four distinct tensor sizes are identified: 1) n × tin, 2) n x w x kin, 3) n x tout, and 4) n x w x kout. Given that tin= w x kinand tout= w x kout, these tensors contribute two different space costs: O(ntin) and O(ntout). Considering the weight tensors associated with different components, only the weight matrix from the linear layer of the cross-period sparse forecast component scales with the input time-series size. The space complexity of this weight matrix is O(tintout) or O(t2in). For spatio-temporal datasets, the typical relationship between n, tin, and toutis n > tin≥ tout. Consequently, the overall space complexity of the method disclosed in this specification is O(ntin). This space complexity is equivalent to that of the SparseTSF baseline method, indicating that the approach described in this specification is suitable for large-scale datasets.

[0091] The number of parameters within the method disclosed in this specification can be computed with the following equation.[—I + 1 + (nblock— 1) (w2+ 2wd + + (w2+ 2wd +inL2J \ w21 \ w2J

[0092] The first term, [y] + 1, is from the convolutional aggregation module, e.g., the filter of the convolutional layer. In each block, the term w2+ 2wd is from the ultra-compact shape bank disclosed in this specification, and the termsandm2ltare from the cross-period sparse forecast module. Comparing to the SparseTSF model, the extra cost in terms of learnable parameters is the w2+ 2wd term from each block.

[0093] The experiments disclosed in this specification utilized the LargeST datasets, which encompass traffic data from 8,600 sensors across California. Following this methodology four distinct sub-datasets were generated: SD, GBA, GLA, and CA. These sub-datasets represent sensor data from San Diego (716 sensors), the Greater Bay Area (2,352 sensors), Greater Los Angeles (3,834 sensors), and the entire California, respectively. To ensure consistency with the experimental setup in, the focus was exclusively on traffic data from the year 2019. The original sensor readings, recorded every 5 minutes, were aggregated into 15-m inute intervals, resulting in 96 intervals per day and a total of 35,040 time steps. Each sub-datasetAttorney Docket No. 250127PCT / 9975WO01was then split into training, validation, and test sets in a 6:2:2 ratio. The primary task was to forecast the next 12 intervals for each sensor at each timestamp. Performance was evaluated using mean absolute error (MAE), root mean squared error (RMSE) and mean absolute percentage error (MAPE).

[0094] Benchmark experiments included 19 baseline methods. One solution for addressing the limited learning capabilities problem is to increase the number of parameters in the model. One way to achieve this goal is by replacing the linear model with a two-layer multilayer perceptron (MLP). Therefore, the SparseTSF+MLP variant is included as one of the baseline methods. Additionally, another variant where an eight-layer MLP (e.g., two-layer MLPx4) is used instead of a two-layer MLP (e.g., SparseTSF+MLPx4).

[0095] To demonstrate the benefits of the ultra-compact attention module disclosed in this specification, a variant of SuperSparseTSF is introduced that uses standard attention for the shape bank mechanism. Additionally, other general time-series forecasting methods were included in the comparison, including the linear model, TSMixer, RPMixer, and iTransformer. The same hyperparameter setting (nblock= 4, d = 16, w = 12) is used for the SuperSparseTSF method disclosed in this specification across all four datasets. This hyperparameter configuration was determined based on the optimization study as shown in FIG. 8.

[0096] Comparing the SuperSparseTSF method with other methods, it was observed that the disclosed method achieved the best performance across all four datasets, attaining state-of-the-art level performance. Moreover, when considering the model size (e.g., number of learnable parameters), it is also relatively lightweight. The second-best method across different datasets uses at least 10 times more parameters than the method disclosed in this specification.

[0097] Next, the focus was placed on the performance of SparseTSF and its variants, as these methods serve not only as baseline methods but also for ablation studies. First, SparseTSF shows much worse performance compared to the method disclosed in this specification, indicating significant room for improvement. The first attempted improvement utilizes MLP instead of a linear layer in the cross-period sparse forecast component. This improvement enhances the SparseTSF method, but its performance still falls short of the method disclosed in this specification.Attorney Docket No. 250127PCT / 9975WO01

[0098] The number of layers in the MLP was increased to match the parameter count of the method disclosed in this specification. This variant is called SparseTSF+MLPx4 in the table. Increasing the layer count further improves performance, allowing for a fair comparison between systems with and without the ultra-compact shape bank component disclosed in this specification. When comparing these two methods, the method disclosed in this specification again outperforms the alternative, demonstrating the necessity of adopting the ultra-compact shape bank component disclosed in this specification in the forecasting system.

[0099] Lastly, SparseTSF+SA also uses a shape bank component, but instead of the ultra-compact shape bank design disclosed in this specification, it employs a standard attention design. SparseTSF+SA improves upon the SparseTSF+MLPx4 method, showing the importance of modeling intra-period dependency. However, the standard attention design also increases the cost of deploying the model as it dramatically increases the model size. Comparing SparseTSF+SA with the SuperSparseTSF disclosed in this specification, it was observed that the method disclosed in this specification is not only much lighter but also performs better. This observation further reinforces the necessity of the ultra-compact design disclosed in this specification over the standard design.

