Modular framework for time series analysis using functional neural network

Abstract

Systems and methods described herein can involve a customizable application framework that allows for fast implementation and efficient application of functional neural network architectures, ease of use, shareability, and reproducibility of results. The application framework improves model performance by capturing underlying complex functions and non-linear relationship information in time series data to solve time series analysis tasks.

Description

MODULAR FRAMEWORK FOR TIME SERIES ANALYSIS USING FUNCTIONALNEURAL NETWORKBACKGROUNDField

[0001] The present disclosure is generally directed to functional data analysis and deep learning. and more specifically, to a modular framework and methods for time senes analysis within a neural network architecture.Related Art

[0002] Time series data, which comprises data points collected over time, has become a prevalent form of data in today’s world. Time series data offers valuable insights into trends, anomalies, and patterns, and is found in numerous sectors such as finance, healthcare, manufacturing, and environmental monitoring. With the rapid advancement of technology, data is being recorded at an unprecedented rate, and in the realm of time series, the growth of information has been exponential. However, current approaches and codes are limited in then functionalities. Accordingly, what is needed are robust and scalable networks that can handle the escalating volume and complexity of time series data. Ideally, such networks are designed with modularity in mind to facilitate easy integration with existing deep learning network architectures. It is also necessary to have systems and methods that can folly leverage temporal information, which is difficult to capture and map in models; incorporate non-linear mappings; and accommodate diverse modeling structures. This would enable them to perform a wide range of tasks, making them more versatile and adaptable to various industry needs. Furthermore, it is desirable to have improved solutions that simplify the process of scaling models to novel or deep architectures, thereby reducing the need for extensive coding and making them more accessible for practical applications.SUMMARY

[0003] A modular architecture that comprises functional layers witliin a functional neural network, serves as a building block that can also be easily merged with any deep learningarchitecture, such as Long Short Tenn Memory (LSTM), Convolutional Neural Network (CNN), transformer , etc., or replace any number of layers therein. Advantageously, this aids in scaling and enables the construction of deeper yet more flexible Functional Neural Network (FNN) architectures.

[0004] The modular framework effectively learns temporal information by mathematically mapping time series data to its output, which can be used to enhance the performance of models that perform series analysis tasks such as forecasting, prediction, classification, dimension reduction, etc. For instance, vibration data and weather data may be used to model the power output of a wind turbine and detect deviations from optimum conditions (anomaly detection). As another example, forecasting weather patterns may be used to plan for agriculture, energy, and disaster events. Furthermore, efficient dimension reduction without loss of information may be achieved for audio data or health care data inputs.

[0005] This customizable application framework allows for fast implementation and efficient application of FNN (Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN)) architectures, ease of use, shareability, and reproducibility of results. It also improves model performance by capturing underlying complex functions and non-lmear relationship information in time series data to solve time series analysis tasks.

[0006] In some aspects of the disclosure, a modular framework for processing time series analysis in a neural network architecture, wherein the framework uses a structure that serves as a building block for a deep learning architecture to cause the deep learning architecture to learn a mapping of time series data to its output and adds a functional layer to the deep learning architecture. The deep learning architecture may comprise a convolutional neural layer, a long short-term memory layer, an attention layer, a recurrent layer, a fully connected layer, etc.

[0007] In some aspects of the disclosure, a modular framework for processing time series analysis in a neural network architecture , wherein the framework obtains a set of operators from a library, uses the set of operators to generate a functional equation or an algorithm, and implements the functional equation or algorithm in a deep learning architecture such that the deep learning architecture is scalable and can be processed by a hardware accelerator.

[0008] Fire modular framework preserves the nature of the time senes data and is configured to implement a set of FNN layers in a multi-modal architecture. Advantageously, increasing the number of neurons, lay ers, basis functions, or a grid size of the deep learning architecture does not7significantly increase the number of coding lines. The modular framework is also compatible with an automatic differentiation process that increases the speed and efficiency of the modular framework, also enables an optimizer process, a transfer learning process, or a regularization process. The FNN is extended with two basis functions along with b-splines and may be used to simplify using, sharing, or reproducing results, wherein the basis functions are Wavelet or Fourier basis functions. The modular framework is further configured to perform tasks comprising a function-on-function model used for prediction or forecasting or dimension reduction, a scalar-on- function model used for prediction, forecasting, or classification, a function-on-scalar model.

