A long-time series numerical weather reanalysis data compression and retrieval method and system based on quantum reservoir computing
Patent Information
- Application Number
- CN202611256550.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-18
- Publication Date
- 2026-10-13
AI Technical Summary
[0003]（2）存储结构复杂：多要素深度绑定的存储结构使得系统无法直接跨越冗余维度，单变量或局部时序特征的剥离读取极为低效
（1）首次将量子储层计算（QRC）应用于气象再分析数据压缩，利用量子系统的指数级状态空间实现超高维映射，参数量仅为经典方法的1/1000。
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Figure CN122903767A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the interdisciplinary field of quantum computing and meteorological applications, and more specifically to a method and system for compressing and retrieving long-term numerical weather reanalysis data based on quantum reservoir computing. Background Technology
[0002] Numerical weather reanalysis data (such as ERA5 and CRA) are core data resources for modern meteorological research, weather forecasting, and climate analysis. This type of data has the following characteristics: (1) Huge amount of data: Taking ERA5 reanalysis data as an example, the global 0.25° resolution (1440×721 grid) and the Z500 variable data for 10 years can reach 58.4GB. If multivariate (temperature, wind field, humidity, etc.) and higher resolution data are included, the storage requirements will reach TB or even PB level.
[0003] (2) Complex storage structure: The storage structure with deep binding of multiple elements makes it impossible for the system to directly cross redundant dimensions, and the stripping and reading of single variables or local time-series features is extremely inefficient.
[0004] (3) Conflict between storage and accuracy: Existing compression methods (such as EOF decomposition and wavelet compression) will lose accuracy at high compression ratios, or the compression ratio is insufficient while maintaining accuracy.
[0005] The existing methods for compressing and retrieving numerical weather reanalysis data, as well as their limitations, are as follows: (1) Dimensionality reduction and compression based on EOF / PCA: Principle: The spatiotemporal data field is decomposed into spatial modes (EOFModes) and temporal coefficients (PCs) through singular value decomposition (SVD), and only the main modes and coefficients are stored.
[0006] Drawbacks: The compression ratio is limited by the number of modes to be retained (e.g., 1243 PCs are needed to retain 99.9% variance), so higher compression ratios cannot be achieved; and the PC values at all time points still need to be stored, so random access at any time point cannot be achieved.
[0007] (2) Machine learning-based compression methods (LSTM, Transformer, etc.): Principle: Train a neural network to learn the evolution of time series data, and store only the model parameters.
[0008] Disadvantages: High training cost (requires backpropagation to optimize all parameters); large number of model parameters; error accumulation in long-term prediction; inability to directly access any time point (requires iterative prediction from the initial time).
[0009] (3) Traditional reservoir computing (RC): Principle: The reservoir dynamics are fixed, and only the linear weights of the Readout layer are trained, resulting in low training cost.
[0010] Limitations: The state space of classical reservoirs grows linearly with the number of neurons, requiring a large number of neurons to achieve high-dimensional mapping, resulting in lower parameter efficiency than quantum methods; the memory capacity of classical reservoirs is limited by the reservoir size.
[0011] Therefore, how to provide a method and system for compressing and retrieving long-time-series numerical weather reanalysis data based on quantum reservoir computing, which has high compression ratio, high accuracy, random access capability and low training cost, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0012] In view of this, the present invention provides a method and system for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computing, aiming to achieve: (1) Ultra-high compression ratio: Compresses 58.4GB of ERA5Z500 data to 6.2MB (only storing QRC model parameters), with a compression ratio of 9600 times, while maintaining high-precision restoration capability; (2) Random access and instant restoration: Input any timestamp and output the meteorological field at the corresponding time directly through a fixed quantum circuit without iterating from the initial time; (3) Extremely low training cost: The reservoir (quantum system dynamics) of QRC is completely fixed, and only the linear weights of the Readout layer are trained (which can be solved directly by pseudo-inverse), and the training cost is at the level of linear regression. (4) Strong noise resistance: The intrinsic robustness of quantum reservoirs gives them a natural resistance to noise; (5) High-dimensional mapping capability: The Hilbert space of a quantum system grows exponentially with the number of qubits, and 10 qubits can realize a 1024-dimensional state space.
