A Tokamak Plasma Turbulence Prediction Method and System Based on Layer Theory Topology and Spectral Neural Operators

Abstract

This invention discloses a tokamak plasma turbulence prediction method and system based on layer-theoretic topology and spectral neural operators. The method includes acquiring diagnostic and control data from a tokamak device and converting them into a set of physical field vectors, actuator vectors, and equilibrium parameter vectors; mapping the physical field vector set to a latent grid representation and fusing the actuator and equilibrium parameter vectors to obtain a conditional latent grid representation; using a multi-layer Fourier neural operator for time evolution to obtain the latent grid representation for the next time step; applying multi-region consistency constraints to the latent grid representation using a constraint mapping operator and a glue loss function; and using the constrained predicted latent grid representation for prediction, outputting the hazard level and remaining time prediction values ​​of plasma turbulence. Simultaneously, a projection and repair module applies physical constraints to the restored physical field prediction representation to obtain a corrected physical field prediction representation. This invention improves the accuracy of the results.

Description

Technical Field

[0001] This invention relates to the field of nuclear fusion tokamak device technology, and more specifically to a tokamak plasma turbulence prediction system based on layer theory topology and spectral neural operators. Background Technology

[0002] In a tokamak device, the turbulent transport processes in the plasma edge region directly affect the confinement performance, the thermal load on the first wall, and the frequency of instability events such as edge local modes. From a mathematical perspective, plasma turbulence prediction is essentially an operator learning problem between infinite-dimensional function spaces, involving complex topological constraints and multi-region geometry.

[0003] While existing neural operator surrogate models have made significant progress in inference speed, they still have several technical shortcomings: In terms of spectral processing, standard Fourier neural operators are prone to spectral aliasing when dealing with high-frequency turbulent structures; in terms of multi-region consistency, the complex geometry of tokamak devices requires maintaining the continuity and consistency of the physical field between different regions, and existing methods lack a systematic region-binding mechanism; in terms of energy stability, the model output is prone to energy divergence during multi-step rolling prediction; and in terms of ELM early warning, existing models lack specific feature extraction and risk quantification mechanisms for ELM precursor structures.

[0004] Therefore, constructing a tokamak plasma turbulence prediction system with strong generalization ability and topological consistency guarantee is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above problems, this invention is proposed to provide a tokamak plasma turbulence prediction method and system based on layer theory topology and spectral neural operators to overcome or at least partially solve the above problems. This invention combines the mathematical ideas of layer theory with neural operators, solves the multi-region consistency problem through the Sheaf glue mechanism, and constructs a tokamak plasma turbulence prediction system with strong generalization ability and topological consistency guarantee.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a tokamak plasma turbulence prediction method based on layer-theoretic topology and spectral neural operators, comprising the following steps: S1. Collect diagnostic and control data of the tokamak device at time t and convert them into corresponding physical field vector sets, actuator vectors and equilibrium parameter vectors. The diagnostic data includes physical field measurement data collected by the diagnostic system, and the control data includes actuator state data read by the actuator control system and plasma equilibrium parameters obtained by the equilibrium reconstruction system. S2. Map the set of physical field vectors to the initial potential mesh representation, and map the actuator vector and equilibrium parameter vector to the corresponding condition vectors. Use the addition injection mechanism to fuse the condition vectors with the initial potential mesh representation to obtain the conditional potential mesh representation at time t. S3. The latent grid representation at time t+1 is obtained by performing time evolution on the conditional latent grid representation at time t using multi-layer Fourier neural operators; S4. Input the latent grid representation at time t+1 into the layer theory glue layer, and apply multi-region consistency constraints to the latent grid representation at time t+1 by restricting the mapping operator and the glue loss function to obtain the predicted latent grid representation after applying the constraints. S5. Input the predicted potential grid representation after applying constraints into the ELM early warning head, and output the predicted hazard level and remaining time of plasma turbulence in the tokamak device; S6. The predicted latent mesh representation after applying constraints is restored to the physical field prediction representation through the decoder, and physical constraints are applied to the restored physical field prediction representation using the projection and repair module to obtain the corrected physical field prediction representation.

[0008] Furthermore, in S2, the actuator vector and the equilibrium parameter vector are mapped to the corresponding condition vectors. The condition vectors are then fused with the initial latent mesh representation using an additive injection mechanism to obtain the final latent mesh representation at time t, which specifically includes: S21. Input the balance parameter vector into the balance encoder for encoding to obtain the balance condition vector. The balance encoder adopts a multilayer perceptron structure. S2-2. The actuator vector is input into the actuator encoder for encoding to obtain the actuator condition vector. The actuator encoder adopts a multilayer perceptron structure. S2-3. The conditional vector is incorporated into the initial latent mesh representation through an additive injection mechanism to obtain the conditional latent mesh representation. :

[0009] in, This represents the initial potential mesh representation; Represents the equilibrium condition vector; Represents the executor condition vector; This represents a spatial broadcast operation, used to copy a condition vector across spatial dimensions.

[0010] Furthermore, in S3, a multi-layer Fourier neural operator is used to perform time evolution on the conditional latent grid representation at time t to obtain the latent grid representation at time t+1, specifically including: S31. Conditioned latent mesh representation The frequency domain representation is obtained by performing a three-dimensional Fourier transform. ; S32. Representation in the frequency domain Learnable weight tensors can be applied in this context. and anti-aliasing filter This yields a frequency domain representation that suppresses high-frequency aliasing; S33. Perform an inverse Fourier transform on the frequency domain representation of the suppressed high-frequency aliasing. We obtain the spatial domain representation after time evolution; S34. Compare the temporally evolved spatial domain representation with the potential mesh representation. The convolutional results are concatenated, and the concatenated result is activated to obtain the latent mesh representation at time t+1. .

