Data processing system and data processing method
By using the encoder, decoder, and QSRU network in the quantum recurrent neural network model to process high-dimensional partial differential equation data, the problem of low efficiency in existing technologies is solved, and efficient and fast data processing is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-16
- Publication Date
- 2026-03-31
AI Technical Summary
In existing technologies, data processing for high-dimensional partial differential equations is inefficient and time-consuming, and there is a lack of sophisticated data processing systems.
A quantum recurrent neural network model with a composite structure based on encoder, decoder and quantum simple recurrent unit (QSRU) network is adopted. The high-dimensional data is mapped to the low-dimensional latent space through encoding, prediction is performed using QSRU network, and the result is restored to the high-dimensional space by decoder. Combined with the determination module, the target solution at the current time is determined.
It enables efficient and rapid compression, prediction, and reconstruction of high-dimensional partial differential equation data, improving data processing efficiency and reliability while shortening processing time.
Smart Images
Figure CN121765345A_ABST
Abstract
Description
Technical Field
[0001] This disclosure generally relates to data processing techniques, and more particularly to a data processing system and a data processing method. Background Technology
[0002] Partial differential equations (PDEs) are a fundamental mathematical tool for modeling various phenomena in numerous fields such as physics, biology, chemistry, and economics. For many complex, high-dimensional PDEs, analytical solutions are often unattainable due to their intricate structure and nonlinear characteristics. To address this problem, numerical methods such as the finite difference method, the finite element method, and the finite volume method have emerged to provide approximate solutions.
[0003] However, due to the computational complexity of partial differential equations, there is currently no perfect data processing system for them, resulting in problems such as low data processing efficiency and long processing times. Therefore, proposing an efficient and time-saving data processing system for partial differential equations has become an important research direction. Summary of the Invention
[0004] This disclosure addresses some of the shortcomings mentioned in the background art by providing a data processing system and a data processing method.
[0005] In a first aspect, embodiments of this disclosure provide a data processing system, including: a quantum recurrent neural network model and a determination module; wherein, the quantum recurrent neural network model includes: an encoder, a decoder, and a quantum simple recurrent unit (QSRU) network; both the encoder and the decoder employ a multilayer perceptron structure; the encoder is used to acquire data of a target partial differential equation to be solved, and to encode the data of the target partial differential equation to be solved to obtain a low-dimensional latent space encoding result; the QSRU network is used to make predictions based on the low-dimensional latent space encoding result to obtain a prediction result; the decoder is used to decode the prediction result to obtain a decoded result of the original-dimensional latent space; and the determination module is used to determine the target solution of the partial differential equation data to be solved at the current time based on the decoded result of the original-dimensional latent space.
[0006] In a second aspect, embodiments of this disclosure provide a data processing method applicable to the data processing system of the first aspect. The data processing system includes: a quantum recurrent neural network model and a determination module; wherein the quantum recurrent neural network model includes: an encoder, a decoder, and a quantum simple recurrent unit (QSRU) network; both the encoder and the decoder employ a multilayer perceptron structure; the method includes: the encoder acquiring target partial differential equation data to be solved and encoding the target partial differential equation data to obtain a low-dimensional latent space encoding result; the QSRU network making a prediction based on the low-dimensional latent space encoding result to obtain a prediction result; the decoder decoding the prediction result to obtain an original-dimensional latent space decoding result; and the determination module determining the target solution of the partial differential equation data to be solved at the current time based on the original-dimensional latent space decoding result.
[0007] In a third aspect, embodiments of this disclosure provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements the method described in the second aspect.
[0008] In a fourth aspect, embodiments of this disclosure provide a processor-readable storage medium storing a computer program for causing a processor to perform the method described in the second aspect.
[0009] In a fifth aspect, embodiments of this disclosure provide a computer program product including a computer program that, when executed by a processor, implements the method described in the second aspect.
[0010] The embodiments provided in this disclosure have at least the following beneficial technical effects: According to an embodiment of this disclosure, a data processing system can encode the target partial differential equation data to be solved using an encoder to obtain a low-dimensional latent space encoding result. A QSRU network then predicts the result based on this low-dimensional latent space encoding result, and a decoder decodes the result to obtain the original-dimensional latent space decoding result. Furthermore, a determination module can determine the current-time target solution of the partial differential equation data based on the original-dimensional latent space decoding result. Therefore, this disclosure, based on a quantum recurrent neural network model and determination module with a composite structure including an encoder, decoder, and QSRU network, enables efficient and rapid compression, prediction, reconstruction, and analysis of high-dimensional partial differential equation data, improving the efficiency and reliability of high-dimensional partial differential equation data processing and shortening the processing time.