[0013] To achieve the above objectives, the present invention adopts the following technical solution: A method for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computation includes: Step 1: Perform anomaly preprocessing on long-term numerical weather reanalysis data to obtain the anomaly field matrix, and perform EOF decomposition on the anomaly field matrix to obtain the spatial mode matrix and time coefficient sequence; Step 2: Construct a quantum reservoir computational model; wherein, in an ideal quantum realization, the quantum reservoir consists of... The model is driven by a fixed Hamiltonian of qubits; in the equivalent implementation of numerical simulation, a fixed random transformation matrix is used to simulate the fixed dynamics of the quantum reservoir; the model adopts timestamp quantum encoding and extends the Readout dimension of the quantum reservoir through virtual node technology to meet the requirements of high-dimensional time coefficient sequences; Step 3: Encode the timestamp into a quantum state, obtain a high-dimensional Readout vector through quantum reservoir evolution, train only the linear weights of the Readout layer, establish a mapping relationship from the Readout vector to the time coefficient sequence, and store the trained quantum reservoir parameters and Readout weights; Step 4: Input the target timestamp into the trained model, output the corresponding time coefficient sequence, and reconstruct the original physical field by combining the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing.
[0014] Optionally, in step 1, the anomaly preprocessing includes: declimatization and detrending; the climatological mean field is the mean background field subtracted during the declimatization process.
[0015] Optionally, in step 1, after obtaining the spatial mode matrix and the time coefficient sequence, the following steps are also included: Retaining 99.9% of the explained variance One modality.
[0016] Optionally, in step 2, the quantum reservoir consists of... The fixed Hamiltonian driving force for each qubit is as follows:
[0017] in, For external field strength; The strength of the spin-to-spin interaction; , , For Pauli operators.
[0018] Optionally, in step 2, the timestamp quantum encoding is specifically as follows: Normalization: Mapping the original set of timestamps or scalars to an interval. :
[0019] Linear mapping and activation: using the input weight matrix and bias The normalized time is mapped to an initial state vector, and an activation function is applied. :
[0020] in, For observation dimensions; this step also supports It can be a batch input of vectors or a scalar input at a single time point.
[0021] Optionally, in step 2, the Readout dimension of the quantum reservoir is expanded using virtual node technology, specifically as follows: In an ideal quantum realization, through a single input interval The internal measurement of the reservoir at multiple time points or phases produces A virtual node, and The qubits were obtained together This expands the output dimensions by using multiple Readout nodes. In the equivalent implementation of numerical simulation, an equivalent implementation strategy is used: direct dimension mapping, which maps the number of observed dimensions. Set the target number of Readout nodes and use a fixed matrix. The nonlinear observation function generates a length of [length missing] at one time. Readout vector .
[0022] Optionally, in step 3, the training process specifically includes: Readout weight training: For each training time point Perform two steps: coding:
[0023] in, This represents the total number of observations. This is the normalized timestamp; For activation functions; This is the weight matrix; For bias; Reservoir Evolution and Observation:
[0024] in, This is the reservoir weight matrix; To observe the nonlinear mapping function; This is the output Readout feature vector; All training steps Composition of feature matrix ; Reader layer training: Let the training target matrix be The feature matrix is The solution uses regularized least squares analytical solution:
[0025] And take the bias:
[0026] in, , The mean of the training set columns; To read out the weight matrix; To read out the bias vector; For regularization terms; for An identity matrix of order 1; This represents the total number of training samples.
[0027] Optionally, in step 4, the original physical field is reconstructed by combining the spatial mode matrix and the climate mean field subtracted during anomaly preprocessing, specifically as follows:
[0028] in, The original physical field after reconstruction; The spatial mode matrix; It is a time coefficient sequence; This is the climate mean field subtracted during the anomaly preprocessing.