[0011] Further, in step S32, the anti-aliasing filter In the frequency domain representation In each spatial dimension, the first 2 / 3 of the frequency modes are retained, and high-frequency modes exceeding the cutoff frequency are directly set to zero.

[0012] 5. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, in S4, the layered cementing layer applies multi-region consistency constraints to the potential grid representation at time t+1 by restricting the mapping operator and the cementing loss function, thereby obtaining the predicted potential grid representation after applying the constraints, specifically including the following steps: S41. Spatial domain in the latent grid representation at time t+1 Divided evenly along the circumference into overlapping subdomains ; S42. For circumferential grid size Determine the first The circular index range occupied by each subdomain; Each subdomain It covers the entire space radially and longitudinally, but is localized only in the circumferential direction; Interconnect adjacent subdomains through overlapping regions Establish an association with an overlap width of 2. 4 grid points; S43. For adjacent subfield pairs Using restricted mapping Subdomain The potential mesh on the surface is limited to the overlapping region: Similarly, using constraint mapping Subdomain The potential mesh on the surface is limited to the overlapping region: S44. Define the glue loss according to the constraint mapping: , in For the set of adjacency relations of subdomains, Represents a restriction mapping Subdomain The region obtained after limiting the potential mesh to the overlapping area, Represents a restriction mapping Subdomain The region obtained after limiting the potential mesh to the overlapping area; S45. By minimizing the cementation loss, a prediction pattern that maintains a smooth and continuous physical field across different regions is learned, outputting a predicted latent mesh representation with constraints applied. .

[0013] Furthermore, the constraint mapping in S43 is implemented through sparse matrix indexing or interpolation operators.

[0014] Furthermore, in S5, the ELM early warning head outputs the predicted hazard level and remaining time of plasma turbulence in the tokamak device, specifically including: Predicted latent grid representation from adhesive layer Perform global pooling to compress the spatial dimension into a single pooled feature vector; Through multilayer perceptron Pooling feature vectors are mapped to risk levels The sigmoid function converts risk level into a probability value; Predicting the head using the remaining time The pooling feature vector is mapped to a non-negative time value. The remaining time prediction head adopts a two-layer fully connected network structure, with the middle layer using the GELU activation function and the output layer using the Softplus activation function to ensure that the predicted value is non-negative.

[0015] Furthermore, in S6, the predicted latent mesh representation after applying constraints is restored to the physical field prediction representation through a decoder, specifically including: The predicted latent mesh representation obtained from S4 is input into the decoder module, and the predicted latent representation is restored to the physical field prediction representation using the learnable 3D convolutional layer in the decoder.

[0016] Furthermore, in S6, the projection and repair module applies physical constraints to the restored physical field prediction representation. Specifically, it includes: Positive projection: via clamping operation Negative values ​​in the physical field prediction representation are corrected to zero; Divergence free projection: A scalar potential is obtained by solving the Poisson equation, and then the gradient of the scalar potential is subtracted from the original vector field to obtain the corrected field, such that the corrected vector field... satisfy ; Energy target projection: When a specified target energy is projected in the physical field prediction representation. Once determined, the total energy represented by the predicted physical field is first calculated. Then through scaling factor Rescale the state field to match the target value with the corrected total energy; Boundary condition projection: When the physics prediction representation provides a boundary mask, the predicted values ​​for the boundary regions are forcibly replaced with the specified boundary condition values.

[0017] In a second aspect, the present invention also discloses a tokamak plasma turbulence prediction system based on layer-theoretic topology and spectral neural operators, used to execute the tokamak plasma turbulence prediction method described in any one of the first aspects, including: The diagnostic subsystem collects diagnostic and control data of the tokamak device at time t and converts them into corresponding physical field vector sets, actuator vectors, and equilibrium parameter vectors. The diagnostic data includes physical field measurement data collected by the diagnostic system, and the control data includes actuator state data read by the actuator control system and plasma equilibrium parameters obtained by the equilibrium reconstruction system. The data processing unit receives the data output by the diagnostic subsystem and executes steps S2-S6, outputting the hazard level of plasma turbulence in the tokamak device, the predicted value of remaining time, and the corrected physical field prediction. The actuator control unit determines whether the pre-approval control threshold is met based on the hazard level and remaining time prediction value output by the data processing unit. If the control threshold is met, the corrected physical field prediction representation is transmitted to the MPC controller. The MPC controller calculates the optimal actuator adjustment amount based on the predicted field and sends the actuator command formed based on the adjustment amount to the actuator mechanism of the tokamak device through the control interface.

[0018] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a tokamak plasma turbulence prediction method and system based on layer theory topology and spectral neural operators, which has the following beneficial effects: In terms of generalization ability, this invention directly learns the mapping between infinite-dimensional function spaces based on neural operator theory, making the model invariant to the discretization method. The Sheaf glue mechanism provides a strict global consistency guarantee for multi-region physics prediction, and anti-aliasing filtering accurately expresses physical constraints at the frequency domain level. Experiments show that under geometric configurations and operating parameters not covered by the training data, the model's prediction accuracy decreases by no more than 15%, significantly outperforming traditional data-driven methods.

[0019] Regarding spectral fidelity, the anti-aliasing filter effectively suppresses high-frequency aliasing in the frequency domain through a 2 / 3 cutoff rule. The anti-aliasing filter of this invention retains only the first two-thirds of the frequency modes in each spatial dimension, directly setting high-frequency modes exceeding the cutoff frequency to zero, effectively preventing the generation and accumulation of high-frequency aliasing components. Experimental data show that after using the anti-aliasing filter, the prediction error in the edge region is reduced from 11.2% to 6.7%, and the spectral purity of the field reconstruction is improved by approximately 40%.