[0009] Aspects of the present disclosure can involve a system, which can involve means for using a structure that selves as a building block for a deep learning architecture to cause the deep learning architecture to leant a mapping of time series data to its output and adds a functional layer to the deep learning architecture.

[0010] Some aspects of the disclosure can involve means for obtaining a set of operators from a library, using the set of operators to generate a functional equation or an algorithm, and implementing the functional equation or algorithm in a deep learning architecture such that the deep learning architecture is scalable and can be processed by a hardware accelerator.BRIEF DESCRIPTION OF DRAWINGS

[0011] FIG. 1 illustrates a flow diagram for general architectoe for an FNN, according to various embodiments of the present disclosure.

[0012] FIG. 2 illustrates a general architecture of an FNN for any time series task, according to various embodiments of the present disclosure.

[0013] FIG. 3 illustrates a flow diagram for a general modular architecture, according to various embodiments of the present disclosure.

[0014] FIG. 4 illustrates a flow within a functional layer for an FDNN implementation of continuous neurons, according to various embodiments of the present disclosure.

[0015] FIG. 5 utilizes a bi-fimctional autoencoder (BFAE) to remap temperature data, according to various embodiments of the present disclosure.

[0016] FIG. 6 utilizes temperature data in a function-ori-fimction model to predict power consumption, according to various embodiments of the present disclosure.

[0017] FIG. 7 shows a forecasting example, according to various embodiments of the present disclosure.

[0018] FIG. 8 shows a forecasting example for a step function, according to various embodiments of the present disclosure.

[0019] FIG. 9 illustrates an example computing environment with an example computer device suitable for use in various embodiments of the present disclosure.DETAILED DESCRIPTION

[0020] Hie following detailed description provides details of the figures arid example implementations of the present application. Reference numerals and descriptions of redundant elements between figures are omitted for clarity. Terms used throughout the description are provided as examples and are not intended to be limiting. For example, the use of the term “automatic” may involve folly automatic or semi-automatic implementations involving user or administrator control over certain aspects of the implementation, depending on the desired implementation of one of ordinaiy skill in the art practicing implementations of die present application. Selection can be conducted by a user through a user interface or other input means, or it can be implemented through a desired algorithm. Example implementations as described herein can be utilized either singularly or in combination and the functionality of the example implementations can be implemented through any means according to the desired implementations. In this document, the terms “functional” and “continuous” are used interchangeably. Similarly, the terms “FNN” and “FDNN” or the terms “FNN” and “FBNN” may be used interchangeably.

[0021] Time series analysis is used in a variety of applications such as forecasting, predic tion, classification, and dimension reduction, across numerous industrial and real-world tasks. For instance, in the finance sector, it can aid in distinguishing between fraudulent and legitimate financial transactions. In healthcare, it can assist in diagnosing diseases based on patient monitoring data. In manufacturing, it can forecast equipment demand, and in the energy sector, time series analysis of sensor and weather data can be used to predict wind turbine output.

[0022] However, the rapidly increasing volume of time series data presents challenges for storage, transfer, and analysis. This makes mathematical dimension reduction, which plays a key role in time series analysis. a critical factor. Oftentimes, the information in time series data is not independent and exhibits complex relationships, making it a challenging problem to solve. The goal of time series analysis is therefore to extract information from the temporal patterns in the data mathematically.

[0023] FNNs can perform all the above-mentioned tasks. However, traditional FNN architectures suffer from scalability issues and lack modularity, thus preventing their widespread adoption and application. Existing implementations of FNNs are limited in that scaling the model to novel or very deep architectures is non-trivial and impractical. This is because they necessitateextensive coding to add more neurons or layers to the architecture. Additionally, these networks lack modularity, preventing their integration with existing Deep Learning Network architectures, which significantly restricts the practical application of FNNs.