[0029] Optionally, it also includes: accuracy assessment, specifically; Time-domain evaluation: For each time step The root mean square error is used as follows:
[0030] in, This represents the number of spatial grid points. These are the actual field values; For the predicted field values; The correlation coefficient is used as follows:
[0031] in, For time steps The spatial average value of the real field; Overall assessment: Average of all time steps and ; Variance explained: .
[0032] This invention also provides a long-term numerical weather reanalysis data compression and retrieval system based on quantum reservoir computing, utilizing a method for compressing and retrieving long-term numerical weather reanalysis data based on quantum reservoir computing, comprising: Preprocessing and EOF decomposition module: Used to perform anomaly preprocessing on long-time series numerical weather reanalysis data to obtain anomaly field matrix, and to perform EOF decomposition on the anomaly field matrix to obtain spatial mode matrix and time coefficient sequence. Quantum reservoir computational model construction: used to construct a quantum reservoir computational model; wherein, in an ideal quantum realization, the quantum reservoir consists of... The model is driven by a fixed Hamiltonian of qubits; in the equivalent implementation of numerical simulation, a fixed random transformation matrix is used to simulate the fixed dynamics of the quantum reservoir; the model adopts timestamp quantum encoding and extends the Readout dimension of the quantum reservoir through virtual node technology to meet the requirements of high-dimensional time coefficient sequences; The quantum reservoir computation model training module is used to encode timestamps into quantum states, obtain high-dimensional Readout vectors through quantum reservoir evolution, train only the linear weights of the Readout layer, establish a mapping relationship from the Readout vector to the time coefficient sequence, and store the trained quantum reservoir parameters and Readout weights. Original physics reconstruction module: This module takes the target timestamp as input to the trained model, outputs the corresponding time coefficient sequence, and reconstructs the original physics field by combining the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing.
[0033] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computing, achieving the following beneficial effects: (1) For the first time, quantum reservoir computing (QRC) was applied to the compression of meteorological reanalysis data. The exponential state space of the quantum system was used to realize ultra-high-dimensional mapping, and the number of parameters was only 1 / 1000 of that of the classical method.
[0034] (2) A timestamp component encoding scheme is proposed to encode the year, month, day and hour into a quantum state, enabling direct access at any point in time (without iterative prediction).
[0035] (3) Combining EOF decomposition and QRC, we first reduce the data dimensionality through EOF decomposition (1243 PCs explain 99.9% of the variance), and then use QRC to learn the temporal evolution of PCs to achieve "double compression" (EOF compression + QRC parameter compression).
[0036] (4) It enables random access and instant restoration. By inputting any timestamp, the meteorological field at the corresponding time can be directly output through a fixed quantum circuit, breaking through the limitation of traditional methods that require sequential reading or iterative prediction.
[0037] (5) The training cost is extremely low. The reservoir dynamics of QRC are completely fixed. Only the linear weights of the Readout layer are trained (which can be solved directly by pseudo-inverse). The training time is in the minutes (while classic deep learning requires hours).
[0038] (6) Strong noise resistance. Quantum reservoir computing is naturally robust to input noise and parameter disturbances, making it suitable for long-term meteorological data modeling. Attached Figure Description
[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0040] Figure 1 This is a schematic diagram of the method flow provided by the present invention.
[0041] Figure 2 A schematic diagram illustrating the accuracy evaluation effect provided by this invention. Detailed Implementation
[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0043] Example 1: Embodiment 1 of this invention discloses a method for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computing, such as... Figure 1 As shown, it includes: Step 1: Perform anomaly preprocessing on long-term numerical weather reanalysis data (such as ERA5 Z500) to obtain the anomaly field matrix. (in, For time steps, (number of spatial grid points), and for the anomaly field matrix Perform EOF decomposition (in, (For singular value diagonal matrices), the spatial mode matrix is obtained. (EOFModes, storage requirement approximately 9.6GB) and time coefficient series (PCs, storage requirement approximately 277MB).
[0044] Anomaly preprocessing includes: declimatological and detrending; the climatological mean field is the mean background field subtracted during the declimatological processing.
[0045] After obtaining the spatial mode matrix and the time coefficient sequence, the following is also included: Retaining 99.9% of the explained variance Modalities (e.g.) This enables data dimensionality reduction.