[0020] Regarding multi-region consistency, the Sheaf gluing mechanism mathematically guarantees the consistency of predictions from adjacent subdomains by restricting mapping and gluing loss. This invention applies a gluing loss to overlapping subdomains, explicitly penalizing inconsistencies in overlapping regions during training, forcing the model to learn a consistent prediction pattern across regions. Experiments show that after applying Sheaf gluing, the field jump amplitude at region boundaries decreases from an average of 8.3% to 1.2%, and the flux conservation error decreases from 15.7% to 3.4%.

[0021] Regarding energy stability, the projection and repair module achieves energy stability through a combination of a soft energy upper bound and an energy target projection. The soft energy upper bound, acting as a regularization loss, guides the model to learn an energy-stable evolution pattern during the training phase; the energy target projection, acting as a hard constraint during the inference phase, forcibly corrects the total energy of the predicted field to a physically reasonable value. Experiments show that after using projection repair, the energy drift of the 10-step rolling prediction is reduced from 32.5% to 4.7%, and the long-term stability of the predicted trajectory is improved by approximately 7 times.

[0022] Regarding ELM early warning capabilities, the integrated ELM early warning head provides hazard and remaining time predictions, and balanced conditionalization enables the model to have condition awareness capabilities, supporting proactive early warning and control decisions.

[0023] In terms of real-time deployment, TorchScript and ONNX exports and optimized inference pipelines achieve millisecond-level response, with single-step inference latency controlled within three milliseconds, meeting the real-time requirements of tokamak control systems. Attached Figure Description

[0024] 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.

[0025] Figure 1 is a schematic diagram of the overall architecture of the tokamak plasma turbulence prediction system provided by the present invention.

[0026] Figure 2 is a schematic diagram of the dense grid encoder and k-nearest neighbor aggregation mechanism provided by the present invention.

[0027] Figure 3 shows the core structure of the spectral neural operator and the design of the anti-aliasing filter provided by the present invention.

[0028] Figure 4 is a schematic diagram of the region division and restriction mapping of the sheaf adhesive layer provided by the present invention.

[0029] Figure 5 is a flowchart of the projection and repair module provided by the present invention.

[0030] Figure 6 is a schematic diagram of the ELM early warning head and balance conditionalization mechanism provided by the present invention.

[0031] Figure 7 is a timeline diagram of the training strategy, showing the order of introduction and weight changes of different loss terms and constraints in each training stage.

[0032] Figure 8 is a schematic diagram of the Data tab interface provided by the present invention.

[0033] Figure 9 is a schematic diagram of the Training tab interface provided by the present invention, showing the 30%-70% horizontal column layout of the PlasmaFusion Master model training configuration interface. The left side of the figure includes control panels for model selection, basic training parameters, loss function weights, layer theory glue parameters, anti-aliasing filter settings, and energy stability configuration. The right side of the figure includes real-time training metric charts and metric log display areas.

[0034] Figure 10 is a schematic diagram of the Evaluation tab interface provided by the present invention, showing the interactive interface for plasma parameter configuration, ELM event modeling, data generation control and model evaluation configuration, including parameter input form, 3D field preview window, channel histogram and evaluation result display. Detailed Implementation

[0035] The following will refer to the appendices in the embodiments of the present invention. Figure 1-10The technical solutions in the embodiments of the present invention are clearly and completely described herein. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0036] The main symbols and their physical meanings of the tokamak device used in this invention are as follows: The set of physical field vectors of the diagnostic system at time t :Include Each channel contains electron density, electron temperature, ion temperature, electric potential, vorticity, parallel current density, radial magnetic field component, and circumferential magnetic field component. The physical field vector set is mapped onto a regular mesh using k-nearest neighbor aggregation. get.

[0037] Actuator vector obtained from actuator control system Dimension It includes 8 NBI heating power channels, 4 ECRH heating power channels, and 4 gas injection rate channels.

[0038] The equilibrium parameter vector obtained by the equilibrium reconstruction system Dimension Includes edge security factors Cross-sectional elongation ratio Triangle deformation degree Normalized specific pressure Total heating power Total gas injection rate .

[0039] Potential mesh representation: The initial potential grid representation at time t. The number of potential channels; The latent network representation after applying conditional vectors. This represents the initial potential mesh representation; Represents the equilibrium condition vector; Represents the executor condition vector; This represents a spatial broadcast operation, used to copy the condition vector across spatial dimensions; : The potential mesh representation at time t+1 after applying the glue constraint.

[0040] Physics field prediction at time t+1 ELM risk level logit value ELM remaining time prediction (unit: ms) ; Mesh parameters: Radial grid size; Vertical grid size; Circular grid size; Number of subdomain partitions; : Spatial domain; : The i-th subfield; : Restricted mapping operator from subdomain i to subdomain j; Fourier transform operator; Inverse Fourier transform operator; Anti-aliasing filter; : Encoder weight matrix.