[0100] In summary, comparison with SparseTSF+MLPx4 demonstrates the importance of modeling intra-period dependency. Comparison with SparseTSF+SA shows that the ultra-compact shape bank design disclosed in this specification is both more efficient and effective than the standard design. Finally, the SuperSparseTSF disclosed in this specification is the best method, achieving superior performance while being at least 10 times lighter than the second-best method.

[0101] To evaluate the generalization capability of different models across different regions, the models were trained on one dataset and tested on another. The CA dataset was excluded from this set of experiments as it is a superset of the other three datasets. Only methods capable of handling dimension mismatches between the training and test datasets were included in this study. These comprise methods applied through the channel independent strategy (e.g., Linear, SparseTSF, and SuperSparseTSF) and a method that learns dependencies between different dimensions using an attention mechanism (e.g., iTransformer). The results of the generalization capability study are reported in Table 2.Attorney Docket No. 250127PCT / 9975WO01Table 2. Model generalization capability across different regions (values in average MAE).Train Test DataMethod Param Data SD GBA GLA Linear 3.5K 26.30 28.14 28.80 iTransformer 6.5M 19.63 108.10 110.56 SparseTSF 73 24.66 28.03 27.36 SD SparseTSF+MLP 2K 21.85 23.66 23.66 SparseTSF+MLPx4 13.5K 20.14 21.84 21.87 SparseTSF+SA 8.4M 18.13 35.31 37.80 SuperSparseTSF 13K 16.48 18.41 18.01 Linear 3.5K 27.96 26.40 27.83 SparseTSF 73 25.33 25.55 25.68 SparseTSF+MLP 2K 22.16 22.36 22.88 SparseTSF+MLPx4 13.5K 20.84 21.23 21.33 SparseTSF+SA 8.4M 18.68 19.42 19.49 SuperSparseTSF 13K 16.83 17.69 17.59 Linear 3.5K 29.40 28.87 26.75 SparseTSF 73 24.74 25.88 25.06 SparseTSF+MLP 2K 22.26 23.36 22.61GLASparseTSF+MLPx4 13.5K 20.77 21.72 20.94 SparseTSF+SA 8.4M 32.37 29.65 18.57 SuperSparseTSF 13K 16.46 17.68 16.79

[0102] Methods adopting the channel independent strategy typically demonstrate good generalizability. The performance difference between results obtained from the test set of the same region and a different region is minimal. This highlights the advantage of methods utilizing the channel independent strategy. Conversely, iTransformer, which learns relationships between dimensions, cannot generalize effectively across datasets. Its performance degraded significantly when tested on datasets from different regions. Due to scalability issues faced by iTransformer when training with larger datasets, only the iTransformer model trained with the SD dataset was tested.

[0103] This specification discloses SuperSparseTSF, a method that combines an ultra-compact shape bank component with a cross-period sparse forecast component. SuperSparseTSF effectively leverages the inherent periodicity typically found in spatio-temporal data, modeling intra-period dependencies through the shape bankAttorney Docket No. 250127PCT / 9975WO01component and inter-period dependencies via the cross-period sparse forecast component.

[0104] Experiments demonstrated that SuperSparseTSF achieves state-of-the-art performance while maintaining a lightweight architecture compared to alternative solutions. Notably, SuperSparseTSF exhibits remarkable generalization capabilities across different datasets, highlighting its potential as an effective model architecture for a time-series foundation model. The lightweight nature of SuperSparseTSF makes it an attractive candidate for edge computing applications and real-time forecasting scenarios.

[0105] SuperSparseTSF represents a significant advancement in efficient and accurate time-series forecasting, striking a balance between model expressiveness and computational efficiency. Its strong performance, generalization capabilities, and potential for wide-ranging applications position it as a valuable tool for researchers and practitioners across various domains dealing with time-series analysis and forecasting.Compute Environments

[0106] Implementation of the foregoing forecasting techniques may be realized in one or more computing environments. In particular, the system 100 and the time series forecast module 160 (including the convolutional aggregation module 161, transform module 162, segmentation module 163, shape bank module 164, and cross-period sparse forecast module 165) may be implemented as computer-executable instructions stored on one or more non-transitory computer-readable media and executed by one or more processors. FIG. 11 illustrates a representative computer apparatus 1100 that may serve as any of the processor elements 150 and / or execute the time series forecast module 160 to generate one or more time-series forecasts that are assembled into the final forecast 180. FIG. 12 illustrates an example computer system 1200 that may provide a host machine 1202 and, in some implementations, a virtualized or cloud-based execution environment in which multiple instances of the time series forecast module 160 execute in parallel to process respective spatially distinct time-series datasets 110 and to produce the final forecast 180.