[0024] Current approaches, including machine learning methods like random forest, linear regression, MiniRocket, functional approaches like functional linear model, functional principal component analysis, functional autoencoder, and deep learning methods, such as neural networks, LSTM, and autoencoder, have certain limitations in comparison to FNNs. These methods may completely disregard temporal information, employ linear mapping, are constrained in their modeling structure, or are capable of performing only a specific task.

[0025] Despite these challenges, time series analysis remains instrumental in smart manufacturing, where it helps in optimizing production processes and enabling predictive maintenance strategies, and in energy management, where it plays a vital role hi predicting energy consumption and promoting sustainable practices. As a versatile and essential tool, time series analysis continues to drive advancements in various industries, enhancing efficiency, and enabling informed decision-making in the face of complex and dynamic data. Its importance has attracted the interest of researchers from the science community, especially in areas where non-scalar types of data have become prevalent.

[0026] Therefore, what is needed are modular frameworks that can adeptly learn the mathematical mapping of time series data to its corresponding output, whether the task involves prediction, forecasting, classification, or dimension reduction. This learning should leverage temporal information to enhance performance, The ideal modular framework not only facilitates scalability but also provides the capability to integrate functional layers with existing models, thereby promoting more efficient and effective time series analysis.

[0027] Embodiments herein comprise a modular system or framework that applies a functional neural network to the time series. The system may comprise a data collection and storage module, which collects data and stores historical data; a model learning module, which utilizes time series data to build a model using an FNN architecture; and a model deployment module, w'hich deploys the learned model on streaming data to produce and transmit real-time data-driven information.

[0028] FIG. 1 illustrates a flow diagram for general architecture for an FNN, according to various embodiments of the present disclosure. System 100 comprises pre-processing module 104 that receives raw data 102 (e.g., time series data) to generate pre-processed time series data 106.System 100 further comprises modular framework 108 that generates output 114. Modular framework 108 may comprise training module 110 and inference module 112 that, as depicted in FIG. 1, may be integrated within modular framework 108.

[0029] In operation, pre-processing module 104 may comprise additional modules (not shown) that are configured to monitor the time series data used in subsequent calculations over time, e.g., to ensure that no significant time gaps occur between adjacent observations. In addition, preprocessing module 104 may detect and eliminate outliers.

[0030] In a training phase, modular framework 108 may utilize training module 110 to train a model to learn an FNN model using processed data 106 generated by pre-processing module 104 to obtain a trained model. Conversely, in an inference phase, inference module 112 in modular framework 104 may use the trained model to perform an inference operation to generate output 114.

[0031] It is understood that pre-processing module 104 may perform any steps to manipulate raw data 102 to prepare raw data 102 for input to modular framework 108, which may operate Machine Learning (ML) or Deep Learning (DL) algorithms. Such data preparation steps are performed on the input data before the data is input into an algorithm. Exemplary data preparation steps comprise noise removal, outlier removal, imputation of missing data, etc.

[0032] Once raw data 102 has been processed in this manner, it may be divided mto training and testing data sets. The training set is used dur ing the model training phase, while the testing set is used for evaluating the model.

[0033] FIG. 2 illustrates a general architecture of an FNN for an any time series task, according to various embodiments of the present disclosure. FNN architecture 200 comprises input layer 202 that receives data in the form of functions (e.g., 203). The functions are provided to any number of user-definable continuous liidden layers 204, 206 that each comprises any number of continuous neurons (e.g., 205) having incoming and outgoing connections, each associated with a weight function (not shown). Architecture 200 further comprises continuous output layer 208 that generates one or more outputs 209, which may comprise functions, scalar values, or labels. It is understood that architecture 200 may comprise any number of continuous liidden layers. As persons of skill in the ail will appreciate continuous hidden layers 204, 206 and the number of continuous neurons 205 in each of continuous hidden layers 204, 206 may be considered hyperparameters .