[0011] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description
[0012] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein: Figure 1 This is a schematic diagram of a data processing system; Figure 2 This is a schematic diagram of a QSRU network in a data processing system; Figure 3 This is a schematic diagram of a variable quantum circuit in a data processing system; Figure 4 This is a schematic diagram of an encoder in a data processing system; Figure 5 This is a schematic diagram of another data processing system; Figure 6 This is a schematic diagram of the processing procedure of a data processing system; Figure 7 This is a flowchart illustrating a data processing method. Figure 8 This is a schematic diagram of an electronic device.
[0013] In the picture: 1000 - Data processing system; 100 - Quantum recurrent neural network model control components (including 101 - encoder, 102 - decoder and 103 - QSRU network); 200 - Deterministic module; 300 - Data processing module. Detailed Implementation
[0014] The present disclosure will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present disclosure and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present disclosure are shown in the drawings, not the entire structure.
[0015] It should be noted that, in the existing technology, numerical methods such as the finite difference method, the finite element method, and the finite volume method have been proposed to approximate solutions to partial differential equations. However, although the aforementioned techniques have achieved certain results in various applications, they still have significant limitations in terms of computational complexity, stability, and scalability, especially when dealing with nonlinear or high-dimensional problems.
[0016] With the development of neural networks and quantum machine learning technologies, quantum recurrent neural networks (QRNNs) and their variants have provided new approaches to solving complex partial differential equations. Among them, QRNN is a novel quantum neural network model that combines classical recurrent neural networks (RNNs) and quantum machine learning (QML).
[0017] RNNs are neural network models with a recurrent structure that can effectively capture dependencies in sequential data and learn the dynamic characteristics of spatial and temporal variables in PDEs. However, standard RNN networks suffer from problems such as vanishing gradients.
[0018] Furthermore, variants of RNNs, such as Long Short-Term Memory (LSTM) networks and Gated Recurrent Unit (GRU) networks, introduce gating mechanisms, enabling them to learn long-term dependencies more effectively. Meanwhile, QML utilizes quantum mechanics for computation, introducing Variational Quantum Circuits (VQCs) to achieve quantum entanglement and superposition properties, effectively enhancing the expressive power of classical neural networks.
[0019] In this way, the combination of RNN and QML technology laid the foundation for the development of QRNN, forming two typical quantum recurrent neural networks, such as Quantum Long Short-Term Memory (QLSTM) and Quantum Gated Recurrent Unit (QGRU). Numerous experiments have demonstrated that QRNN and its variants are adept at modeling complex time dependencies.
[0020] However, existing technical solutions only focus on one aspect of the encoder / decoder or quantum neural network, ignoring the computational complexity of quantum neural networks in processing high-dimensional data. Furthermore, both QLSTM and QGRU networks, due to their fixed model structure and inherent characteristics in state computation, will cause the number of model parameters to become extremely large as the time series deepens, and the computational complexity will increase exponentially, resulting in the computational efficiency of the algorithm model being far lower than the theoretical level.
[0021] Therefore, in order to solve the above problems, this disclosure proposes a data processing system based on a composite structure model and determination module including an encoder, a decoder and a quantum simple recurrent unit (QSRU) network. This system can efficiently and quickly compress, predict, reconstruct and analyze high-dimensional partial differential equation data to obtain reliable target solutions for high-dimensional partial differential equation data at the current time.
[0022] Figure 1 This is a schematic diagram of a data processing system provided in an embodiment of this disclosure. Figure 1 As shown, the data processing system 1000 includes: a quantum recurrent neural network model 100 and a determination module 200; wherein, the quantum recurrent neural network model 100 includes: an encoder 101, a decoder 102, and a QSRU network 103; both the encoder 101 and the decoder 102 adopt a multilayer perceptron structure. Encoder 101 is used to acquire the target partial differential equation data to be solved and to encode the target partial differential equation data to obtain the low-dimensional latent space encoding result.
[0023] The QSRU network 103 is used to make predictions based on the low-dimensional latent space encoding results.
[0024] Decoder 102 is used to decode the prediction results to obtain the original dimension latent space decoding results.
