Fourier series time sequence prediction method based on KoImogorov-ArnoId theory

Abstract

The invention belongs to the technical field of time series data prediction, and particularly provides a time series data prediction method based on a KoImogorov-ArnoId representation theory and Fourier series, high-dimensional nonlinear time series data is decomposed into a plurality of low-dimensional sub-problems through a multi-layer nested structure in the Kolmogorov-Arnold representation theory, and frequency domain analysis of the Fourier series is combined, so that the time series data is predicted. And efficient modeling and prediction of complex time series data are realized. Frequency domain decomposition is performed on time series data by using Fourier series, main frequency components of the time series data are extracted, and a multi-layer nested prediction model is constructed through a nonlinear mapping relation in a Kolmogorov-Arnold representation theory, so that long-term trend and short-term fluctuation of complex nonlinear time series data are predicted. The generalization ability and the prediction precision of the time sequence prediction model are effectively improved, and meanwhile, the dependence of the model on the data scale and computing resources is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of time series data prediction, and in particular relates to a Fourier series time series prediction method based on the KoImogorov-ArnoId theory. Background Art

[0002] Time series forecasting is a core research area in data analytics. It involves mathematically modeling and analyzing time series of historical data to predict the state or behavior of a system at a specific point in the future. Time series forecasting helps researchers and decision makers understand and explore the patterns, trends, and dynamic characteristics of data over time, facilitating subsequent planning, decision-making, and optimization. It has applications in a variety of fields, including finance, meteorology, industrial production, and healthcare.

[0003] Among time series forecasting methods, hybrid approaches that combine mechanism and data fusion establish an intrinsic state space representation of the data and learn model parameters in a data-driven manner, combining the advantages of both theoretical analysis and data learning. These methods include autoregressive models, moving average models, and vector autoregressive models. However, these methods perform poorly for robust forecasting applications requiring low computational complexity, high precision, and robustness, as they cannot achieve an accurate state space. When processing complex, nonlinear time series data, existing time series forecasting models are limited by the fixed nature of their model structure and their ability to capture the inherent complexity of the data. They lack sufficient flexibility to adapt to complex dynamics in the data, such as long-term dependencies and mutation points, which limits the accuracy and reliability of the forecast results. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the defect that the time series prediction method in the prior art cannot effectively process complex nonlinear time series data, resulting in insufficient prediction accuracy and reliability, thereby providing a Fourier series time series prediction method based on the KoImogorov-ArnoId theory.

[0005] A Fourier series time series prediction method based on Kolmogorov-Arnold theory includes the following steps: obtaining original input data and generating a training sample set through a sliding window method; extracting frequency domain features through adaptive Fourier series decomposition; dynamically fusing Fourier feature components of different time resolutions and harmonic orders through a learnable weight matrix, and compressing them to a low-dimensional space through a nonlinear activation function to form a fusion feature; constructing a multi-layer nonlinear mapping network based on the Kolmogorov-Arnold representation theorem; the multi-layer nonlinear mapping network includes an internal function and an external function, the internal function performs nonlinear encoding on the input features through a parameterized cosine basis function, and the external function uses a fully connected network aggregation encoding; inputting the time-frequency fusion feature into the multi-layer nonlinear mapping network, and optimizing the network's fundamental frequency parameters, phase offset and weight coefficients through end-to-end training; inputting the time series data to be predicted into the multi-layer nonlinear mapping network, and realizing multi-step rolling prediction through a sliding window mechanism.

[0006] Furthermore, the original input data includes a multidimensional input sequence and a target output sequence, the multidimensional input sequence includes multiple input features for each time step, and the target output sequence includes output features for each time step; and further includes: standardizing the input features of the multidimensional input sequence to eliminate the dimension; and normalizing the output features of the target output sequence.