[0034] In operation, continuous neurons (e.g., 205) may receive functions 203, for example, a time series, to learn from these functional inputs (e.g., random curves) a mapping or functional representations and generate functional outputs. In this manner, continuous hidden layers 204, 206, which comprise continuous neurons 205, may be used to learn a continuous mapping from layer to layer throughout FNN 200. The three types of layers pass functions 203 through the network to leant functional weights over time to optimize the neural network model. Using continuous neurons 205 in this manner advantageously maintains the functional nature of the data throughout model 200. In other words, the learned mapping allows FNN 200 to identify important temporal variables or features and their interactions to fmd complex temporal dependencies between the variables and, thus, underlying patterns in time series data wliile preserving the functional (time series) nature of the data and capturing complex relations even in even in deep networks.

[0035] To facilitate a detailed description of the operation of architecture 200, the following mathematical notations are provided: Assuming that for each of a number of samples, N, time series data are observed within a time range T, the observed data can be defined using Xq(ty). withExample modeling tasks for architecture 200 include prediction, forecasting, classification, and dimension reduction. Further, depending on the particular task, a suitable loss function, output, and output activation function may be defined.

[0036] The Ithcontinuous hidden layer 204 in FNN 200 and the kt!lcontinuous neuron 205 in architecture 200 are defined as follows:

[0037] where a is a non-linear activation function, b^(s) is the parameter function, and ivjp-i(,s’, t) is the bivariate parameter function.

[0038] Using this definition, forward propagation steps may be performed. This involves calculating and storing intermediate variables for a neural network in order from the input layer to the output layer. Then, in a back propagation step, partial derivatives of the weight functions may be computed to update the parameter functions. A person of skill in the art will appreciate that forward and backpropagation steps are alternated unit a stop condition, e.g., a desired accuracy of a loss function is achieved.

[0039] The flexibility of FNN architecture 200 allows for the addition of other and / or functional features to further improve the obtained results. The number of continuous hidden layers 204, the number of continuous neurons 205 in each of the continuous hidden layers, and the activation functions (not shown in FIG. 2) may be user-defined. This manner of optimizing the network results in an FDNN implementation.

[0040] For an FDNN, forward propagation for continuous neurons is defined as:

[0042] Backward propagation for a continuous neuron can be expressed as:

[0045] where cr' represents the first derivative of a.

[0046] Another way of solving FNN architecture 200 involves an FBNN implementation, where FNN 200 learns the weights of the basis functions (e.g., B splines, wavelet, or Fourier) rather than the weight function itself, e.g.. by replacing weight functions with a combination of basis functions.

[0047] For a FBNN, forward propagation for continuous neurons 205 is defined as:

[0050] And backward propagation for a continuous neuron may be expressed as:

[0051] where <7' represents the first derivative of c; are respective unknownweight vectors and matrixes; an (t) are known basis function.

[0052] FIG. 3 illustrates a flow diagram for a general modular architecture, according to various embodiments of the present disclosure. Modular architecture 300 comprises input 302, functional layers 304-308, and output 310. Input 302 is a multivariate time series that has the dimensions b x c x m, wherein h represents the batch size, c represents the number of features, and m represents the number of time points. As depicted in FIG. 3, architecture 300 comprises a three three-layer FNN, where k represents the number of continuous (functional) neurons in each respective functional (continuous) layer 304-308 (denoted as FL) and J represents the number of time points. The dimensions of output 310 depend on the underlying time series task. A FNN is made up of one or more modular FL layers, which may be connected to each other or other deep learning networks. It is noted that in contrast to the embodiments disclosed herein, traditional neural networks and neural network layers are not designed for and are not capable of accepting these inputs.

[0053] As previously mentioned, a functional layer that corresponds to a continuous hidden layer (e.g., layer 204 in FIG. 2). and a continuous neuron in that functional layer is defined as:

[0055] where b^(s) represents the intercept function (bxkxlxs) andrepresents the bi-variate parameter function (bxkxcxmxs).represents the output of the continuous neuron that has dimensions bxkxs. Fur ther, t denotes the layer , r r epresents the number of neurons in the current layer, and j represents the number of neurons in the previous layer.