[0041] The tokamak plasma turbulence prediction method based on layer-theoretic topology and spectral neural operators disclosed in this invention includes the following steps: S1. Acquire diagnostic and control data of the tokamak device at time t, specifically including: S11. Collect physical field measurement data at time t from the diagnostic system, including electron density. Electronic temperature ion temperature electric potential vorticity Parallel current density Radial magnetic field component Circumferential magnetic field component This constitutes a diagnostic point cloud; S12. The diagnostic point cloud is mapped to a three-dimensional regular mesh of the tokamak device using the k-nearest neighbor aggregation method. The three-dimensional regular mesh adopts a spatial coordinate system. ,in For the large radius direction, For vertical coordinates, For each target point on the regular grid, the k nearest neighbors in the diagnostic point cloud are found, and the physical field measurements of the k neighbors are aggregated using a distance-weighted average to obtain a regularized set of physical field vectors. ; S13. Read the actuator status data at time t from the actuator control system, including NBI heating power, ECRH heating power, and gas injection rate, to form the actuator vector. ; S14. Obtain the plasma equilibrium parameters at time t from the equilibrium reconstruction system, including the edge safety factor. Cross-sectional elongation ratio Triangle deformation degree Normalized specific pressure Total heating power Total gas injection rate This constitutes the equilibrium parameter vector. ; S2. Set the physical vector fields Executor vector and balance parameter vector Input dense mesh encoder module, where the set of physical field vectors The initial latent mesh representation is mapped through a 3D convolutional layer with fixed weights. Balance parameter vector Mapped to a condition vector by a balanced encoder Executor vector Mapped to a condition vector by the actuator encoder The condition vector is injected with the latent mesh representation via an additive injection mechanism. By fusion, a conditional latent mesh representation is obtained. ; S3. Representation of the latent grid at time t using multi-layer Fourier neural operators. Perform time evolution to obtain the potential grid representation at time t+1. ; S4. Represent the potential grid at time t+1 The input layer is a glue layer, which represents the latent mesh at time t+1 by restricting the mapping operator and the glue loss function. By applying multi-region consistency constraints, the predicted latent grid representation after applying the constraints is obtained. ; S5. Represent the predicted potential mesh after applying constraints. The input is an ELM warning head, which includes a global pooling layer and a multilayer perceptron. The global pooling layer compresses the spatial dimension of the predicted potential grid representation into a feature vector, and the multilayer perceptron extracts ELM-related features to output the hazard level of plasma turbulence in the tokamak device. and remaining time forecast The ELM-related features include pressure gradients, pedestal heights, energy statistics, and frequency domain modal amplitudes in the edge regions. S6. Represent the predicted potential mesh after applying constraints. The input decoder module uses learnable 3D convolutional layers to restore the predicted latent mesh representation to the physical field prediction representation. Then, the physical field prediction is represented by the projection and repair module. By applying physical constraints, we obtain the corrected physical field prediction representation. As the final physical field prediction output.

[0042] In step S3, the condition vector is injected with the potential mesh representation via an additive injection mechanism. The integration process specifically includes: balance parameter vector The input is a balanced encoder, which employs a multilayer perceptron structure, to obtain a balance condition vector. ; Executor vector The input actuator encoder, which employs a multilayer perceptron structure, obtains the actuator condition vector. ; By incorporating the conditional vectors into the latent mesh representation through an additive injection mechanism, a conditional latent mesh representation is obtained. ,in This indicates a spatial broadcast operation, which copies the condition vector in spatial dimensions; S2-4. Representing the Conditioned Latent Mesh As input to the subsequent spectral neural operator module.

[0043] The above method can be implemented using a neural operator system, which consists of the following core modules: Physics field encoder module: employs a fixed-weight 3D convolutional layer ( The convolutional kernel elevates the input physics field from the original number of channels to a high-dimensional latent representation space. This convolutional layer generates a weight matrix through orthogonal initialization and keeps it fixed and unupdated during training. The core of the spectral neural operator is composed of multiple stacked Fourier neural operator layers. Each layer contains a 3D fast Fourier transform module, a frequency-domain learnable weight tensor, an anti-aliasing filter, an inverse Fourier transform module, and local convolution branches. (Convolutional layer) and GELU activation function; Layer-based glued layer: By restricting the mapping operator and glued loss function, this layer achieves multi-region consistency constraints and imposes continuity and flux conservation constraints on the prediction of different subdomains in the latent representation space. Decoder module: Employs learnable 3D convolutional layers ( The convolutional kernel restores the latent representation to the physics prediction, and the convolutional layer maps the high-dimensional latent channels back to the original number of physics channels; Projection and Repair Module: A physics-driven post-processing module that ensures the predicted physical field satisfies physical rationality through constraints such as positive projection, divergence free projection, energy target projection, and boundary condition projection.

[0044] ELM warning head: It consists of a global pooling layer and a multilayer perceptron (MLP). The global pooling layer compresses the spatial dimension into a feature vector. The multilayer perceptron contains two fully connected network layers. The middle layer uses the GELU activation function, and the output layer uses the Sigmoid and Softplus activation functions to generate the danger level and remaining time prediction, respectively.

[0045] Overall data flow: Input includes time... physical field Geometric point sets and executor vector First, it is mapped to a latent mesh representation through a 3D convolutional layer of the encoder. Subsequently, time evolution was performed using multi-layer Fourier neural operators to obtain... Then, by applying multi-region consistency constraints through layered adhesive layers, we obtain... Then, the 3D convolutional layer of the decoder restores the latent mesh into physical field predictions. Finally, the hazard level is output through global pooling of the ELM warning head and multilayer sensor. and remaining time estimation In this data stream, the physical field Covering channels such as density, temperature, and potential, actuator vector It includes control quantities such as heating power and gas injection, and the symbol definitions between modules are kept consistent to ensure the correctness of data transmission.

[0046] Each module is described in detail below: The function of the dense grid encoder is to upscale the input dense grid physical field to a high-dimensional latent representation space, laying the foundation for subsequent frequency domain processing. This module receives the regularized dense grid physical field from the data preprocessing stage. Output latent mesh ,in To input the number of physics channels, This represents the potential number of channels.

[0047] The encoder uses fixed weights 3D convolution achieves channel enhancement, a design that ensures the determinism and repeatability of the encoding process. Specifically, the encoder weight matrix... Generated through orthogonal initialization, each row vector is normalized to maintain numerical stability. The encoding formula can be expressed as follows: The convolution operation operates independently on each grid point in the spatial dimension, and the weights remain fixed and are not updated during training.

[0048] This encoding method has several important properties. First, the fixed-weight design eliminates learnable parameters in the encoder, reducing model complexity and improving training stability, while ensuring that the same input always produces the same latent representation. Second, The convolutional kernel does not introduce receptive field expansion in the spatial dimension, preserving the spatial resolution and geometric structure of the input grid, enabling subsequent frequency domain operations to accurately correspond to physical spatial locations. Finally, the orthogonally initialized weight matrix ensures approximate orthogonality between different latent channels, which is beneficial for the decoupled representation of frequency domain features.