[0107] A system of one or more computers can be configured to perform particular operations or actions associated with the system for forecasting spatio-temporal data described herein by virtue of having software, firmware, hardware, or a combinationAttorney Docket No. 250127PCT / 9975WO01thereof installed on the system that in operation causes the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. Other embodiments include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0108] FIG. 11 is a block diagram of a computer apparatus 1100 with data processing subsystems or components, according to at least one aspect of the present disclosure. The computer apparatus 1100 is representative of the system 100 shown in FIG. 1. The subsystems shown in FIG. 11 are interconnected via a system bus 1102. Additional subsystems such as an output device 1104 (e.g., printer, monitor, speaker, display adapter), an input device 1106 (e.g., keyboard), a storage device 1108 (e.g., fixed disk) (or other memory comprising computer readable media), and others are shown. Peripherals and input / output (I / O) devices, which couple to an I / O controller 1110 (which can be a processor or other suitable controller), can be connected to the computer apparatus 1100 by any number of means known in the art, such as a serial port 1112. For example, the serial port 1112 or an external interface 1114 can be used to connect the computer apparatus 1100 to a wide area network such as the Internet, a mouse input device, or a scanner. The interconnection via the system bus 1102 allows a central processor 1116 to communicate with each subsystem and to control the execution of instructions from system memory 1118 or the storage device 1108, as well as the exchange of information between subsystems. The system memory 1118 and / or the storage device 1108 may embody a computer-readable medium. The processor 1116 and the system bus 1102 may couple various system components including the system memory 1118, such as read only memory 1120 (ROM) and random-access memory 1122 (RAM), to the processor 1116. The computer apparatus 1100 can include a cache 1124 of high-speed memory connected directly with, in close proximity to, or integrated as part of the processor 1116.

[0109] The computer apparatus 1100 can copy data from the system memory 1118, ROM 1120, RAM 1122, and / or the storage device 1108 to the cache 1124 for quick access by the processor 1116. In this way, the cache 1134 can provide a performance boost that avoids processor delays while waiting for data. These andAttorney Docket No. 250127PCT / 9975WO01other modules can control the processor 1116 to perform various actions. Other system memory 1118 may be available for use as well. The system memory 1118 can include multiple different types of memory with different performance characteristics. The processor 1116 can include any general-purpose processor and a hardware module or software module, such as modules 1126 (e.g., MOD 1 - MOD n) stored in the storage device 1108, to control the processor 1116 as well as a special-purpose processor where software instructions are incorporated into the actual processor design. The processor 1116 may essentially be a completely self-contained computing system, containing multiple cores or processors, a system bus, memory controller, cache, etc. A multi-core processor may be symmetric or asymmetric.

[0110] In the example of FIG. 11, the processor 1116 executes one or more software modules 1126 stored in the system memory 1118 and / or the storage device 1108. The software modules 1126 may include computer-executable instructions implementing the time series forecast module 160 and, in some implementations, one or more of the convolutional aggregation module 161, transform module 162, segmentation module 163, shape bank module 164, and cross-period sparse forecast module 165. During operation, the processor 1116 obtains one or more spatially distinct time-series datasets 110 via the external interface 1114 and / or the serial port 1112, processes the datasets through the time series forecast module 160, and outputs one or more forecasts via the output device 1104. In some implementations, the AI / ML module(s) 1128 accelerate one or more computations associated with the shape bank module 164 and / or cross-period sparse forecast module 165, including matrix multiplications, activation functions, and linear projections performed on period-aligned subsequences of length, w. When the computer apparatus 1100 serves as a processor element 150, the control logic 130 may assign the spatially distinct timeseries datasets 110 to the processor 1116 for execution by the time series forecast module 160, and the resulting time-series forecasts may be provided for assembly into the final forecast 180.

[0111] To enable user interaction with the computer apparatus 1100, the input device 1106 can represent any number of input mechanisms, such as a microphone for speech, a touch-protected screen for gesture or graphical input, keyboard, mouse, motion input, speech and so forth. The output device 1104 can also be one or more of a number of output mechanisms, such as, for example, printers, monitors, speakers,Attorney Docket No. 250127PCT / 9975WO01display adapters. In some instances, multimodal systems enable a user to provide multiple types of input to communicate with the computer apparatus 1100. The external interface 1114 (communications interface) can govern and manage the user input and system output. There may be no restriction on operating on any particular hardware arrangement and therefore the basic features here may be substituted for improved hardware or firmware arrangements as they are developed.

[0112] The storage device 1108 can be a non-volatile memory and can be a hard disk or other types of computer readable media which can store data that are accessible by the computer apparatus 1100, such as magnetic cassettes, flash memory cards, solid state memory devices, digital versatile disks, cartridges, random access memory, read only memory, and hybrids thereof.

[0113] The storage device 1108 can include software modules for controlling the processor 1116. Other hardware or software modules are contemplated. The storage device 1108 can be connected to the system bus 1102. In some embodiments, a hardware module that performs a particular function can include a software component stored in a computer-readable medium in connection with the necessary hardware components, such as the processor 1116, system bus 1102, output device 1104, and so forth, to carry out the function. For clarity of explanation, in some instances the present technology may be presented as including individual functional blocks comprising devices, device components, steps or routines in a method embodied in software, or combinations of hardware and software.