[0056] FIG. 4 illustrates a flow within a functional layer for an FDNN implementation of continuous neurons, according to various embodiments of the present disclosure. Functional layer 400 comprises inputs 402-406, term 1 through term 4410-416, bi-variate parameter function 408, intercept function 418, and output 420. hi FIG. 4, both forward and backpropagation paths are depicted. The notation for the dimensions displayed in FIG. 4 are the same as those for FIG. 4 and are not repeated herein for purposes of brevity.

[0057] Flow 400 may start when input 402, e.g.. an input time series or an output of a previous functional layer is received. Input 402 is transformed to input 404 by expanding its dimension and is further transformed when the expansion is broadcasted to all k continuous neurons to obtaininput 406. Input 406 is then tensor-multiplied with bi-variate parameter function to obtain term 1 410. An integral approximation is applied to the multiplication result to obtain term 2 412. Tire features of term 2 are summed up and the input feature dimension is removed to obtain term 3 414. Term 3414 is then added to intercept function 418 by tensor addition to obtain term 4416. Finally, term 4 416 undergoes, in a third transformation. a dimension reduction that ultimately results in output 420.

[0058] It is noted these transformations and processes may be supported and optimized by hardware accelerators, such as GPUs and TPUs. As previously mentioned, the functional layer may serve as a modular block that can be used in other FNNs and can relatively easily be merged with, other deep learning networks or multi-modal architectures. A person of skill in the ait will appreciate that corresponding operations may be performed in the backward step and that (1) certain steps may optionally be performed; (2) steps may not be limited to the specific order set forth herein; (3) certain steps may be performed in different orders; and (4) certain steps may be done concurrently.

[0059] A person of skill in the art will further appreciate that a corresponding flow within a functional layer for an FBNN implementation operates similarly to that for the FDNN shown inFIG. 4. The main exception to this is that both parameters, intercept function and bi-variate function, are expanded by utilizing basis functions as follows:

[0060] Term 408,t), having dimension bxkxcxmxs, equals a tensor multiplication between, having dimension bxkxcxmxrl,having dimension bxkxcxrlxr2, and having dimension bxkxcxr2xs.

[0061] And term 416, b^(s) (dimension bxkxlxs) equals a tensor multiplication betweenB^, having dimension bxkxlxr, andhaving dimension bxkxrxs, whereare basis functions such as b-splmes, wavelet, Fourier functions, etc., andB^y' are tensor parameters, and rl and r2 are hyperparameters, which indicate the number of basis functions to use.

[0062] In embodiments, an FDNN or an FBNN may be implemented using an automatic differentiation (autodifi) software package. These packages comprise numerical computing libraries that provide tools for computing derivatives of numeric functions with respect to theirinputs and evaluating functions at specific points. Since autodiff packages typically support both forward and reverse modes of automatic differentiation, a gradient-based optimization algorithm (e.g., gradient descent) may use those derivatives in backpiopagation to find the minimum of a loss function. The loss function measures the discrepancy between model prediction results and actual data, allowing model parameters to be iteratively adjusted to enhance performance, convergence, flexibility, regularization, and transfer learning. It is noted that although examples herein are discussed within the context of PyTorch written in Python, any numerical computing libraries (e.g,, PyTorch, TensorFlow, J AX) and programming languages may be used.

[0063] In embodiments, a single function call may be used to add a functional layer having any number of functional neurons, thereby drastically reducing the amount of code required, e.g., from potentially hundreds or thousands of lines to a single line. This greatly simplifies the definition of deep networks and allows for easy addition, merging, or swapping of functional layers into any existing network. Further, given an existing deep learning architecture, some or all layers of a neural network can be replaced with functional layers. Furthermore, the modular framework presented herein facilitates multi-modal architectures and applications and easy implementation of FNN layers and scaling of FNN modules or models with a functional layer, which enables efficient implementation of functional equations and algorithms by using existing operators in common libraries, which can be accelerated on hardware accelerators, such as Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs).