[0049] encoder output For shape The four-dimensional tensor, in which For the number of potential channels, These represent the grid dimensions in the radial, longitudinal, and circumferential directions, respectively. This potential grid representation will serve as the input to the core of the next-stage spectral neural operator.

[0050] The spectral neural operator core is the core computational module of this invention, responsible for learning the temporal evolution of the physical field in the frequency domain. This module receives the latent mesh from the encoder. Output the evolved potential mesh To address the spectral aliasing problem in the standard Fourier neural operator, this invention introduces an anti-aliasing filtering mechanism.

[0051] The computational structure of the Fourier layer can be described as follows: First, the input potential grid... Perform 3D Fast Fourier Transform We obtain the frequency domain representation, and then apply the learnable weight tensor in the frequency domain. and anti-aliasing filter Then perform the inverse Fourier transform. Returning to the spatial domain, the result is finally added to the local convolution branch and passed through the activation function. The complete Fourier layer formula is as follows: ,in The weights are learnable complex weight tensors, whose dimensions correspond to the number of output channels, the number of input channels, and the number of modes preserved in the three spatial directions, respectively. For local Convolution weights For GELU activation function, This indicates element-wise multiplication.

[0052] Anti-aliasing filter The design is crucial for suppressing high-frequency aliasing. This filter is defined in the frequency domain and employs the classic 2 / 3 cutoff rule to achieve high-frequency suppression. Specifically, for each spatial dimension, the filter retains the first 2 / 3 of the frequency modes, directly setting high-frequency modes exceeding the cutoff frequency to zero. Mathematically, this is expressed as: when the wavenumber satisfies... , , hour, ;otherwise ,in These are the grid sizes for the three spatial dimensions. This indicates rounding down. This hard truncation strategy strikes a balance between computational efficiency and aliasing suppression. By limiting the bandwidth of the frequency domain representation, it effectively prevents high-frequency aliasing components introduced by nonlinear operations, ensuring the physical plausibility of the predicted field.

[0053] The core of a spectral neural operator is typically composed of multiple stacked Fourier layers, with the output of each layer serving as the input to the next. During inter-layer propagation, the number of latent channels... The number of modes retained can be kept constant or varied layer by layer, with the specific settings determined based on a trade-off between computational efficiency and expressive power. The multi-layered structure enables the model to learn the complex nonlinear characteristics of the physical field evolution, while anti-aliasing filtering plays a role in each layer to ensure that high-frequency noise does not accumulate and propagate between layers.

[0054] Output of the spectral neural operator core Keep and input The same tensor shape will be used as input for the next stage of the sheaf adhesive layer.

[0055] The Sheaf adhesive layer ensures global consistency in multi-region predictions, addressing the boundary matching problem between different physical regions in the complex geometry of a tokamak. This module receives the latent mesh from the spectral neural operator core. Output the potential mesh after applying consistency constraints. .

[0056] This invention will use the spatial domain Along the circumference ( (Direction) evenly divided into overlapping subdomains This utilizes the toroidal symmetry of the tokamak to achieve efficient topological constraints. Specifically, for circumferential mesh sizes... , No. The circular index range occupied by each subdomain is ,in , (The last subdomain extends to) Each subdomain It covers the entire space radially and longitudinally, localizing only in the circumferential direction. Adjacent subdomains are separated by overlapping regions. Establish association, overlap width is There are 2 grid points, typically with a value of 2. 4.

[0057] Constraint mapping is a core concept in layer theory, used to describe the local constraints on global data. In this invention, for adjacent subdomain pairs... Restricted mapping Subdomain The potential grid on the surface is limited to the overlapping region, i.e. Similarly In engineering implementation, constraint mapping can be achieved through sparse matrix indexing or interpolation operators to extract grid point values ​​located in overlapping regions of the subdomain grid.

[0058] Glue consistency is constrained through a loss function. The glue loss is defined as follows: ,in The set of subdomain adjacency relationships is used, and this loss penalizes inconsistencies between adjacent subdomains in overlapping regions. By minimizing the glue loss, the model learns a predictive pattern that maintains a smooth and continuous physical field across different regions, avoiding non-physical jumps at region boundaries.

[0059] In addition to basic glue loss, this invention introduces flux-weighted glue to emphasize the consistency of boundary flux. Flux-weighted loss is defined as... ,in For the regional boundary, The loss is the boundary normal vector. This loss ensures that the normal derivative of the physical field is continuous at the boundary, which is particularly important for the identification of ELM precursor structures, since the triggering of ELM is often closely related to the pressure gradient and flux in the edge region.

[0060] Sheaf adhesive layer output The tensor retains the same shape as the input, but its eigenvalues ​​have been adjusted for consistency constraints. This output will be used as input to the decoder to reconstruct the physics prediction.

[0061] The projection and restoration module is a physics-driven post-processing step used to ensure the physical plausibility of the prediction results. This module receives the physics field predictions from the decoder. Output corrected predictions that satisfy physical constraints .

[0062] Positive projection imposes constraints on physical quantities that must be non-negative. Plasma density. and pressure Physically, the value must be positive, but neural network predictions can produce negative values, especially in low-density areas at the edges. Positive projection is achieved through clamping operations. and Negative values ​​are corrected to zero to ensure the physical acceptability of the prediction results.

[0063] Divergence-free projection is for divergence-free constraints on vector fields. Magnetic field. Physically, it must satisfy Velocity field of incompressible fluid Similar constraints must also be satisfied. Divergence free projection is achieved by solving the Poisson equation. Obtain scalar potential Then, the gradient of the scalar potential is subtracted from the original vector field to obtain the corrected field. .because The corrected vector field satisfies In practice, the Poisson equation can be solved efficiently using frequency domain methods.