[0025] The determination module 200 is used to determine the target solution of the partial differential equation data to be solved at the current time based on the decoding results of the original dimension latent space.
[0026] It should be noted that the data processing system proposed in this disclosure is capable of processing high-dimensional partial differential equation data, and in particular, it has a more significant advantage in providing high-quality solutions for nonlinear time-varying partial differential equations such as the Burgers equation and the HJB (Hamilton-Jacobi-Bellman) equation.
[0027] In this embodiment of the disclosure, the data processing system 1000 can use the high-dimensional target partial differential equation data to be solved as the input data of the quantum recurrent neural network model 100. First, the encoder 101 in the quantum recurrent neural network model 100 encodes the input data to realize feature extraction of the input data and mapping it to a low-dimensional data space. Then, the low-dimensional latent space encoding result obtained by the encoding process is input into the QSRU network 103 in the quantum recurrent neural network model 100.
[0028] Furthermore, the QSRU network 103 receives the feature input from the encoder 101, makes predictions based on the low-dimensional latent space encoding results, and inputs the prediction results into the decoder 102 in the quantum recurrent neural network model 100. The QSRU network is a novel variant of QRNN, capable of efficiently learning the temporal evolution of partial differential equation data.
[0029] Furthermore, the decoder 102 receives the prediction results output by the QSRU network 103, performs decoding processing on the prediction results, restores the prediction results to a high-dimensional data space, and sends the decoded original dimension latent space decoding results to the determination module 200.
[0030] Furthermore, the module 200 receives the model output of the quantum recurrent neural network model 100, identifies the decoding result of the original dimension latent space, and determines the target solution of the partial differential equation data to be solved at the current time based on the identification result.
[0031] It should also be noted that in this embodiment, both the encoder 101 and the decoder 102 adopt a multilayer perceptron (MLP / MLPs) structure. A multilayer perceptron is a feedforward artificial neural network model that can map multiple input datasets to a single output dataset.
[0032] According to an embodiment of this disclosure, a data processing system can encode the target partial differential equation data to be solved using an encoder to obtain a low-dimensional latent space encoding result. A QSRU network then predicts the result based on this low-dimensional latent space encoding result, and a decoder decodes the result to obtain the original-dimensional latent space decoding result. Furthermore, a determination module can determine the current-time target solution of the partial differential equation data based on the original-dimensional latent space decoding result. Therefore, this disclosure, based on a quantum recurrent neural network model and determination module with a composite structure including an encoder, decoder, and QSRU network, enables efficient and rapid compression, prediction, reconstruction, and analysis of high-dimensional partial differential equation data, improving the efficiency and reliability of high-dimensional partial differential equation data processing and shortening the processing time.
[0033] The main structural components of the quantum recurrent neural network model 100 in the data processing system 1000 of this disclosure will be explained below with reference to embodiments.
[0034] First, regarding the QSRU network 103, it's important to note that as a crucial component of the quantum recurrent neural network model 100, QSRU network 103 incorporates multiple adaptive Variational Quantum Circuits (VQCs). This allows QSRU network 103 to superimpose multiple VQCs onto the classic Simple Recurrent Unit (SRU) network structure. Compared to models like QLSTM and QGRU, it uses fewer parameters while retaining the gating mechanism's ability to learn long-term dependencies. Unlike classic LSTM and GRU networks, the classic SRU network, to reduce the time-dependent complexity of recurrences, uses the forget and reset gates instead of relying on the previous hidden state, relying instead on the previous intermediate state. Simultaneously, a highway network unit is introduced, employing a skip connection structure, similar to a residual network structure, to optimize gradient propagation, thereby ensuring better information flow across layers.
[0035] In this embodiment of the disclosure, the QSRU network 103 includes a plurality of variable quantum lines that are respectively connected to the input gate, forget gate and reset gate of the QSRU network 103.
[0036] It should be noted that in this disclosure, the input gate, forget gate, and reset gate are each connected to at least one corresponding variable quantum line.
[0037] For example, such as Figure 2 As shown, the QSRU network 103 includes an input gate, a forget gate, a reset gate, and three variable quantum lines: VQC1 - VQC3 ,and VQC1 Acting on the input gate, VQC2 It acts on the forgetting gate. VQC3 It is used to reset the door.