[0114] Artificial intelligence (Al) and machine learning (ML) modules 1128 (Al I ML) embedded within the computer apparatus 1100 enables advanced predictive analytics, transforming historical and real-time data into actionable insights. High-performance Tensor Processing Units (TPUs) and Graphical Processing Unites (GPUs), and Central Processing Units (CPUs) support continuous training of Al I ML models that enhance slotting optimization, pick-path efficiency, and demand forecasting. Al-driven algorithms analyze real-time operational data to anticipate potential stockouts, bottlenecks, or equipment failures, allowing the system to adjust task allocations proactively. These Al I ML models are housed on cloud servers 1130, enabling parallel processing and providing adaptive, scalable insights across multiple cloud 1132 environments or cloud service providers. In some embodiments, the Al I ML modules 1128 may be located remotely from the computer apparatus 1100. InAttorney Docket No. 250127PCT / 9975WO01these instances, data may be provided to the Al I ML modules 1128 via the system bus 1102, the cloud 1132, and I or the servers 1130.

[0115] Leveraging TPUs, GPUs, and CPUs, the computer apparatus 1100, through the Al I ML modules 1128, continuously trains the ML models to improve functions such as distributing compute load across the one or more processor elements, for example. Al-driven algorithms analyze real-time operational data to enable the computer apparatus 1100 to proactively adjust task allocations and priorities. These Al models are housed on cloud servers 1130, where large datasets can be processed in parallel, providing scalable, adaptive insights to the computer apparatus 1100 for managing functions such as distributing compute load across to the one or more processor elements, for example.

[0116] FIG. 12 is a diagrammatic representation of an example computer system 1200 that includes a host machine 1202 within which a set of instructions to perform any one or more of the methodologies discussed herein may be executed, according to at least one aspect of the present disclosure. The computer system 1200 is representative of the system 100 shown in FIG. 1. In various aspects, the host machine 1202 operates as a standalone device or may be connected (e.g., networked) to other machines. In a networked deployment, the host machine 1202 may operate in the capacity of a server or a client machine in a server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The host machine 1202 may be a computer or computing device, a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a cellular telephone, a portable music player (e.g., a portable hard drive audio device such as an Moving Picture Experts Group Audio Layer 3 (MP3) player), a web appliance, a network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine. Further, while only a single machine is illustrated, the term “machine” shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein.

[0117] The example computer system 1200 includes the host machine 1202, running a host operating system (OS) 1204 on a processor or multiple processor(s) / processor core(s) 1206 (e.g., a central processing unit (CPU), a graphics processing unit (GPU), or both), and various memory nodes 1208. The host OS 1204Attorney Docket No. 250127PCT / 9975WO01may include a hypervisor 1210 which is able to control the functions and / or communicate with a virtual machine (“VM”) 1212 running on machine readable media. The VM 1212 also may include a virtual CPU or vCPU 1214. The memory nodes 1208 may be linked or pinned to virtual memory nodes or vNodes 1216. When the memory node 1208 is linked or pinned to a corresponding vNode 1216, then data may be mapped directly from the memory nodes 1208 to the corresponding vNode 1216.

[0118] All the various components shown in host machine 1202 may be connected with and to each other or communicate to each other via a bus (not shown) or via other coupling or communication channels or mechanisms. The host machine 1202 may further include a video display, audio device or other peripherals 1218 (e.g., a liquid crystal display (LCD), alpha-numeric input device(s) including, e.g., a keyboard, a cursor control device, e.g., a mouse, a voice recognition or biometric verification unit, an external drive, a signal generation device, e.g., a speaker,) a persistent storage device 1220 (also referred to as disk drive unit), and a network interface device 1222. The host machine 1202 may further include a data encryption module (not shown) to encrypt data. The components provided in the host machine 1202 are those typically found in computer systems that may be suitable for use with aspects of the present disclosure and are intended to represent a broad category of such computer components that are known in the art. Thus, the system 1200 can be a server, minicomputer, mainframe computer, or any other computer system. The computer may also include different bus configurations, networked platforms, multi-processor platforms, and the like. Various operating systems may be used including UNIX, LINUX, WINDOWS, QNX ANDROID, IOS, CHROME, TIZEN, and other suitable operating systems.

[0119] The disk drive unit 1224 also may be a Solid-state Drive (SSD), a hard disk drive (HDD) or other which includes a computer or machine-readable medium on which is stored one or more sets of instructions and data structures (e.g., data / instructions 1226) embodying or utilizing any one or more of the methodologies or functions described herein, for example, the Time Series Forecast Module 160 and the Final Forecast Module 170. The data / instructions 1226 also may reside, completely or at least partially, within the main memory node 1208 and / or within the processor(s) 1206 during execution thereof by the host machine 1202. The data / instructions 1226 may further be transmitted or received over a network 1228 viaAttorney Docket No. 250127PCT / 9975WO01the network interface device 1222 utilizing any one of several well-known transfer protocols (e.g., Hyper Text Transfer Protocol (HTTP)).