[0064] Energy target projection is used to prevent energy divergence in multi-step rolling forecasts. When a target energy is specified... First, calculate the total energy of the predicted field. Then through scaling factor The state field is rescaled to match the corrected total energy to the target value. This projection can be used in conjunction with PlasmaFusion Pilot, which provides a physically plausible estimate of the energy target.

[0065] Boundary condition projection ensures that the predicted field satisfies the specified boundary conditions at the boundaries. When a boundary mask is provided, the predicted values ​​for the boundary regions are forcibly replaced with the specified boundary condition values. Periodic boundary conditions projected in the circumferential direction force periodicity. This is a necessary constraint for the toroidal geometry of the tokamak.

[0066] The soft energy upper bound limits energy growth through regularization loss, rather than directly modifying the predicted value. The soft energy loss is defined as follows: ,in This represents the upper limit threshold for energy. The loss only produces a non-zero gradient when the predicted energy exceeds this threshold, guiding the model to learn energy-stable prediction patterns.

[0067] These projection operations can be flexibly combined according to specific application scenarios, playing a role in ensuring stability and physical consistency in both single-step prediction and multi-step rolling processes.

[0068] The ELM warning head extracts ELM-related features from the global statistics of the potential grid and outputs the hazard level and remaining time prediction. This module receives potential grid data from the sheaf adhesive layer. Output the risk level logit and remaining time estimation .

[0069] Hazard prediction is achieved through global pooling and a multilayer perceptron. First, a global pooling operation is performed on the potential grid. This compresses the spatial dimension into a single feature vector, using pooling methods such as mean pooling, max pooling, or a combination of both. Then, a dedicated multilayer perceptron is used. Map pooling features to risk level logit The risk level logit is converted into a probability value using the sigmoid function, representing the likelihood of an ELM event occurring at the current moment.

[0070] The remaining time estimation uses a similar structure, but the design of the output layer is different. Remaining Time Prediction Header Map pooling features to non-negative time values , representing the estimated time until the next ELM event. This prediction head employs a two-layer fully connected network structure, with the middle layer using the GELU activation function and the output layer using the Softplus activation function to ensure the predicted value is non-negative. During training, a smoothed L1 loss (Huber loss) is used to improve robustness to outliers; the loss is defined as... The SmoothL1 function approximates the L2 loss when the error is small and the L1 loss when the error is large, thus achieving a balance between accuracy and robustness.

[0071] Equilibrium conditioning endows the model with operational condition awareness, enabling it to adjust its predictive behavior based on different plasma equilibrium states and operating parameters. Equilibrium parameters include edge safety factors. Cross-sectional elongation ratio Triangle deformation degree Normalized specific pressure Heating power and gas injection rate These parameters are first passed through a balanced encoder. Mapped to condition vector .

[0072] Conditional vectors are incorporated into the latent representation space through an additive injection mechanism. Specifically, conditional vectors... First, it passes through a balanced encoder. Mapped to an embedding vector with the same number of potential channels. Then it is broadcast in the spatial dimension and added to the latent mesh output by the encoder: ,in The dimension expansion operation replicates the embedding vector across the spatial dimension. This additive injection method preserves the numerical scale of the underlying representation, avoids gradient instability that may be introduced by multiplicative modulation, and ensures that the equilibrium parameter information is uniformly distributed throughout the spatial domain. In this way, the model can dynamically adjust its internal representation based on the current equilibrium parameters, achieving turbulence prediction that is both predictive and condition-aware.

[0073] Overall loss function and training strategy Considering the constraints of the above modules, the overall training objective of PlasmaFusion Master is a weighted sum of multiple losses. The complete loss function can be expressed as: The meaning and weighting factors of each loss term need to be explained in detail.

[0074] Data fitting loss The mean squared error between the predicted and actual fields is a fundamental loss term in supervised learning, and its weighting factors are also important. It is usually set to 1 as the normalization benchmark.

[0075] Physical residual loss This measures the degree to which the predicted field satisfies the drift-reduced MHD equations. The drift-reduced MHD equations include the continuity equations. vorticity equation and pressure equation The physical residual loss is the weighted sum of squares of the residuals of each equation. .

[0076] Boundary condition loss The measure is the degree to which the predicted field satisfies the specified boundary conditions at the boundary, where For boundary condition operators.

[0077] Bonding loss As described in Section 4, ensure consistency in multi-regional forecasts. Energy loss. As described in Section 5, the growth of predicted energy is limited.

[0078] ELM loss It includes risk loss and remaining time loss. Risk loss is calculated using binary cross-entropy. ,in The binary label is used for ELM. The remaining time loss uses smoothed L1 loss. As described in Section 6, this loss approximates L2 loss when the error is small and L1 loss when the error is large, providing robustness to outliers.

[0079] To improve the lead time and ranking quality (AUROC) of ELM alerts, this invention adds the following advanced training objectives to the basic ELM loss: (1) Pairwise sorting loss Pairwise ranking loss directly optimizes the ranking ability of risk scores, forcing samples with earlier actual ELM events to have higher risk scores:

[0080] in For all samples that meet the requirements Compared to the sample The set of sample pairs that occurred earlier in ELM This is a boundary parameter (typical value 0.1). The loss is logit, representing the respective hazard level. This loss ensures that the model's hazard score has a strong monotonic relationship with the actual event time.

[0081] (2) Difficulty in bearing sample mining loss The main challenge of long-term early warning is false alarm control. This invention employs a hard negative sample mining strategy, focusing on penalizing negative samples that are incorrectly assigned high-risk scores (the actual events occurred much later than the early warning timeframe):

[0082] in For the difficult negative sample set (event time exceeds the maximum warning time domain) However, the danger level remains higher than at the border. ), The number of difficult negative samples to select (typically the top 20% of negative samples in the batch).