[0038] To further explain in detail the components and processing procedures in the QSRU network 103, the following explanation will be based on the core formulas:
[0039]
[0040]
[0041]
[0042]
[0043] in, represent t Input at any time represent t The output of the input gate is always in use. f t represent t The output of the Forget Gate r t represent t The output of the gate is reset at all times. C t represent t Unit state at any given time h t represent t The final output of the time-hidden layer.
[0044] For the input gate, VQC2 The input data is encoded and compressed, and then the output of the input gate is determined through a simple linear transformation. The input gate determines how much of the network's input at the current moment needs to be saved to the cell state. C t middle.
[0045] For the forget gate and reset gate, the hidden layer output from the previous time step is not introduced. h t-1 Add only based on the input at the current moment. VQC1 and VQC3 The input data is processed by an activation function (Sigmoid) to encode and extract features, and then the output of the forget gate is determined by the Sigmoid activation function. f t As a unit state C t The input, the output of the input gate, and the cell state at the previous time step. C t-1 Together they determine the current cell state C t ; Reset gate output r t With unit state C t Together they determine the hidden layer at the current moment h t The final output.
[0046] Therefore, unlike models such as QLSTM and QGRU, the QSRU network does not incorporate the hidden layer output from the previous time step into the computation of the input gate, forget gate, and reset gate. Instead, it uses the unit state to integrate information from past states and the current input, thus eliminating the temporal dependency in the computation of the input gate, forget gate, and reset gate. While retaining temporal dependency for the unit state, the use of the Hadamard product allows for concurrent computation of all dimensions of the hidden feature vector and intermediate state vector, significantly improving the training speed of the network model. Furthermore, based on the Skip Connection structure, the input data is directly incorporated into the computation. This operation is similar to the bridging operation in residual networks, ensuring that the derivative of the input does not disappear with increasing network depth, greatly optimizing the gradient propagation process of deep QSRU networks.
[0047] The structure of the variable quantum circuit in the QSRU network 103 will be further explained below with reference to the embodiments.
[0048] In this embodiment of the disclosure, any variational quantum circuit includes: a data encoding unit, a variational unit, and a quantum measurement unit; the data encoding unit uses amplitude encoding, and the variational unit is composed of multiple stackable variational quantum units. Each variational quantum unit includes: multiple quantum controlled NOT gates (CNOT gates) and a rotation gate with trainable parameters, wherein any qubit is connected to each other qubit through CNOT gates.
[0049] It should be noted that this disclosure does not limit the specific number of multiple stackable variable molecular units, which can be set according to the actual situation.
[0050] For example, such as Figure 3 As shown, the variational quantum circuit includes a data encoding unit P that uses amplitude encoding, and a variational unit U composed of N stackable variational units (U1-U2). N ), where N is an integer greater than 1.
[0051] Among them, the data encoding unit P is implemented using amplitude encoding, which can further compress high-dimensional data. For a given data unit P... Input vector of elements , Data amplitude encoding can be completed using only n qubits. Amplitude encoding is typically implemented using a hierarchical control rotating gate, and the encoded quantum state can be represented as:
[0052]
[0053] in, Represents the probability distribution of quantum states. .
[0054] The variational unit U is the trainable part of the variational quantum circuit, composed of multiple stackable variational units. The number of variational units can be controlled according to actual conditions. Using multiple variational units helps to increase the parameter scale of the quantum neural network, thereby enhancing the network's expressive power. Each variational unit contains multiple CNOT gates and parameter-trainable rotation gates. The CNOT gates are connected in pairs to ensure that each qubit can generate entanglement.
[0055] In this disclosure, the quantum measurement unit in a variable quantum circuit can convert the state of the quantum circuit back into classical information for decision-making or output. Due to the inherent probabilistic nature of quantum systems, the measurement module typically calculates the expected value for output. The expected value calculation can be expressed as:
[0056] in, Represents Hermitian operators Regarding quantum states The expected value, which converts the probability amplitude of the quantum state into a classically tractable real value, is used for subsequent QSRU network 103 gating operations and state updates.
[0057] According to an embodiment of the present disclosure, a data processing system uses a quantum recurrent neural network model that superimposes multiple variable quantum circuits on the classical SRU network structure, thereby enhancing the expressive power of the neural network. Based on the inherent characteristics of the SRU network, prediction is achieved with fewer parameters, while retaining the learning ability of the gating mechanism for long-term dependencies, further improving the efficiency of the data processing process and shortening the processing time.