[0007] Furthermore, adaptive Fourier series decomposition is used to extract frequency domain features; Fourier feature components of different time resolutions and harmonic orders are dynamically fused through a learnable weight matrix, and compressed to a low-dimensional space through a nonlinear activation function to form a fusion feature, including the following method: Fourier series decomposition is performed on all features of each time step in each training sample in the training sample set to extract frequency domain features; the same features of different time steps are dynamically weighted and fused through a learnable weight matrix to obtain the Fourier feature components of the training sample; the Fourier feature components are compressed to a low-dimensional space through a nonlinear activation function to form a fusion feature.

[0008] Furthermore, a multi-layer nonlinear mapping network is constructed, including the following method steps: a multi-layer nonlinear mapping network is constructed based on the David Sprecher variant of the stacked multi-layer Kolmogorov-Arnold representation theorem, each layer of the network includes multiple internal functions, the internal functions are adjusted by weight parameters, and translation parameters are introduced in each layer of the network; in the multi-layer nonlinear mapping network, the internal function adopts a PReLU activation function, and the PReLU activation function calculates a PReLU activation function processing tensor based on an input tensor and a slope parameter.

[0009] Furthermore, in the multi-layer nonlinear mapping network, the network layer of the external function includes two layers of fully connected networks for aggregating features and introducing temporal dependencies, and the output layer of the multi-layer nonlinear mapping network constrains the range of output values to within the interval [0,1] through the Sigmoid function.

[0010] Furthermore, the multi-layer nonlinear mapping network is optimized by an end-to-end training method, and the mean square error is used as the loss function. In the loss function, all samples are traversed, and the square error of each sample is calculated and accumulated based on the true value vector and the predicted value vector, and the average value is calculated to obtain the MSE loss value.

[0011] Furthermore, in the training of the multi-layer nonlinear mapping network, mean square error is used as the loss function, combined with the Adam optimizer, and the early stopping mechanism is used to ensure model convergence.

[0012] Furthermore, the time series data prediction method is used for time series data prediction of the petroleum hydrocracking process, wherein the original input data is the processing data of the petroleum hydrocracking process, and the original input data includes a multidimensional input sequence and a target output sequence. The input characteristics of the multidimensional input sequence include the total outlet temperature, the reactor inlet temperature, the reactor pressure difference, the tower top pressure, the water injection rate, and the tower top reflux rate. The output characteristics of the target output sequence are the diesel 10% recovery temperature.

[0013] Beneficial effects: The present invention provides a time series data prediction method based on Kolmogorov-Arnold representation theory and Fourier series. Through the multi-layer nested structure in the Kolmogorov-Arnold representation theory, high-dimensional nonlinear time series data is decomposed into multiple low-dimensional sub-problems, and combined with the frequency domain analysis of the Fourier series, efficient modeling and prediction of complex time series data is achieved. The present invention uses Fourier series to perform frequency domain decomposition on time series data, extracts its main frequency components, and constructs a multi-layer nested prediction model through the nonlinear mapping relationship in the Kolmogorov-Arnold representation theory to predict the long-term trend and short-term fluctuation of complex nonlinear time series data, effectively improving the generalization ability and prediction accuracy of the time series prediction model, while reducing the model's dependence on data scale and computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0015] Figure 1 It is a schematic block diagram of the method steps of the present invention; Figure 2 Schematic diagram of the time series prediction model structure of the present invention. DETAILED DESCRIPTION

[0016] To make the above-mentioned objects, features, and advantages of the present application more clearly understood, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the scope of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0017] In the description of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. In the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0018] In this application, unless otherwise specified or limited, the terms "installed," "connected," "connect," "fixed," etc. should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, or integration; mechanical connection or electrical connection; direct connection or indirect connection through an intermediate medium; internal communication between two elements or interaction between two elements, unless otherwise specified. Those skilled in the art will understand the specific meanings of the above terms in this application based on specific circumstances.