[0083] (3) Loss of utility in advance This loss simultaneously optimizes the early warning time and false alarm rate, ensuring that the early warning signal is both early and reliable:

[0084] in This is the set of positive samples (where ELM is about to occur). For the negative sample set, The minimum operable lead time (determined by the actuator response time). This is the false alarm probability threshold. This represents the probability of danger.

[0085] Combining these high-level objectives, the complete ELM training loss is:

[0086] In scenarios where it is necessary to further extend the early warning time and improve stability, a status-based early warning stack can be optionally added on top of the basic early warning head. This stack contains two core components: a "sentinel early warning head" and a "fusion gating".

[0087] (1) Feature extraction of grid precursors At each time step, a compact precursor feature vector is extracted from the decoded physics field and energy statistics. : Platform height proxy: edge area ( ) and core area ( The pressure mean difference Edge gradient proxy: Calculate edge regions using 3D finite difference. average value Global energy: Approximated by numerical integration Sheaf energy: the constraint mapping norm generated by the adhesive layer. sum Gauge loss: Residuals of the gauge constraint on the magnetic vector potential

[0088] Topological features (if available): Betti number extracted by the topology scheduler, persistent barcode digest (2) Exponential smoothing refiner Historical buffer for maintaining precursor features (Window length) Typically 15-30 steps), apply exponential smoothing:

[0089] smoothness coefficient Simultaneously calculate drift statistics:

[0090] (3) GRU Sentinel Early Warning Head The sentinel uses a GRU to read the smoothed feature sequence and outputs independent ELM risk level and remaining time:

[0091]

[0092] (4) Integration of gating mechanisms Fusion gating based on logit space combination of early warning heads and the sentry :

[0093]

[0094] in This represents the confidence level (the absolute value of the logit). The optional critical slowing features are (variance and hysteresis first-order autocorrelation of the pedestal height sequence). The training objective of the fusion gating is to minimize the error of the fusion warning.

[0095] The Fourier neural operator of this invention processes physical fields in the frequency domain, which naturally aligns with the spectral characteristics of ELM precursors. Before an ELM event, coherent mode growth with specific moduli (such as circumferential moduli) often occurs in the edge regions. to The MHD mode, whose energy is concentrated in the low-frequency wavenumber.

[0096] Anti-aliasing filtering mechanisms naturally enhance these coherent mode signals by preserving low-frequency components and suppressing high-frequency aliasing. In the ELM warning branch, modal amplitude features can optionally be extracted from the frequency domain latent representation:

[0097] These frequency domain amplitude features can be directly input into the early warning head as a supplement to the slab / gradient features, further enhancing early detection capabilities.

[0098] The training strategy employs a course-based learning approach, introducing different loss terms and constraints in stages. In the early stages of training, only data fitting loss is used to quickly converge to a reasonable prediction accuracy. In the middle stages of training, physical residual loss and boundary condition loss are gradually introduced to inject physical knowledge. In the later stages of training, glue loss, energy loss, and ELM loss are used to fine-tune multi-region consistency and early warning capabilities.

[0099] The tokamak plasma high-fidelity simulation and instability early warning system based on layer theory topology and spectral neural operators disclosed in this invention is an intelligent plasma prediction device specifically optimized for high-resolution frequency domain processing. This system integrates a high-performance GPU computing platform, high-speed multi-channel diagnostic data acquisition hardware, a real-time communication network, and a multi-actuator drive system to achieve millisecond-level high-fidelity prediction and ELM early warning of the plasma state of a tokamak device.

[0100] This invention is applicable to various tokamak devices (including conventional conductor and superconducting tokamak), and its technical specifications are as follows: Geometric parameters of the vacuum chamber in the vacuum chamber and plasma confinement system: large radius R0 = 0.5-3.0m (distance from the center of the ring to the center of the plasma), small radius a = 0.2-0.8m (characteristic radius of the plasma cross section), aspect ratio A = R0 / a = 2.5-4.0, plasma cross section shape: D-shaped or elliptical (cross section elongation ratio κ = 1.4-2.0 (longitudinal stretching degree), triangular deformation degree δ = 0.2-0.6 (triangulation degree of the cross section)).

[0101] Magnet system: The circumferential field coil (TF) generates a circumferential magnetic field Bt=1.5-8.0T (12-18 sets of coils), and the poloidal field coil (PF) includes the CS coil and 6-12 sets of peripheral coils for plasma configuration control. The magnetic flux varies from 10-30Wb, and the current range is ±10-50kA.

[0102] Auxiliary heating systems: NBI (1-40MW, E_beam=50-500keV), ECRH (0.5-20MW, f=110-170GHz), ICRH (1-20MW, f=25-80MHz), LHCD (1-10MW, f=2.45-5.0GHz).

[0103] Diagnostic systems: magnetic diagnostics (Rogowski coils, magnetic probe arrays, magnetic flux loops), density diagnostics (microwave interferometers, Thomson scattering), temperature diagnostics (ECE systems, CXRS systems), and radiation diagnostics (visible light spectroscopy, soft X-ray arrays).

[0104] Plasma operating parameter range: plasma current I_p = 100kA - 2mA, line average density _e=(1-10)×10¹ 9 m - ³, electron temperature T_e=0.5-10keV, ion temperature T_i=0.5-15keV, normalized specific pressure β_N=1.0-3.5, energy confinement time τ_E=10-500ms, safety factor q_95=3.0-6.0.

[0105] The hardware configuration of the system of this invention is optimized for the requirements of dense grid spectral neural operators and anti-aliasing filtering, and includes the following core components: Main computing server configuration The main computing server is the core computing node of the system, responsible for model training and real-time inference tasks. Its hardware configuration is as follows: The processor configuration adopts a dual-socket server architecture, with either an Intel Xeon Platinum 8380 processor (80 cores, 160 threads, base clock speed of 2.3GHz, maximum turbo frequency of 3.4GHz) or an AMD EPYC 7763 processor (64 cores, 128 threads, base clock speed of 2.45GHz, maximum turbo frequency of 3.5GHz).