[0058] Secondly, regarding the encoder 101 and decoder 102, after explaining the QSRU network 103 and its structure above, the structure of the encoder 101 and decoder 102 respectively set before and after the QSRU network 103 will be further explained below with reference to the embodiments.
[0059] Encoder 101 consists of an N-layer neural network with trainable parameters and activation functions, where N is an integer greater than or equal to 1. In this case, encoder 101 is also used to map the target partial differential equation data to a low-dimensional latent space.
[0060] Optionally, before mapping the target partial differential equation data to a low-dimensional latent space, the number of neurons in the next layer of the neural network gradually decreases from the first layer to the (N-1)th layer.
[0061] As one possible implementation, such as Figure 4 As shown, encoder 101 uses fully connected layers, where each neuron is connected to every neuron in subsequent layers, enabling the network to capture complex hierarchical representations. Encoder 101 employs a progressive dimensionality reduction approach, where the number of neurons in each neural network layer is reduced according to (2...) before the input data reaches the compressed latent space. n ,2 n-1 ,2 n-2 ...) gradually reduce the input dimensionality using a pattern (e.g., 4096, 2048, 1024, 512), ultimately achieving the goal of reducing the input data... Mapping to latent space .
[0062]
[0063] in, Indicates encoder parameters, x Low-dimensional data representing the compressed latent space.
[0064] Furthermore, decoder 102 is a mirror structure of encoder 101, and converts the output of QSRU network 103. Expand to the original input size, that is:
[0065] in, This represents the final output of the QSRU network. Indicates decoder parameters, This represents the predicted value restored to the original resolution.
[0066] Decoder 102 is a mirror image of encoder 101, and will not be described further here.
[0067] According to an embodiment of this disclosure, a data processing system can encode high-dimensional model inputs through a pre-set encoder in a QSRU network of a quantum recurrent neural network model. This means compressing the high-dimensional spatial data of the target partial differential equation to be solved into a low-dimensional latent space before inputting it into the QSRU network, ensuring the operability and reliability of the QSRU network's prediction processing. Furthermore, a post-set decoder in the QSRU network can decode the network's output, allowing the prediction results obtained by the QSRU network to be converted back to the high-dimensional space, reconstructing the original spatial resolution, further improving the reliability of the data processing process.
[0068] After explaining the quantum recurrent neural network model 100 and its structure above, the data processing module 300 will be explained below in conjunction with the embodiments.
[0069] It should be noted that, in order to further improve the efficiency and reliability of the data processing system, the initial partial differential equation data to be solved can be preprocessed before inputting the target partial differential equation data to be solved into the quantum recurrent neural network model 100, and the processed data can be used as the target partial differential equation data to be solved.
[0070] In this embodiment of the disclosure, such as Figure 5 As shown, the data processing system 1000 also includes a data processing module 300.
[0071] The data processing module 300 is used to: acquire the initial partial differential equation data to be solved, and normalize the initial partial differential equation data to obtain the intermediate partial differential equation data to be solved. Further, the intermediate partial differential equation data to be solved is subjected to dimensional expansion processing to obtain the target partial differential equation data to be solved.
[0072] For example, the data processing module 300 can acquire the initial partial differential equation data to be solved and perform initialization processing such as normalization on the initial partial differential equation data to be solved. Optionally, the initial partial differential equation data V to be solved can be discretized. In this case, the data dimension is ( n t ,n x ,n y The parameters of QSRU network 103 are: θ QSRU The parameters of encoder 101 are: θ enc The parameters of decoder 102 are θ dec .
[0073] Furthermore, the input data, i.e., the initial partial differential equation data V to be solved, can be normalized to obtain... V norm And will V norm Data according to target spatial dimensions ( n t ) Perform dimensional expansion to obtain two-dimensional input data V input That is, the target partial differential equation data V to be solved input In this case, the parameters of QSRU network 103 θ QSRU Parameters of encoder 101 θ enc Parameters of decoder 102 θ dec All parameters are randomly initialized, thus completing the initialization process for the initial data.
[0074] According to an embodiment of the present disclosure, a data processing system can preprocess the initial partial differential equation data to be solved before inputting the target partial differential equation data to be solved into the quantum recurrent neural network model 100, and use the processed data as the target partial differential equation data to be solved, thereby further improving the efficiency and reliability of the data processing system.
[0075] After explaining the quantum recurrent neural network model 100 and the data processing module 300 above, the determination module 200 will be explained below in conjunction with the embodiments.