[0064] Modular framework embodiments disclosed herein can be solved using the either direct method or by basis expansion. They can perform any downstream time series tasks and can be used in a wide range of real-world applications where time series problems are common and time series information is available. A comparison of various features of existing approaches is presented in Table 4.Table 4

[0065] A comparison of a PyTorch embodiment and existing R implementation, running for100 epochs is presented in Table >.Table 5

[0066] Results for experiments with time series data inputs have been performed to predict fat content in meat using spectrometric data samples in a scalar-on-function model, classify boys and girls using height curves using a classification model, and more. FIG. 5 - FIG. 8 show additional experimental results, according to various embodiments of the present disclosure. It is noted that these experiments and results are provided by way of illustration and were performed under specific conditions using a specific embodiment or embodiments; accordingly, neither these experiments nor then results shall be used to limit the scope of the disclosure of the present disclosure.

[0067] FIG. 5 utilizes a BFAE to remap temperature data. FIG. 6 utilizes temperature data hi a function-on-function model to predict power consumption. FIG. 7 shows a forecasting example, and FIG. 8 shows a forecasting example for a step function. These experimental results demonstrate the superiority of the presented embodiments over existing methods as indicated, for example, by the relatively low Root Mean Square Error (RSME) numbers.

[0068] FIG. 9 illustrates an example computing environment with an example computer device suitable for use in various embodiments of the present disclosure. Computer device 905 incomputing environment 900 can include one or more processing units, cores, or processors 910, memory 915 (e.g., RAM, ROM, and / or the like), internal storage 920 (e.g., magnetic, optical, solid-state storage, and / or organic), and / or I / O interface 925, any of which can be coupled on a communication mechanism or bus 930 for communicating information or embedded in the computer device 905. I / O interface 925 is also configured to receive images from cameras or provide images to projectors or displays, depending on the desired implementation.

[0069] Computer device 905 can be communicatively coupled to input / user interface 935 and output device / interface 940. Either one or both of uiput / user interface 935 and output device / interface 940 can be a wired or wireless interface and can be detachable. Ihput / user interface 935 may include any device, component, sensor, or interface, physical or virtual, that can be used to provide input (e.g. , butons, touch-screen interface, keyboard, a poiiiting / cuTsor control, microphone, camera, braille, motion sensor, optical reader, and / or the like). Output device / interface 940 may include a display, television, monitor, printer, speaker, braille, or the like, hi some example implementations, input / user interface 935 and output device / interface 940 can be embedded with or physically coupled to the computer device 905. hi other example implementations, other computer devices may function as or provide the functions of input / user interface 935 and output device / interface 940 for a computer device 905.

[0070] Examples of computer device 905 may include highly mobile devices (e.g., smartphones, devices in vehicles and other machines, devices carried by humans and animals, and the like), mobile devices (e.g., tablets, notebooks, laptops, personal computers, portable televisions, radios, and the like), and devices not designed for mobility (e.g., desktop computers, other computers, information kiosks, televisions with one or more processors embedded therein and / or coupled thereto, radios, and the like).

[0071] Computer device 905 can be communicatively coupled (e.g., via I / O interface 925) to external storage 945 and network 950 for communicating with any number of networked components, devices, and systems, including one or more computer devices of the same or different configurations. Computer device 905 or any connected computer device can be functioning as, providing services of, or referred to as a server, cheat, thin server, general machine, special-purpose machine, or another label.

[0072] I / O interface 925 can include wired and / or wireless interfaces using any communication or I-'O protocols or standards (e.g., Ethernet, 802.1 lx, Universal System Bus,WiMax, modem, a cellular network protocol, and the like) for communicating information to and / or from at least all the connected components, devices, and network in computing environment 900. Network 950 can be any network or combination of networks (e.g., the Internet, local area network, wide area network, a telephonic network, a cellular network, a satellite network, and the like).

[0073] Computer device 905 can use and / or communicate using computer-usable or computer- readable media, including transitory media and non-transitory media. Transitory media include transmission media (e.g,, metal cables, fiber optics), signals, earlier waves, and the like, Non- transitory media include magnetic media (e.g., disks and tapes), optical media (e.g., CD ROM, digital video disks, Blu-ray disks), solid-state media (e.g., RAM, ROM, flash memory, solid-state storage), and other non-volatile storage or memory7.