[0019] Reference Figure 1 and Figure 2 As shown, this embodiment provides a Fourier series time series prediction method based on the KoImogorov-ArnoId theory, including the following method steps: Step S1: Obtain the original input data and generate a training sample set using the sliding window method; Step S2: Adaptive Fourier series decomposition is used to extract frequency domain features; Fourier feature components of different time resolutions and harmonic orders are dynamically fused through a learnable weight matrix, and compressed into a low-dimensional space through a nonlinear activation function to form a fused feature; Step S3: Based on the Kolmogorov-Arnold representation theorem, a multi-layer nonlinear mapping network is constructed; the multi-layer nonlinear mapping network includes an internal function and an external function, the internal function performs nonlinear encoding on the input features through parameterized cosine basis functions, and the external function uses a fully connected network aggregation encoding; the time-frequency fusion features are input into the multi-layer nonlinear mapping network, and the fundamental frequency parameters, phase offset, and weight coefficients of the network are optimized through end-to-end training; Step S4: Input the time series data to be predicted into the multi-layer nonlinear mapping network, and realize multi-step rolling prediction through the sliding window mechanism.

[0020] Specifically, the Kolmogorov–Arnold theorem states that any multivariate continuous function can be expressed as a finite combination of single-variable continuous functions. For every multivariate continuous function f:[0,1] n →R can be expressed as the superposition of continuous single variable functions, specifically as follows: ; As a preferred embodiment of this invention, the David Sprecher variant of the Kolmogorov–Arnold representation theorem is selected to save computing resources, which is specifically expressed as follows: ; In this variant, a single internal function with appropriate parameter shift is used. Replace internal functions , thereby reducing the number of internal functions, simplifying the representation of multivariate continuous functions, reducing the number of parameter learning during model training, and optimizing the model structure.

[0021] In this embodiment, the Fourier series is introduced to further enhance the modeling capability of the model for complex time series data. The Fourier series is specifically expressed as: ; in, represents the order of harmonics, represents the period of the signal, represents the harmonic amplitude, Indicates the phase, Represents the fundamental frequency, through which any periodic signal can be decomposed into the superposition of a finite or infinite number of simple harmonic waves.

[0022] In this embodiment, the base frequency Decompose any periodic signal into a superposition of finite or infinite simple harmonic waves, with powerful frequency domain feature extraction capabilities, and introduce a finite, learnable truncation frequency coefficient s to approximate the infinite series, finding the optimal value that balances model complexity and fitting ability. is replaced by a truncated finite Fourier series, thus expressing it as: ; Therefore, in this embodiment, the time series data prediction model is expressed as: ; Among them, the weight parameter Used to adjust the contribution of each input variable to the final result, represents the DC component of the Fourier series, represents the baseline value of the data, Indicates the Amplitude of the order harmonic, cosine function Used to extract and characterize the periodicity and frequency characteristics in complex time series data, which is a multivariate function Provide support for accurate modeling of complex data, The value can be used to shift each summation term to adjust the final function value.

[0023] Specifically, in step S1, the original input data includes a multidimensional input sequence and a target output sequence, the multidimensional input sequence includes multiple input features for each time step, and the target output sequence includes output features for each time step; and further includes: normalizing the input features of the multidimensional input sequence to eliminate the dimension; and normalizing the output features of the target output sequence to scale to the interval [0,1].

[0024] In this embodiment, the original input data is collected through sensors or data interfaces, and can be data in the fields of power load, meteorological parameters, or financial indicators. In the original input data, the multidimensional input sequence is represented as: ; Where n represents the number of input features at each time step, Represents the input features.

[0025] The normalized data is processed using a sliding window with a window size of , for the processed training data, The training samples are represented as ,in , indicating that from the time step to the The input feature sequence of time steps, It is The actual output of each time step.

[0026] Specifically, in step S2, for each training sample in the training sample set All features at each time step in Perform Fourier series decomposition to extract frequency domain features; through a learnable weight matrix The same features at different time steps are dynamically weighted and fused to obtain the Fourier feature components of the training samples; the Fourier feature components are compressed to a low-dimensional space through a nonlinear activation function to form fusion features.