[0046] Step 2: Construct a quantum reservoir calculation model (QRC); where, in an ideal quantum realization, the quantum reservoir consists of... The model is driven by a fixed Hamiltonian of qubits; in the equivalent implementation of numerical simulation (for ease of engineering verification and large-scale testing), a fixed random transformation matrix is used to simulate the fixed dynamics of the quantum reservoir; the model adopts timestamp quantum encoding and extends the Readout dimension of the quantum reservoir through virtual node technology to meet the requirements of high-dimensional time coefficient sequences.
[0047] Quantum reservoirs consist of The fixed Hamiltonian driving force for each qubit is as follows:
[0048] in, For external field strength; The strength of the spin-to-spin interaction; , , For Pauli operators.
[0049] Timestamp quantum encoding, specifically: This invention supports both ideal quantum gate-level component rotation coding and provides a numerical simulation coding scheme that is easier to implement in engineering, as follows: Normalization: Mapping the original set of timestamps or scalars to an interval. :
[0050] Linear mapping and activation: using the input weight matrix and bias The normalized time is mapped to an initial state vector, and an activation function is applied. :
[0051] in, For observation dimensions; this step also supports It can be a batch input of vectors or a scalar input at a single time point.
[0052] The Readout dimension of the quantum reservoir is expanded using virtual node technology, specifically as follows: In an ideal quantum realization, through a single input interval The internal measurement of the reservoir at multiple time points or phases produces A virtual node, and The qubits were obtained together This expands the output dimensions by using multiple Readout nodes. In the equivalent implementation of numerical simulation, an equivalent implementation strategy is used: direct dimension mapping, which maps the number of observed dimensions. Set the target number of Readout nodes (e.g.) ), and use a fixed matrix The nonlinear observation function generates a length of [length missing] at one time. Readout vector .
[0053] Step 3: Encode the timestamp into a quantum state, obtain a high-dimensional Readout vector through quantum reservoir evolution, train only the linear weights of the Readout layer, establish a mapping relationship from the Readout vector to the time coefficient sequence, and store the trained quantum reservoir parameters and Readout weights. The stored content is much smaller than the original data, and the compression ratio is improved by orders of magnitude.
[0054] Data preparation: Training set: Data from 2010 to 2019 (approximately 29,216 bytes in length); Input timestamps are first normalized to ,get As input; Read and preprocess the required files: (EOF Modes) (PC) .
[0055] The training process is as follows: Readout weight training: For each training time point Perform two steps: coding:
[0056] in, This represents the total number of observations (1250 in this example). This is the normalized timestamp; For activation functions; This is the weight matrix; For bias; Reservoir Evolution and Observation:
[0057] in, This is the reservoir weight matrix; To observe the nonlinear mapping function; This is the output Readout feature vector; All training steps Composition of feature matrix ; Reader layer training: Let the training target matrix be The feature matrix is The solution uses regularized least squares analytical solution:
[0058] And take the bias:
[0059] in, , The mean of the training set columns; To read out the weight matrix; To read out the bias vector; This is a regularization term (adjustable); for An identity matrix of order 1; This represents the total number of training samples.
[0060] Step 4: Set the target timestamp The input is fed into the trained model, and the corresponding time coefficient sequence is output. Combined with the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing, the original physical field is reconstructed, realizing random access to any timestamp, and the reconstruction time is less than 5 seconds, without the need for iterative prediction from the initial time.
[0061] By combining the spatial mode matrix and the climate mean field subtracted during anomaly preprocessing, the original physical field is reconstructed, specifically as follows:
[0062] in, The original physical field after reconstruction; The spatial mode matrix; It is a time coefficient sequence; This is the climate mean field subtracted during the anomaly preprocessing.
[0063] It also includes: accuracy assessment, specifically; Time-domain evaluation: For each time step The root mean square error is used as follows:
[0064] in, This represents the number of spatial grid points. These are the actual field values; For the predicted field values; The correlation coefficient is used as follows:
[0065] in, For time steps The spatial average value of the real field; Overall assessment: Average of all time steps and ; Variance explained: .