[0074] Computer device 905 can be used to implement techniques, methods, applications, processes, or computer-executable instructions in some example computing environments. Computer-executable instructions can be retrieved from transitory media, and stored on and retrieved from non-transitory media. The executable instructions can originate fr om one or more of any programming, scripting, and machine languages (e.g., C, C++, C#, Java, Visual Basic, Python, Peri, JavaScript, and others).

[0075] Processor(s) 910 can execute under any operating system (OS) (not shown), in a native or virtual environment. One or more applications can be deployed that include logic unit 960, application programming interlace (API) unit 965, input unit 970. output unit 975, and inter-unit communication mechanism 995 for the different units to communicate with each other, with the OS, and with other applications (not shown). The described units and elements can be varied in design, function, configuration, or implementation and are not limited to the descriptions provided. Processors) 910 can be in the form of hardware processors such as central processing units (CPUs) or a combination of hardware and software units.

[0076] In some example implementations, when information or an execution instruction is received by API unit 965, it may' be communicated to one or more other units (e.g., logic unit 960, input unit 970, output unit 975). hi some instances, logic unit 960 may be configured to control the information flow among the units and direct the services provided by API unit 965, input unit 970, and output unit 975, in some example implementations described above. For example, the flow of one or more proc esse s or implementations may be controlled by logic unit 960 alone or inconjunction with API unit 965. The input unit 970 may be configured to obtain input for the calculations described in the example implementations, and the output unit 975 may be configured to provide output based on the calculations described in example implementations.

[0077] Processor(s) 910 can be configured to execute a method or computer instructions which can involve, using a structure that serves as a building block for a deep learning architecture, such as that shown in FIG. 5, to cause the deep learning architecture to learn a mapping of time series data to its output, and adding a functional layer to the deep learning architecture. Processors) 910 can be further configured to execute a method or computer instructions which can involve, obtaining a set of operators from a library, using the set of operators to generate a functional equation or an algorithm, and implementing the functional equation or algorithm in a deep learning architecture, such as that shown in FIG. 4, in a maimer such that the deep learning architecture is scalable and can be processed by a hardware accelerator.

[0078] Processor(s) 910 can be configured to execute a method or computer instructions that implement a set of FNN layers in a multi-modal architecture, while preserving the nature of the time series data and wherein increasing the number of neurons, layers, basis functions, or a grid size of the deep learning architecture does not significantly increase the number of coding lines.

[0079] Processors) 910 can be further configured to execute a method or computer instructions which can involve using an automatic differentiation, an optimizer process, a transfer learning process, or a regularization process to increase speed and efficiency. This may involve extending an FNN with two basis functions, such as Wavelet or Fourier basis functions, along with b-splines, which simplifies using, sharing, or reproducing results.

[0080] Processor(s) 910 can be further configured to execute a method or computer instructions which can involve performing tasks comprising a fimction-on-fimction model used for prediction or forecasting or dimension reduction, a scalar-on-function model used for prediction, forecasting, or classification, a fimction-on-scalar model. Some portions of the detailed description are presented in terms of algorithms and symbolic representations of operations within a computer. These algorithmic descriptions and symbolic representations are the means used by those skilled in the data processing arts to convey the essence of their innovations to others skilled in the art. An algorithm is a series of defined steps leading to a desired end state or result. In example implementations, the steps carried out require physical manipulations of tangible quantities to achieve a tangible result.

[0081] Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout the description, discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining ” “displaying,” or the like, can include the actions and processes of a computer system or other information processing 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’s memories or registers or other information storage, transmission or display devices.

[0082] Example implementations may also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the required purposes, or it may include one or more general-purpose computers selectively activated or reconfigured by one or more computer programs. Such computer programs may be stored in a computer-readable medium, such as a computer-readable storage medium or a computer-readable signal medium, A computer- readable storage medium may involve tangible mediums such as optical disks, magnetic disks, read-only memories, random access memories, solid-state devices, drives, or any other types of tangible or non-transitory media suitable for storing electronic information. A computer-readable signal medium may include mediums such as carrier waves. The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Computer progr ams can involve pure software implementations that involve instructions that perform the operations of the desired implementation.