[0027] The specific calculation method of Fourier characteristic components is as follows: ; in, Indicates the The weighted frequency domain feature vector of feature dimensions, Represents the weight matrix No. Rank Elements of the column, Indicates the feature dimensions at time steps The Fourier eigenvector of . The frequency domain features obtained by Fourier series decomposition of each time step in the sliding window are finally obtained for all training samples Fourier eigencomponents of .

[0028] For external functions in time series forecasting models , introduce the self-gating activation function Swish activation function, calculate the fusion feature, the specific calculation method is expressed as: ; In this embodiment, the Swish activation function introduces nonlinear features into the time series prediction model, avoiding the problem of gradient vanishing caused by the Sigmoid activation function, and limiting the output value of the negative input in the time series prediction model to a certain range, thereby increasing the stability at a deeper level and solving the problem of using spline functions and grid search to determine activation in the original KAN network, thus saving computing resources. The features after dynamic weighted fusion are further processed by the nonlinear activation function. Compressing the data into a low-dimensional space creates a joint representation that fuses local fluctuation details with global trend changes. This frequency-time coupling not only preserves the periodicity of the original time series but also enhances the model's ability to capture multi-scale time series patterns through a dynamic fusion mechanism. This provides high-information-density input features for the subsequent Kolmogorov-Arnold mapping layer, effectively supporting the modeling and prediction of complex nonlinear time series relationships.

[0029] Specifically, in step S3, a multi-layer nonlinear mapping network is constructed, including the following method steps: a multi-layer nonlinear mapping network is constructed based on the David Sprecher variant of the stacked multi-layer Kolmogorov-Arnold representation theorem, and each layer of the network contains multiple internal functions , the internal function passes the weight parameter Adjustment to capture the contribution of different input variables to the final result and introduce translation parameters at each layer of the network , allowing the model to learn at different time scales. In the multi-layer nonlinear mapping network, the internal function adopts the PReLU activation function, which calculates the PReLU activation function processing tensor based on the input tensor and the slope parameter.

[0030] As a further improvement of this embodiment, in the multi-layer nonlinear mapping network, the network layer of the external function includes two layers of fully connected networks for aggregating features and introducing temporal dependencies, and the output layer of the multi-layer nonlinear mapping network constrains the range of output values to be within the interval [0,1] through the Sigmoid function. Specifically, referring to Figure 2 As shown, the fused features are activated by a nonlinear activation function The input is sent to the hidden layer, which is composed of a multi-layer stack of simplified KA layers (composed of internal and external nonlinear activation functions and fully connected layers) constructed based on the Kolmogorov–Arnold representation theorem expression. This further extracts high-order temporal features and captures the nonlinear relationship and dynamic dependency between input features. The final output layer uses the Sigmoid activation function to limit the prediction results to [0,1] and maps the aggregated features to the target function. The estimated value of can achieve high-precision nonlinear prediction of the input time series.

[0031] In this embodiment, the multi-layer nonlinear mapping network is optimized by an end-to-end training method, and the mean square error is used as the loss function. In the loss function, all samples are traversed, and the square error of each sample is calculated based on the true value vector and the predicted value vector and accumulated. The average value is calculated to obtain the MSE loss value. The specific calculation method is expressed as follows: ; Where n represents the number of samples, Indicates the The true value of the sample, Represents the predicted value of the model.

[0032] As a preference of this embodiment, in the training of the multi-layer nonlinear mapping network, the mean square error is used as the loss function, combined with the Adam optimizer, and the early stopping mechanism is used to ensure model convergence.