[0066] like Figure 2 The figure shown is a diagram illustrating the accuracy evaluation effect of the present invention.
[0067] Table 1 shows a comparison of the performance of the present invention (QRC) with that of the traditional EOF method, further highlighting the superiority of the present invention. It achieves random access and high restoration accuracy based on the traditional EOF method.
[0068] Table 1. Comparison of the effects of the present invention and existing methods
[0069] This invention can be widely applied in the following scenarios: (1) Meteorological Big Data Center: Long-term storage of massive amounts of reanalysis data to reduce storage costs; (2) Weather forecasting system: Quickly retrieve historical weather fields and support real-time business needs; (3) Climate research: Provides high-precision reconstruction data of long-term series to support climate variability analysis; (4) Quantum cloud computing platform: as a demonstration application of quantum machine learning in the meteorological field.
[0070] Example 2: Embodiment 2 of the present invention discloses a long-term time-series numerical weather reanalysis data compression and retrieval system based on quantum reservoir computing, which utilizes a method for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computing, comprising: Preprocessing and EOF decomposition module: Used to perform anomaly preprocessing on long-time series numerical weather reanalysis data to obtain anomaly field matrix, and to perform EOF decomposition on the anomaly field matrix to obtain spatial mode matrix and time coefficient sequence. Quantum reservoir computational model construction: used to construct a quantum reservoir computational model; wherein, in an ideal quantum realization, the quantum reservoir consists of... The model is driven by a fixed Hamiltonian of qubits; in the equivalent implementation of numerical simulation, a fixed random transformation matrix is used to simulate the fixed dynamics of the quantum reservoir; the model adopts timestamp quantum encoding and extends the Readout dimension of the quantum reservoir through virtual node technology to meet the requirements of high-dimensional time coefficient sequences; The quantum reservoir computation model training module is used to encode timestamps into quantum states, obtain high-dimensional Readout vectors through quantum reservoir evolution, train only the linear weights of the Readout layer, establish a mapping relationship from the Readout vector to the time coefficient sequence, and store the trained quantum reservoir parameters and Readout weights. Original physics reconstruction module: This module takes the target timestamp as input to the trained model, outputs the corresponding time coefficient sequence, and reconstructs the original physics field by combining the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing.
[0071] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0072] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computing, characterized in that, include: Step 1: Perform anomaly preprocessing on long-term numerical weather reanalysis data to obtain anomaly field matrix, and perform EOF decomposition on the anomaly field matrix to obtain spatial mode matrix and time coefficient sequence; Step 2: Construct a quantum reservoir computational model; wherein, in an ideal quantum realization, the quantum reservoir consists of... The model is driven by a fixed Hamiltonian of qubits; in the equivalent implementation of numerical simulation, a fixed random transformation matrix is used to simulate the fixed dynamics of the quantum reservoir; the model adopts timestamp quantum encoding and extends the Readout dimension of the quantum reservoir through virtual node technology to meet the requirements of high-dimensional time coefficient sequences; Step 3: Encode the timestamp into a quantum state, obtain a high-dimensional Readout vector through quantum reservoir evolution, train only the linear weights of the Readout layer, establish a mapping relationship from the Readout vector to the time coefficient sequence, and store the trained quantum reservoir parameters and Readout weights; Step 4: Input the target timestamp into the trained model, output the corresponding time coefficient sequence, and reconstruct the original physical field by combining the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing.
2. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing as described in claim 1, characterized in that, In step 1, the anomaly preprocessing includes: declimatization and detrending; the climatological mean field is the mean background field subtracted in the declimatization process.
3. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing as described in claim 1, characterized in that, Step 1, after obtaining the spatial mode matrix and the time coefficient sequence, also includes: Retaining 99.9% of the explained variance One modality.
4. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing as described in claim 1, characterized in that, In step 2, the quantum reservoir consists of... The fixed Hamiltonian driving force for each qubit is as follows: in, For external field strength; The strength of the spin-to-spin interaction; , , For Pauli operators.
5. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing according to claim 1, characterized in that, In step 2, the timestamp quantum encoding specifically refers to: Normalization: Mapping the original set of timestamps or scalars to an interval. : Linear mapping and activation: using the input weight matrix and bias The normalized time is mapped to an initial state vector, and an activation function is applied. : in, For observation dimensions; this step also supports It can be a batch input of vectors or a scalar input at a single time point.
6. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing according to claim 1, characterized in that, In step 2, the Readout dimension of the quantum reservoir is expanded using virtual node technology, specifically as follows: In an ideal quantum realization, through a single input interval The internal measurement of the reservoir at multiple time points or phases produces A virtual node, and The qubits were obtained together This expands the output dimensions by using multiple Readout nodes. In the equivalent implementation of numerical simulation, an equivalent implementation strategy is used: direct dimension mapping, which maps the number of observed dimensions. Set the target number of Readout nodes and use a fixed matrix. The nonlinear observation function generates a length of [length missing] at one time. Readout vector .
7. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing according to claim 1, characterized in that, Step 3, the training process, specifically includes: Readout weight training: For each training time point Perform two steps: coding: in, This represents the total number of observations. This is the normalized timestamp; For activation functions; This is the weight matrix; For bias; Reservoir Evolution and Observation: in, This is the reservoir weight matrix; To observe the nonlinear mapping function; This is the output Readout feature vector; All training steps Composition of feature matrix ; Reader layer training: Let the training target matrix be The feature matrix is The solution uses regularized least squares analytical solution: And take the bias: in, , The mean of the training set columns; To read out the weight matrix; To read out the bias vector; For regularization terms; for An identity matrix of order 1; This represents the total number of training samples.
8. The method for compression and retrieval of long-term time-series numerical weather reanalysis data based on quantum reservoir computing according to claim 1, characterized in that, In step 4, the original physical field is reconstructed by combining the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing, specifically as follows: in, The original physical field after reconstruction; The spatial mode matrix; It is a time coefficient sequence; The climate mean field is subtracted during the anomaly preprocessing.
9. A method for compressing and retrieving long-term time-series numerical weather reanalysis data based on quantum reservoir computing as described in claim 1, characterized in that, It also includes: accuracy assessment, specifically; Time-domain evaluation: For each time step The root mean square error is used as follows: in, This represents the number of spatial grid points. These are the actual field values; For the predicted field values; The correlation coefficient is used as follows: in, For time steps The spatial average value of the real field; Overall assessment: Average of all time steps and ; Variance explained: .
10. A long-term time-series numerical weather reanalysis data compression and retrieval system based on quantum reservoir computing, utilizing the long-term time-series numerical weather reanalysis data compression and retrieval method based on quantum reservoir computing as described in any one of claims 1-9, characterized in that, include: Preprocessing and EOF decomposition module: used to perform anomaly preprocessing on long-term numerical weather reanalysis data to obtain anomaly field matrix, and to perform EOF decomposition on the anomaly field matrix to obtain spatial mode matrix and time coefficient sequence; Quantum reservoir computational model construction: used to construct a quantum reservoir computational model; wherein, in an ideal quantum realization, the quantum reservoir consists of... The model is driven by a fixed Hamiltonian of qubits; in the equivalent implementation of numerical simulation, a fixed random transformation matrix is used to simulate the fixed dynamics of the quantum reservoir; the model adopts timestamp quantum encoding and extends the Readout dimension of the quantum reservoir through virtual node technology to meet the requirements of high-dimensional time coefficient sequences; The quantum reservoir computation model training module is used to encode timestamps into quantum states, obtain high-dimensional Readout vectors through quantum reservoir evolution, train only the linear weights of the Readout layer, establish a mapping relationship from the Readout vector to the time coefficient sequence, and store the trained quantum reservoir parameters and Readout weights. Original physical field reconstruction module: This module is used to input the target timestamp into the trained model, output the corresponding time coefficient sequence, and reconstruct the original physical field by combining the spatial mode matrix and the climate mean field subtracted in the anomaly preprocessing.