[0120] The processor(s) 1206 and memory nodes 1208 also may comprise machine-readable media. The term "computer-readable medium" or “machine-readable medium” should be taken to include a single medium or multiple medium (e.g., a centralized or distributed database and / or associated caches and servers) that store the one or more sets of instructions. The term "computer-readable medium" shall also be taken to include any medium that is capable of storing, encoding, or carrying a set of instructions for execution by the host machine 1202 and that causes the host machine 1202 to perform any one or more of the methodologies of the present application, or that is capable of storing, encoding, or carrying data structures utilized by or associated with such a set of instructions. The term “computer-readable medium” shall accordingly be taken to include, but not be limited to, solid-state memories, optical and magnetic media, and carrier wave signals. Such media may also include, without limitation, hard disks, floppy disks, flash memory cards, digital video disks, random access memory (RAM), read only memory (ROM), and the like. The example aspects described herein may be implemented in an operating environment comprising software installed on a computer, in hardware, or in a combination of software and hardware.

[0121] FIG. 12 illustrates an example computer system 1200 in which the methodologies described herein may be executed by the host machine 1202. In some implementations, the data / instructions 1226 stored in memory node 1208 and / or persistent storage 1220 include instructions implementing the system 100 and the time series forecast module 160 (including one or more of modules 161-165). The processor(s) / processor core(s) 1206 may execute the data / instructions 1226 directly on the host machine 1202 and / or via one or more virtual machines 1212 under control of the hypervisor 1210. In a parallel implementation, multiple instances of the time series forecast module 160 may execute on respective vCPU(s) 1214 to process different spatially distinct time-series datasets 110 (or different partitions of a multivariate dataset), with intermediate and / or final forecasts exchanged via the network 1228 for assembly into the final forecast 180.

[0122] In some implementations, the host machine 1202 communicates with servers 1230 and / or one or more remote computing nodes over the network 1228 toAttorney Docket No. 250127PCT / 9975WO01distribute execution of the time series forecast module 160 and to support processing of large-scale spatio-temporal datasets.

[0123] Artificial intelligence (Al) and machine learning (ML) modules 1232 may be integrated within the host machine 1202 or the computer system 1200 to train the shape bank component on largescale time-series data. These intelligent systems may be accelerated by high-performance Tensor Processing Units (TPUs), Graphics Processing Units (GPUs), and Central Processing Units (CPUs), which collaboratively support the continuous training and refinement of AI / ML models. This ongoing optimization enables significant improvements in slotting accuracy, pick-path efficiency, and demand forecasting across complex operational environments. The underlying Al models may reside on cloud-based servers 1230, where large-scale data can be processed in parallel, supporting training of forecasting components, specifically the shape bank component, on largescale time-series datasets.

[0124] By harnessing the combined processing power of TPUs, GPUs, and CPUs, the computer system 1200 continuously trains and evolves its Al I ML modules 1232 to deliver accurate intra-period shape predictions. The Al algorithms continuously ingest and analyze data to identify signs of potential inefficiencies and provide efficient load balancing across the one or more processor elements. The computer system 1200 may include an enrollment module to register an agent provider (AP) with a payment network and issue a unique AP identifier. A token module associates a consumer’s payment credential with a token and stores the token at the AP. A communication module injects the token and optional consumer-identifying information into a protocol header for transmission to a merchant. A verification module at the merchant uses a public key from the payment network to authenticate the AP and identify the consumer based on the token. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each operable to perform the actions of the methods.

[0125] Implementations of the computer system 1200 for multivariate time-series forecasting may include one or more of the following features. The computer system 1200 where the communication protocol may include HTTP, SMTP, or NFC. The communication module may include the AP identifier and consumer identifier in the protocol header and may further include consumer-specific data such as loyalty pointsAttorney Docket No. 250127PCT / 9975WO01or membership details for merchant recognition. The verification module may also support post-transaction features such as notifying the consumer of the purchase, based on the consumer-identifying information associated with the token. This architecture ensures secure and scalable transactions initiated by trusted agents on behalf of consumers, while allowing merchants to maintain transparency, recognize returning consumers, and deliver enhanced customer experiences. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0126] The Internet service may provide Internet access to one or more computing devices that are coupled to the Internet service, and that the computing devices may include one or more processors, buses, memory devices, display devices, input / output devices, and the like. Furthermore, the Internet service may be coupled to one or more databases, repositories, servers, and the like, which may be utilized to implement any of the various aspects of the disclosure as described herein.

[0127] The computer program instructions also may be loaded onto a computer, a server, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0128] Suitable networks may include or interface with any one or more of, for instance, a local intranet, a PAN (Personal Area Network), a LAN (Local Area Network), a WAN (Wide Area Network), a MAN (Metropolitan Area Network), a virtual private network (VPN), a storage area network (SAN), a frame relay connection, an Advanced Intelligent Network (AIN) connection, a synchronous optical network (SONET) connection, a digital T1, T3, E1 or E3 line, Digital Data Service (DDS) connection, DSL (Digital Subscriber Line) connection, an Ethernet connection, an ISDN (Integrated Services Digital Network) line, a dial-up port such as a V.90, V.34 or V.34bis analog modem connection, a cable modem, an ATM (Asynchronous Transfer Mode) connection, or an FDDI (Fiber Distributed Data Interface) or CDDI (Copper Distributed Data Interface) connection. Furthermore, communications may also include links to any of a variety of wireless networks, including WAP (WirelessAttorney Docket No. 250127PCT / 9975WO01Application Protocol), GPRS (General Packet Radio Service), GSM (Global System for Mobile Communication), CDMA (Code Division Multiple Access) or TDMA (Time Division Multiple Access), cellular phone networks, GPS (Global Positioning System), CDPD (cellular digital packet data), RIM (Research in Motion, Limited) duplex paging network, Bluetooth radio, or an IEEE 802.11 -based radio frequency network. The network can further include or interface with any one or more of an RS-232 serial connection, an IEEE-1394 (Firewire) connection, a Fiber Channel connection, an IrDA (infrared) port, a SCSI (Small Computer Systems Interface) connection, a USB (Universal Serial Bus) connection or other wired or wireless, digital or analog interface or connection, mesh or Digi® networking.