[0076] It should be noted that in this disclosure, the determining module 200 is mainly used to identify the decoding results of the original dimension latent space and determine the target solution of the partial differential equation data to be solved at the current time based on the identification results.
[0077] As one possible implementation, the determining module 200 is further configured to: obtain the current-time loss function based on the decoding result of the original dimensional latent space; and, in response to the current-time loss function satisfying the target condition, use the decoding result of the original dimensional latent space as the current-time target solution of the partial differential equation data to be solved. Further, the determining module 200 is also configured to: adjust the model parameters of the quantum recurrent neural network model based on the loss function in response to the current-time loss function not satisfying the target condition.
[0078] In this embodiment, the determining module 200 can receive the model output of the quantum recurrent neural network model 100 and obtain the current time-instance loss function based on the original dimension latent space decoding result. Then, the current time-instance loss function is identified. If the current time-instance loss function meets the target condition, the original dimension latent space decoding result can be used as the current time-instance target solution of the partial differential equation data to be solved. If the current time-instance loss function does not meet the target condition, the model parameters of the quantum recurrent neural network model 100 can be adjusted until the training termination condition is met. The original dimension latent space decoding result output by the quantum recurrent neural network model 100 after the last adjustment of model parameters is then used as the current time-instance target solution of the partial differential equation data to be solved.
[0079] The target conditions can be set according to the actual situation. For example, the target condition can be set as the loss function calculation result achieving a pre-defined target accuracy.
[0080] It should be noted that this disclosure does not limit the specific method of adjusting the model parameters of the quantum recurrent neural network model according to the loss function, and can be set according to the actual situation.
[0081] As one possible implementation, the variational unit in the variational quantum circuit includes a rotating gate with trainable parameters. In this case, when adjusting the model parameters of the quantum recurrent neural network model according to the loss function, the parameters of the rotating gate can be adjusted according to the loss function.
[0082] For example, with Figure 3 Taking a 6-bit circuit as an example, each qubit is connected to other qubits in pairs through CNOT gates. Each qubit contains a learningable rotating gate with three parameters (α, β, γ). In this case, if the loss function does not meet the target condition at the current time, the determination module 200 can adjust the parameters of the rotating gates according to the loss function. The aforementioned parameters will be updated during the backpropagation of the quantum recurrent neural network model.
[0083] It should be noted that, in this disclosure, before the quantum recurrent neural network model converges, the parameters corresponding to the input gate, forget gate, and reset gate, the parameters corresponding to the variable quantum circuit, and the trainable parameters corresponding to the encoder 101 can all be adjusted, which will not be elaborated here.
[0084] According to an embodiment of the present disclosure, a data processing system can determine whether the decoding result of the original dimension latent space can be used as the target solution for the partial differential equation data to be solved at the current time. Then, based on the current time loss function and the target conditions, it identifies whether the decoding result of the original dimension latent space can be used as the target solution for the partial differential equation data to be solved at the current time. Further, if the current time loss function does not meet the target conditions, the model parameters of the quantum recurrent neural network model can be adjusted according to the loss function until training is complete, resulting in a trained and converged quantum recurrent neural network model. The decoding result of the original dimension latent space output by the converged quantum recurrent neural network model is then determined as the target solution. Therefore, based on a determination module that allows for adjustment of model parameters, the present disclosure ensures the accuracy of the target solution for the partial differential equation data to be solved at the current time obtained from the trained and converged quantum recurrent neural network model, further improving the reliability of the data processing process.
[0085] To provide a clearer explanation of some of the processing procedures and effects of the data processing system proposed in this disclosure, the following will combine... Figure 6 Please provide an explanation.
[0086] It should be noted that the data processing system 1000 proposed in this disclosure includes a quantum recurrent neural network model 100, a determination module 200, and a data processing module 300.
[0087] Among them, the quantum recurrent neural network model 100 adopts a composite model structure of "encoder 101-QSRU network 103-decoder 102" to solve high-dimensional partial differential equation data.
[0088] Furthermore, the setting of "...QSRU network 103..." adds multiple adapted variable quantum circuits to the classic SRU network structure, introducing quantum entanglement and superposition characteristics, thereby enhancing the expressive power of the neural network.
[0089] Furthermore, the setup of "encoder 101-......-decoder 102" can compress high-dimensional spatial data of partial differential equation data into a low-dimensional latent space, and then convert the output of the QSRU network back to the high-dimensional space to reconstruct the original spatial resolution.