[0033] Specifically, in step S4, the preprocessed time series data to be predicted is fed into the trained time series prediction model, achieving multi-step rolling predictions through a sliding window mechanism. During the deployment phase, model parameters are fine-tuned and regularization methods are incorporated to further optimize model performance and adapt to data drift. The final output is a prediction result that combines interpretable frequency domain features with nonlinear mapping capabilities, meeting the real-time requirements of industrial scenarios.

[0034] In this embodiment, the time series data prediction method is used to predict the time series data of the petroleum hydrocracking process. The original input data is the processing data of the petroleum hydrocracking process. The original input data includes a multidimensional input sequence and a target output sequence. The input characteristics of the multidimensional input sequence include the total outlet temperature, the reactor inlet temperature, the reactor pressure difference, the tower top pressure, the water injection rate, and the tower top reflux rate. The output characteristic of the target output sequence is the diesel 10% recovery temperature.

[0035] Specifically, in the hydrocracking process, industrial sensors collect multivariate time-series data from the reactor in real time as raw input data. This data comprehensively reflects the operational status of the hydrocracking process, providing rich information for subsequent data analysis and model building. The raw input data was collected continuously for 20 months at 8-hour intervals, totaling 1,800 samples. After normalization and standardization to eliminate dimensional differences, a sliding window method (with a window size of 3 steps) was used to construct a training sample set. The recovery temperature at the last time step in each sample was predicted, and the data was divided into a training set (70%), a validation set (15%), and a test set (15%) based on the time series.

[0036] In model construction, adaptive Fourier decomposition is first performed on the time series segment of each input feature, with the cutoff frequency set to 5, and the first three harmonic components (fundamental frequency, amplitude, and phase) are extracted. The frequency domain features of different time steps are dynamically fused through a learnable weight matrix to suppress sensor noise interference. The fused features are expanded to 87 dimensions through the Swish activation function to form a joint frequency-time domain representation.

[0037] The intermediate layer, constructed based on the David Sprecher variant of the Kolmogorov-Arnold representation theory, uses the PReLU activation function as its internal function. The fused features are then fed into the hidden layer through a nonlinear activation function to extract high-order temporal features. In the final output layer, a Sigmoid activation function is used to constrain the prediction results to the range [0, 1]. The aggregated features are then mapped to an estimated value of the objective function, achieving high-precision nonlinear prediction of the original input data.

[0038] As a preferred method in this embodiment, during training, mean squared error (MSE) is used as the loss function, combined with the Adam optimizer (initial learning rate η = 0.01, decaying by 5% every 50 epochs), and an early stopping mechanism (terminating if the validation set loss does not decrease for 10 consecutive epochs) is used to ensure model convergence. As a preferred method in this embodiment, the number of iterations Nepoch = 500 and the batch size Nb = 32.

[0039] This embodiment also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above-mentioned time series data prediction method when executing the computer program.

[0040] This embodiment also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned time series data prediction method are implemented.

[0041] This embodiment provides a time series data prediction method based on Kolmogorov-Arnold representation theory and Fourier series. It decomposes high-dimensional nonlinear time series data into multiple low-dimensional sub-problems through the multi-layer nested structure in the Kolmogorov-Arnold representation theory, and combines the frequency domain analysis of the Fourier series to achieve efficient modeling and prediction of complex time series data. The present invention uses the Fourier series to perform frequency domain decomposition on time series data, extracts its main frequency components, and constructs a multi-layer nested prediction model through the nonlinear mapping relationship in the Kolmogorov-Arnold representation theory to predict the long-term trend and short-term fluctuation of complex nonlinear time series data, effectively improving the generalization ability and prediction accuracy of the time series prediction model, while reducing the model's dependence on data scale and computing resources.

[0042] In this example, the proposed time series prediction method, when applied to the hydrocracking process, not only provides higher-precision prediction results than traditional time series prediction methods such as LSTM and TCN, but also meets the requirements of rapid response and real-time control. By dynamically fusing frequency domain features and using nonlinear activation functions, the model also demonstrates greater robustness to noise.