[0129] In general, a cloud-based computing environment is a resource that typically combines the computational power of a large grouping of processors (such as within web servers) and / or that combines the storage capacity of a large grouping of computer memories or storage devices. Systems that provide cloud-based resources may be utilized exclusively by their owners or such systems may be accessible to outside users who deploy applications within the computing infrastructure to obtain the benefit of large computational or storage resources.

[0130] The cloud is formed, for example, by a network of web servers that comprises a plurality of computing devices, such as the host machine, with each server (or at least a plurality thereof) providing processor and / or storage resources. These servers manage workloads provided by multiple users (e.g., cloud resource customers or other users). Typically, each user places workload demands upon the cloud that vary in real-time, sometimes dramatically. The nature and extent of these variations typically depend on the type of business associated with the user.

[0131] It is noteworthy that any hardware platform suitable for performing the processing described herein is suitable for use with the technology. The terms “computer-readable storage medium” and “computer-readable storage media” as used herein refer to any medium or media that participate in providing instructions to a CPU for execution. Such media can take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as a fixed disk. Volatile media include dynamic memory, such as system RAM. Transmission media include coaxial cables, copper wire and fiber optics, among others, including the wires that compriseAttorney Docket No. 250127PCT / 9975WO01one aspect of a bus. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a flexible disk, a hard disk, magnetic tape, any other magnetic medium, a CD-ROM disk, digital video disk (DVD), any other optical medium, any other physical medium with patterns of marks or holes, a RAM, a PROM, an EPROM, an EEPROM, a FLASH EPROM, any other memory chip or data exchange adapter, a carrier wave, or any other medium from which a computer can read.

[0132] Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to a CPU for execution. A bus carries the data to system RAM, from which a CPU retrieves and executes the instructions. The instructions received by system RAM can optionally be stored on a fixed disk either before or after execution by a CPU.

[0133] Computer program code for carrying out operations for aspects of the present technology may be written in any combination of one or more programming languages, including an object-oriented programming language such as Java, Smalltalk, C++, or the like and conventional procedural programming languages, such as the “C” programming language, Go, Python, or other programming languages, including assembly languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0134] The foregoing detailed description has set forth various forms of the systems and / or processes via the use of block diagrams, flowcharts, and / or examples. Insofar as such block diagrams, flowcharts, and / or examples contain one or more functions and / or operations, it will be understood by those within the art that each function and / or operation within such block diagrams, flowcharts, and / or examples can be implemented, individually and / or collectively, by a wide range of hardware, software, firmware, or virtually any combination thereof. Those skilled in the art will recognize that some aspects of the forms disclosed herein, in whole or in part, can beAttorney Docket No. 250127PCT / 9975WO01equivalently implemented in integrated circuits, as one or more computer programs running on one or more computers (e.g., as one or more programs running on one or more computer systems), as one or more programs running on one or more processors (e.g., as one or more programs running on one or more microprocessors), as firmware, or as virtually any combination thereof, and that designing the circuitry and / or writing the code for the software and or firmware would be well within the skill of one of skill in the art in light of this disclosure. In addition, those skilled in the art will appreciate that the mechanisms of the subject matter described herein are capable of being distributed as one or more program products in a variety of forms, and that an illustrative form of the subject matter described herein applies regardless of the particular type of signal bearing medium used to actually carry out the distribution.

[0135] As used in any aspect herein, the term “logic” may refer to an app, software, firmware and / or circuitry configured to perform any of the aforementioned operations. Software may be embodied as a software package, code, instructions, instruction sets and / or data recorded on non-transitory computer-readable storage medium. Firmware may be embodied as code, instructions or instruction sets and / or data that are hard-coded (e.g., nonvolatile) in memory devices.

[0136] As used in any aspect herein, the terms “component,” “system,” “module” and the like can refer to a computer-related entity, either hardware, a combination of hardware and software, software, or software in execution.

[0137] As used in any aspect herein, an “algorithm” refers to a self-consistent sequence of steps leading to a desired result, where a “step” refers to a manipulation of physical quantities and / or logic states which may, though need not necessarily, take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It is common usage to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like. These and similar terms may be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities and / or states.