[0090] like Figure 6 As shown in this disclosure, the data processing module 300 can acquire the initial partial differential equation data to be solved, and normalize the initial partial differential equation data to obtain the intermediate partial differential equation data to be solved. Further, the intermediate partial differential equation data to be solved is subjected to dimensional expansion processing to obtain the target partial differential equation data to be solved, and the target partial differential equation data to be solved is used as the input to the quantum recurrent neural network model 100.
[0091] In the quantum recurrent neural network model 100, the encoder 101 can extract the features of the input data and map them to a low-dimensional data space. The QSRU network 103 can receive the feature input from the encoder, complete parameter training and update, and the decoder 102 can receive the output of the QSRU network and restore the output to a high-dimensional data space.
[0092] Optionally, the encoder 101 in the quantum recurrent neural network model 100 can acquire the target partial differential equation data to be solved, encode the target partial differential equation data to obtain a low-dimensional latent space encoding result, and input the low-dimensional latent space encoding result into the QSRU network 103 in the quantum recurrent neural network model 100. The low-dimensional latent space encoding result includes the training sequence x_train and the target sequence y_train. The QSRU network 103 in the quantum recurrent neural network model 100 can make predictions based on the low-dimensional latent space encoding result, obtain prediction results, and input the prediction results into the decoder 102 in the quantum recurrent neural network model 100. The prediction results include z_bar. The decoder 102 in the quantum recurrent neural network model 100 can decode the prediction results to obtain the original-dimensional latent space decoding result.
[0093] The determination module 200 can obtain the loss function at the current time step based on the decoding result of the original dimension latent space. If the loss function at the current time step satisfies the target condition, the decoding result of the original dimension latent space is used as the target solution for the partial differential equation data to be solved at the current time step. If the loss function at the current time step does not satisfy the target condition, the Adam optimizer is used to minimize the loss function, and backpropagation is used to update the parameters until the training termination condition is met. Based on inverse normalization, the decoding result of the original dimension latent space output by the quantum recurrent neural network model 100 after the last adjustment of model parameters is used as the target solution for the partial differential equation data to be solved at the current time step. The inverse normalization process restores the output of the quantum recurrent neural network model 100 to its original dimensions, ensuring that the target solution at the current time step is readily applicable in practice.
[0094] In summary, the above process enables the prediction and solution of high-dimensional partial differential equation data. The "encoder-QSRU-decoder" composite model structure has lower parameter requirements and training speed compared to QLSTM and QGRU, while retaining the characteristics of capturing complex spatiotemporal patterns and handling high-dimensional spaces. It provides a high-quality solution for solving nonlinear time-varying partial differential equation data (such as Burgers equations and HJB equations).
[0095] Figure 7 This is a flowchart illustrating a data processing method provided in an embodiment of the present disclosure, applicable to a data processing system 1000. The data processing system 1000 includes a quantum recurrent neural network model 100 and a determination module 200. The quantum recurrent neural network model 100 includes an encoder 100, a decoder 102, and a QSRU network 103. Both the encoder and decoder employ a multilayer perceptron structure. As one possible implementation, such as... Figure 7 As shown, the specific steps include: S701, the encoder acquires the target partial differential equation data to be solved, and encodes the target partial differential equation data to obtain the low-dimensional latent space encoding result.
[0096] The S702 QSRU network makes predictions based on the low-dimensional latent space encoding results.
[0097] S703, the decoder decodes the prediction results to obtain the original dimension latent space decoding results.
[0098] S704, the determination module determines the target solution of the partial differential equation data to be solved at the current time based on the decoding results of the original dimension latent space.
[0099] According to an embodiment of this disclosure, a data processing method can encode the target partial differential equation data to be solved using an encoder to obtain a low-dimensional latent space encoding result. A QSRU network then predicts the result based on this low-dimensional latent space encoding result, and a decoder decodes the result to obtain the original-dimensional latent space decoding result. Furthermore, a determination module can determine the current-time target solution of the partial differential equation data to be solved based on the original-dimensional latent space decoding result. Therefore, this disclosure, based on a quantum recurrent neural network model and determination module with a composite structure including an encoder, decoder, and QSRU network, can achieve efficient and rapid compression, prediction, reconstruction, and analysis of high-dimensional partial differential equation data, improving the efficiency and reliability of high-dimensional partial differential equation data processing and shortening the processing time.