[0043] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0044] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. The Fourier series time series prediction method based on KoImogorov-ArnoId theory is characterized by: The method comprises the following steps: obtaining original input data, generating a training sample set by a sliding window method; extracting frequency domain features by using adaptive Fourier series decomposition; Fourier feature components of different time resolutions and harmonic orders are dynamically fused through a learnable weight matrix, and compressed into a low-dimensional space through a nonlinear activation function to form a fused feature; based on the Kolmogorov-Arnold representation theorem, a multi-layer nonlinear mapping network is constructed; the multi-layer nonlinear mapping network includes internal functions and external functions, the internal functions perform nonlinear encoding on the input features through parameterized cosine basis functions, and the external functions use fully connected network aggregation encoding; the time-frequency fusion features are input into the multi-layer nonlinear mapping network, and the fundamental frequency parameters, phase offset and weight coefficients of the network are optimized through end-to-end training; the time series data to be predicted is input into the multi-layer nonlinear mapping network, and multi-step rolling prediction is achieved through a sliding window mechanism.

2. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 1, characterized in that: The original input data includes a multidimensional input sequence and a target output sequence, the multidimensional input sequence includes multiple input features for each time step, and the target output sequence includes output features for each time step; It also includes: standardizing the input features of the multidimensional input sequence to eliminate the dimension; and normalizing the output features of the target output sequence.

3. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 1, characterized in that: Adaptive Fourier series decomposition is used to extract frequency domain features; The Fourier feature components of different time resolutions and harmonic orders are dynamically fused through a learnable weight matrix, and compressed into a low-dimensional space through a nonlinear activation function to form a fusion feature. The method includes the following steps: performing Fourier series decomposition on all features of each time step in each training sample in the training sample set to extract frequency domain features; The same features at different time steps are dynamically weighted and fused through a learnable weight matrix to obtain the Fourier feature components of the training samples; the Fourier feature components are compressed to a low-dimensional space through a nonlinear activation function to form a fusion feature.

4. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 1, characterized in that: Constructing a multi-layer nonlinear mapping network includes the following method steps: constructing a multi-layer nonlinear mapping network based on a David Sprecher variant of the stacked multi-layer Kolmogorov-Arnold representation theorem, wherein each layer of the network includes multiple internal functions, the internal functions are adjusted by weight parameters, and a translation parameter is introduced in each layer of the network; in the multi-layer nonlinear mapping network, the internal functions use a PReLU activation function, and the PReLU activation function calculates a PReLU activation function processing tensor based on an input tensor and a slope parameter.

5. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 4, characterized in that: In the multi-layer nonlinear mapping network, the network layer of the external function includes two layers of fully connected networks for aggregating features and introducing temporal dependencies. The output layer of the multi-layer nonlinear mapping network constrains the range of output values within the interval [0, 1] through the Sigmoid function.

6. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 1, characterized in that: The multi-layer nonlinear mapping network is optimized by an end-to-end training method, and the mean square error is used as the loss function. In the loss function, all samples are traversed, and the square error of each sample is calculated and accumulated based on the true value vector and the predicted value vector, and the average value is calculated to obtain the MSE loss value.

7. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 6, characterized in that: In the training of the multi-layer nonlinear mapping network, mean square error is used as the loss function, combined with the Adam optimizer, and the early stopping mechanism is used to ensure model convergence.

8. The Fourier series time series prediction method based on KoImogorov-ArnoId theory according to claim 1, characterized in that: The time series data prediction method is used to predict time series data of a petroleum hydrocracking process. The original input data is processing data of the petroleum hydrocracking process. The original input data includes a multidimensional input sequence and a target output sequence. The input features of the multidimensional input sequence include total outlet temperature, reactor inlet temperature, reactor pressure difference, tower top pressure, water injection rate, and tower top reflux rate. The output feature of the target output sequence is the diesel 10% recovery temperature.

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