[0138] A network may include a packet switched network. The communication devices may be capable of communicating with each other using a selected packet switched network communications protocol. One example communications protocol may include an Ethernet communications protocol which may be capable of permitting communication using a Transmission Control Protocol / Internet Protocol (TCP / IP). TheAttorney Docket No. 250127PCT / 9975WO01Ethernet protocol may comply or be compatible with the Ethernet standard published by the Institute of Electrical and Electronics Engineers (IEEE) titled “IEEE 802.3 Standard”, published in December 2008 and / or later versions of this standard. Alternatively, or additionally, the communication devices may be capable of communicating with each other using an X.25 communications protocol. The X.25 communications protocol may comply or be compatible with a standard promulgated by the International Telecommunication Union-Telecommunication Standardization Sector (ITU-T). Alternatively or additionally, the communication devices may be capable of communicating with each other using a frame relay communications protocol. The frame relay communications protocol may comply or be compatible with a standard promulgated by Consultative Committee for International Telegraph and Telephone (CCITT) and / or the American National Standards Institute (ANSI). Alternatively or additionally, the transceivers may be capable of communicating with each other using an Asynchronous Transfer Mode (ATM) communications protocol. The ATM communications protocol may comply or be compatible with an ATM standard published by the ATM Forum titled “ATM-MPLS Network Interworking 2.0” published August 2001, and / or later versions of this standard. Of course, different and / or after-developed connection-oriented network communication protocols are equally contemplated herein.

[0139] Unless specifically stated otherwise as apparent from the foregoing disclosure, it is appreciated that, throughout the present disclosure, discussions using terms such as “processing,” “computing,” “calculating,” “determining,” “displaying,” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices.

[0140] One or more components may be referred to herein as “configured to,” “configurable to,” “operable / operative to,” “adapted / adaptable,” “able to,” “conformable / conformed to,” etc. Those skilled in the art will recognize that “configured to” can generally encompass active-state components and / or inactive-state components and / or standby-state components, unless context requires otherwise.Attorney Docket No. 250127PCT / 9975WO01

[0141] Those skilled in the art will recognize that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to claims containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and / or “an” should typically be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations.

[0142] In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, typically means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). It will be further understood by those within the art that typically a disjunctive word and / or phraseAttorney Docket No. 250127PCT / 9975WO01presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms unless context dictates otherwise. For example, the phrase “A or B” will be typically understood to include the possibilities of “A” or “B” or “A and B.”

[0143] With respect to the appended claims, those skilled in the art will appreciate that recited operations therein may generally be performed in any order. Also, although various operational flow diagrams are presented in a sequence(s), it should be understood that the various operations may be performed in other orders than those which are illustrated or may be performed concurrently. Examples of such alternate orderings may include overlapping, interleaved, interrupted, reordered, incremental, preparatory, supplemental, simultaneous, reverse, or other variant orderings, unless context dictates otherwise. Furthermore, terms like “responsive to,” “related to,” or other past-tense adjectives are generally not intended to exclude such variants, unless context dictates otherwise.

[0144] It is worthy to note that any reference to “one aspect,” “an aspect,” “an exemplification,” “one exemplification,” and the like means that a particular feature, structure, or characteristic described in connection with the aspect is included in at least one aspect. Thus, appearances of the phrases “in one aspect,” “in an aspect,” “in an exemplification,” and “in one exemplification” in various places throughout the specification are not necessarily all referring to the same aspect. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments.

[0145] As used herein, the singular form of “a”, “an”, and “the” include the plural references unless the context clearly dictates otherwise.

[0146] Any patent application, patent, non-patent publication, or other disclosure material referred to in this specification and / or listed in any Application Data Sheet is incorporated by reference herein, to the extent that the incorporated materials are not inconsistent herewith. As such, and to the extent necessary, the disclosure as explicitly set forth herein supersedes any conflicting material incorporated herein by reference. Any material, or portion thereof, that is said to be incorporated by reference herein, but which conflicts with existing definitions, statements, or other disclosure material set forth herein will only be incorporated to the extent that no conflict arises betweenAttorney Docket No. 250127PCT / 9975WO01that incorporated material and the existing disclosure material. None is admitted to be prior art.

[0147] In summary, numerous benefits have been described which result from employing the concepts described herein. The foregoing description of the one or more forms has been presented for purposes of illustration and description. It is not intended to be exhaustive or limiting to the precise form disclosed. Modifications or variations are possible in light of the above teachings. The one or more forms were chosen and described in order to illustrate principles and practical application to thereby enable one of ordinary skill in the art to utilize the various forms and with various modifications as are suited to the particular use contemplated. It is intended that the claims submitted herewith define the overall scope.

Claims

Attorney Docket No. 250127PCT / 9975WO01CLAIMSWhat is claimed is:

1. A system for forecasting spatio-temporal data, the system comprising:one or more processor elements configured to:obtain one or more spatially distinct time-series datasets; assign each of the one or more spatially distinct time-series datasets to at least one of the one or more processor elements;for each of the one or more spatially distinct time-series datasets assigned to at least one of the one or more processor elements, generate a time-series forecast for the assigned one or more spatially distinct timeseries datasets, wherein each of the one or more processor elements is configured to:process each assigned spatially distinct time-series dataset through a convolutional aggregation module;transform an output of the convolutional aggregation module into a frequency-domain representation;segment the frequency-domain representation into a plurality of subsequences;model intra-period dynamics of each of the plurality of subsequences using a shape bank module;model inter-period dynamics by applying a cross-period sparse forecasting module to the frequency-domain representation;generate a frequency-domain forecast by integrating the intra-period dynamics with the inter-period dynamics; and transform the frequency-domain forecast to a time-series forecast; andassemble the time-series forecasts generated for the one or more spatially distinct time-series datasets to generate a final forecast matching spatial and temporal dimensions of the one or more spatially distinct timeseries datasets.