[0100] According to embodiments of this disclosure, this disclosure also provides an electronic device 3000, such as... Figure 8 As shown, it includes a memory 400, a processor 500, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aforementioned data processing method.
[0101] According to embodiments of this disclosure, a processor-readable storage medium is also provided. This processor-readable storage medium stores a computer program that causes the processor to perform the aforementioned data processing method.
[0102] The processor-readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to magnetic memory (e.g., floppy disk, hard disk, magnetic tape, magneto-optical disk (MO)), optical memory (e.g., CD, DVD, BD, HVD), and semiconductor memory (e.g., ROM, EPROM, EEPROM, non-volatile memory (NAND FLASH), solid-state drive (SSD)).
[0103] According to embodiments of this disclosure, a computer program product is also provided. This computer program product includes a computer program that, when executed by a processor, performs the aforementioned data processing method.
[0104] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this disclosure can be achieved, and this is not limited herein.
[0105] The specific embodiments described herein do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.
Claims
1. A data processing system, characterized in that, include: A quantum recurrent neural network model and a determination module; wherein the quantum recurrent neural network model includes: an encoder, a decoder, and a quantum simple recurrent unit (QSRU) network; the encoder and the decoder both adopt a multilayer perceptron structure; The encoder is used to acquire the target partial differential equation data to be solved, and to encode the target partial differential equation data to obtain the low-dimensional latent space encoding result. The QSRU network is used to make predictions based on the low-dimensional latent space encoding results to obtain prediction results. The decoder is used to decode the prediction result to obtain the original dimension latent space decoding result; The determining module is used to determine the target solution of the partial differential equation data to be solved at the current time based on the decoding result of the original dimension latent space.
2. The data processing system according to claim 1, characterized in that, The QSRU network includes multiple variable quantum lines that are respectively connected to the input gate, forget gate, and reset gate of the QSRU network.
3. The data processing system according to claim 2, characterized in that, Any of the aforementioned variational quantum circuits includes: a data encoding unit, a variational unit, and a quantum measurement unit; wherein the data encoding unit employs amplitude encoding, and the variational unit is composed of multiple stackable variational quantum units.
4. The data processing system according to claim 3, characterized in that, Any of the variable molecular units includes: a plurality of quantum controlled NOT gates and a rotation gate with trainable parameters, wherein any qubit is connected to each other qubit through the quantum controlled NOT gates.
5. The data processing system according to claim 1, characterized in that, The encoder consists of an N-layer neural network with trainable parameters and activation functions, where N is an integer greater than or equal to 1; the encoder is also used to: map the target partial differential equation data to be solved to a low-dimensional latent space.
6. The data processing system according to claim 5, characterized in that, Before mapping the target partial differential equation data to be solved to the low-dimensional latent space, the number of neurons in the next layer of the neural network gradually decreases from the first layer to the (N-1)th layer.
7. The data processing system according to claim 1, characterized in that, The system further includes a data processing module, the data processing module being used for: Obtain the initial partial differential equation data to be solved, and normalize the initial partial differential equation data to be solved to obtain the intermediate partial differential equation data to be solved. The intermediate partial differential equation data to be solved is subjected to dimensional expansion processing to obtain the target partial differential equation data to be solved.
8. The data processing system according to claim 1, characterized in that, The determining module is further configured to: Based on the decoding results of the original dimensional latent space, obtain the loss function at the current time step; In response to the loss function satisfying the target condition at the current time, the decoding result of the original dimension latent space is used as the target solution of the partial differential equation data to be solved at the current time.
9. The data processing system according to claim 8, characterized in that, The determining module is further configured to: In response to the loss function not satisfying the target condition at the current time, the model parameters of the quantum recurrent neural network model are adjusted according to the loss function.
10. A data processing method, characterized in that, The data processing system is applicable to a data processing system, which includes a quantum recurrent neural network model and a determination module; wherein the quantum recurrent neural network model includes an encoder, a decoder, and a quantum simple recurrent unit (QSRU) network; both the encoder and the decoder adopt a multilayer perceptron structure. The method includes: The encoder acquires the target partial differential equation data to be solved and encodes the target partial differential equation data to obtain the low-dimensional latent space encoding result. The QSRU network makes predictions based on the low-dimensional latent space encoding results to obtain prediction results. The decoder decodes the prediction result to obtain the original dimension latent space decoding result; The determining module determines the target solution of the partial differential equation data to be solved at the current time based on the decoding result of the original dimension potential space.