[0083] Various general-purpose systems may be used with programs and modules in accordance with the examples herein, or it may prove convenient to construct a more specialized apparatus to perform desired method steps, hi addition, the example implementations are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the techniques of the example implementations as described herein. The instructions of the programming language(s) may be executed by one or more processing devices, e.g., central processing units (CPUs), processors, or controllers.

[0084] As is known in the art, the operations described above can be performed by hardware, software, or some combination of software and hardware. Various aspects of the example implementations may be implemented using circuits and logic devices (hardware), while other aspects may be implemented using instructions stored on a machine-readable medium (software),which if executed by a processor, would cause the processor to perform a method to cany out implementations of the present application. Further, some example implementations of the present application may be performed solely in hardware, whereas other example implementations may be performed solely in software. Moreover, the various functions described can be performed in a single unit, or can be spread across a number of components in any number of ways. When performed by software, the methods may be executed by a processor, such as a general -purpose computer, based on instructions stored on a computer-readable medium. If desir ed, the instructions can be stored on the medium in a compressed and / or encrypted format.

[0085] Moreover, other implementations of the present application will be apparent to those skilled in the art from consideration of die specification and practice of the techniques of the present application. Various aspects and / or components of the described example implementations may be used singly or in any combination. It is intended that the specification and example implementations be considered as examples only, with the true scope and spirit of the present application being indicated by the following claims.

Claims

CLAIMSWhat is claimed is:

1. A modular framework for processing time series analysis in a neural network architecture, the framework comprising: a structure that serves as a building block for a deep learning architecture, the deep learning architecture configured to leam a mapping of time series data to its output, the building block configured to add a functional layer to the deep learning architecture.

2. The framework according to claim 1. wherein the modular framework is configured to replace or merge with a deep learning model comprising functional neural network (FNN) layers.

3. The framework according to claim 1, wherein the modular framework is configured to implement a set of functional neural network (FNN) layers in a multi-modal architecture.

4. The framework according to claim 1, wherein the modular framework is configured to preserve the nature of the time series data,5. The framework according to claim 1 , wherein increasing a number of neurons, layers, basis functions, or a grid size of the deep learning architecture does not significantly increase a number of coding lines.

6. The framework according to claim 1, wherein the modular framework is compatible with an automatic differentiation process that increases a speed and efficiency of the modular framework, the process comprising at least one of an optimizer process, a transfer learning process, or a regularization process.

7. The framework according to claim 2, wherein the modular framework is configured to use the FNN to simplify using, sharing, or reproducing results.

8. The framework according to claim 7, wherein the FNN comprises at least one of a functional direct neural network (FDNN) or a functional basis neural network (FBNN).

9. The framework according to claim 8, wherein the FBNN is extended with two basis functions along with b-splines.

10. The framework according to claim 9, wherein the basis functions are Wavelet or Fourier basis fimctions.

11. The fr amework according to claim 1 , wherein the modular framework is configured to perform tasks comprising at least one of a function-on-fiinction model used for predictionor forecasting or dimension reduction, a scalar-on-function model used for prediction, forecasting, or classification, a function-on-scalar model12. The framework according to claim 1, wherein the deep learning architecture may comprise at least one of a convolutional neural layer, a long short-term memory layer, an attention layer, a recunent layer, a fully connected layer, etc.

13. A non-transitory computer-readable medium for storing instructions for executing a process, the instructions comprising: using a structure that serves as a building block for a deep learning architecture to cause the deep learning architecture to learn a mapping of time series data to its output; and adding a functional layer to the deep learning architecture.

14. The non-transitory computer -readable medium according to claim 13, wherein the instructions further comprise: obtaining a set of operators from a library’; using the set of operators to generate at least one of a functional equation or an algorithm; and implementing the functional equation or algorithm in a deep learning architecture in a manner such that the deep learning architecture is scalable and can be processed by a hardware accelerator.

15. A method comprising: obtaining a set of operators from a library; using the set of operators to generate at least one of a functional equation or an algorithm; and implementing the functional equation or algorithm in a deep learning architecture in a manner such that the deep learning arcliitecture is scalable and can be processed by a hardware accelerator.

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