2. The system of claim 1, wherein the shape bank module is configured to:generate a query vector using a linear transformation;Attorney Docket No. 250127PCT / 9975WO01calculate an attention score between the query vector and a shape key of a shape bank database, wherein the shape bank database comprises shape keys and corresponding shape values; andmultiply the attention score and the corresponding shape value of the shape key, wherein the multiplying generates an intra-period dynamics output.

3. The system of claim 2, wherein calculating attention scores comprises evaluating an ReLU activation function with respect to the query vectors and shape keys.

4. The system of claim 2, wherein the one or more processors are further configured to:train weights associated with the shape bank database on a plurality of intra-period shape patterns, the intra-period shape patterns having a period length, w; and wherein the trained weights are associated with shape keys and corresponding shape values.

5. The system of claim 4, wherein the one or more processors are further configured to:compare the final forecast with real-time measured time-series data; and retrain the shape bank database based on the comparison.

6. The system of claim 1, wherein each subsequence of the plurality of subsequences corresponds to a period of length w; andwherein a convolutional filter has a size defined by w.

7. The system of claim 1, wherein the one or more processor elements configured to:repeat the steps of modeling intra-period dynamics using a shape-bank module and modeling inter-period dynamics a number of times (nblock), wherein the number of times (nblock) is a learned hyperparameter.

8. The system of claim 1, wherein the spatially distinct time-series datasets are associated with measured indicators, and wherein the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands.Attorney Docket No. 250127PCT / 9975WO019. The system of claim 1, wherein the one or more processors are further configured to:determine optimized hyper-parameters, wherein the optimized hyperparameters comprise an optimal number of intra-period shape patterns and nblock, wherein determining comprises determining associated error and complexity of optimized hyper-parameters.

10. The system of claim 1, wherein the one or more processor elements are configured to operate in parallel.

11. The system of claim 1, wherein two or more spatially distinct time-series datasets are assigned to one of the one or more processor elements.

12. A method for time-series data forecasting, comprising:processing a time-series dataset through a convolutionalaggregation module;transforming an output of the convolutional aggregation module intoa frequency-domain representation;segmenting the frequency-domain representation into a plurality of subsequences each corresponding to a period of length w;modeling intra-period dynamics of each of the plurality ofsubsequences, wherein modeling intra-period dynamics comprises:generating a query vector using a linear transformation; calculating an attention score between the query vector and a shape key, wherein the shape key corresponds to a related shape value; and multiplying the attention score and the related shape value of the shape key, wherein the multiplying generates an intra-period dynamics output; modeling inter-period dynamics by applying a cross-period sparse forecasting module to the frequency-domain representation;generating a frequency-domain forecast by integrating the intra-period dynamics with the inter-period dynamics; andtransforming the frequency-domain forecast to a time-series forecast.Attorney Docket No. 250127PCT / 9975WO0113. The method of claim 12, wherein the time-series dataset is segmented into subsequences corresponding to a period of length, w; andwherein the shape keys and corresponding shape values correspond to the period of length, w.

14. The method of claim 12, further comprising:training shape keys and the related shape values on a plurality of intra-period shape patterns, wherein trained weights are associated with paired shape keys and related shape values.

15. The method of claim 14, further comprising:comparing the time-series forecast with real-time measured time-series data; andretraining the shape keys and the related shapes based on the comparison.

16. The method of claim 12, further comprising:outputting a visual display of the time-series forecast; andbased on the visual display, performing one or more actions affecting realtime measured time-series data.

17. The method of claim 12, wherein the time-series dataset is associated with measured indicators, and wherein the measured indicators are related to one or more of traffic monitoring, transaction monitoring, electrical transmission and distribution monitoring, and market demands.

18. The method of claim 12, further comprising:determining optimized hyper-parameters, wherein the optimized hyperparameters comprise an optimal number of intra-period shape patterns and nblock; anddetermining associated error and complexity of the optimized hyperparameters.Attorney Docket No. 250127PCT / 9975WO0119. The method of claim 12, wherein calculating attention scores comprises evaluating an ReLU activation function with respect to the query vectors and shape keys.

20. A computer-readable medium having instructions stored thereon, that when executed by a processor, cause the processor to:model intra-period dynamics of a time-series dataset, whereinmodeling intra-period dynamics comprises:generating a query vector using a linear transformation; calculating an attention score between the query vector and a shape key, wherein the shape key corresponds to a related shape value; and multiplying the attention score and the related shape value of the shape key, wherein the multiplying generates an intra-period dynamics output.

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