[0106] In terms of GPU accelerator card configuration, the training phase typically uses an NVIDIA A100 Tensor Core GPU (80GB HBM2e memory, 6912 CUDA cores, 432 Tensor Cores, and a memory bandwidth of 2039GB / s), connected to the motherboard via a PCIe 4.0 x16 interface, with a single card floating-point performance of 19.5 TFLOPS (FP32) or 312 TFLOPS (FP16 mixed precision).

[0107] The memory configuration is 512GB DDR4-3200 ECC memory distributed across 16 memory channels (32GB per channel), supporting memory error correction (ECC) to prevent bit flip errors caused by high-energy particle radiation during plasma discharge.

[0108] In terms of storage system, the system disk uses a 2TB NVMe SSD and the data disk uses a 20TB NVMe SSD RAID 0 array.

[0109] The network interface uses dual 10 Gigabit Ethernet cards (Intel X710 or Mellanox ConnectX-5) to support network redundancy, RDMA support (achieving low latency <5μs and high bandwidth close to 10Gbps GPU-to-GPU direct memory access via RoCE v2 protocol) and traffic isolation.

[0110] Regarding the motherboard and expansion slots, the server motherboard provides at least eight PCIe 4.0 x16 slots for GPU, high-speed network card, and data acquisition card expansion, as well as four M.2 NVMe slots for system disks and cache disks. The chassis and cooling system utilize a 4U rackmount chassis with front and rear ventilation, featuring 12 hot-swappable fans (N+2 redundancy configuration) and a large copper heatsink to ensure GPU temperatures remain below 80°C under full load.

[0111] This hardware configuration can support: multi-resolution training of a 1024-sample dataset can be completed within 12 hours (4×NVIDIA A100 GPUs); single-step inference latency of <3ms (including FFT / IFFT calculations) during the inference phase; throughput of >300 times / second; meeting the requirement of real-time warning frequency >200Hz; and multi-task parallel processing can simultaneously handle 8 independent discharges or perform real-time spectrum analysis.

[0112] Example 1: System Configuration and Data Flow In a typical embodiment, the system is deployed using the hardware platform described in the aforementioned "System Apparatus and Hardware Configuration" section, including a computing server running the PlasmaFusion Master model inference service, an interface server exchanging data with the tokamak control system, and a storage component persisting model weights, training logs, and prediction results.

[0113] Input physics field Includes the following 8 channels: electron density (unit: ), dimension Electronic temperature (Unit: keV), dimension ; Ion temperature (Unit: keV), dimension electric potential (Unit: kV), dimension vorticity (unit: ), dimension Parallel current density (unit: ), dimension Radial magnetic field component (Unit: T), Dimensions ; Circumferential magnetic field component (Unit: T), Dimensions ,in The typical range for the number of points in the diagnostic point cloud is: .

[0114] A defined regular grid spatial coordinate system (R, Z, φ) generates a set of geometric points, where each physical quantity corresponds to a value on this grid. Includes spatial coordinates ,in It has a large radius (1.0~2.5m). The vertical coordinate is (-1.0 to 1.0 m). Circumferential angle (0~ ). Executor vector Dimensions Includes: 8 NBI heating power channels (unit: MW, range: 0~5 MW / channel); 4 ECRH heating power channels (unit: MW, range: 0~2 MW / channel); 4 gas injection rate channels (unit: (Range: 0~5).

[0115] Potential grid Size configuration (basic configuration): number of potential channels - Radial grid size Coverage Vertical grid size Coverage Circular grid size Coverage .

[0116] For high-precision applications, enhanced configurations can be adopted: potential number of channels. , , To improve the accuracy and spatial resolution of field reconstruction.

[0117] Subdomain partitioning and restricted mapping construction: spatial domain Along the circumference ( (Direction) evenly divided into One overlapping subdomain (basic configuration): Subdomain 1: Corresponding to the grid index ;Subdomain 2: Corresponding to the grid index ; where the overlap width For each of the three grid points, sufficient overlap is ensured between adjacent subdomains for consistency constraints. Each subdomain covers the entire space radially and longitudinally, and is localized only in the circumferential direction.

[0118] Example 2: Training Data Generation and Model Training During the offline training phase, synthetic training data is generated using the drift-reduced MHD solver (BOUT++ v4.3). The generated data covers the following parameter space: Edge security factor 15 values ​​were sampled; cross-sectional elongation ratio Sample 10 values; triangle deformation Eight values ​​were sampled; normalized specific pressure. 12 values ​​were sampled; heating power 20 values ​​were sampled; gas injection rate 15 values ​​were sampled.

[0119] 3000 parameter combinations were selected from the above parameter space using Latin hypercube sampling (LHS), with each parameter combination corresponding to a simulation condition. The simulation duration for each condition was 100 ms, with a time step of [missing value]. Output 1000 time snapshots. Construct a training sequence by sampling 200 time snapshots from each operating condition, and finally obtain... Training samples.

[0120] ELM tag generation is based on an edge pressure gradient threshold: when the edge region ( Normalized pressure gradient Exceeding the critical value The time marker is designated as the ELM precursor period, and the starting point of the risk period is defined as 20ms after the actual ELM outbreak. The ratio of positive to negative samples in the training data for ELM events is approximately... .

[0121] Model training was performed on the aforementioned hardware platform using a data-parallel strategy. Training hyperparameters were set as follows: Batch size: 8 samples per GPU, global batch size 32; Optimizer: AdamW; Learning rate... Weight decay Learning rate scheduling: cosine annealing, 50 epochs period, minimum learning rate. Total training epochs: 200 epochs; Gradient clipping: global norm 1.0.

[0122] The weighting coefficients of the loss function are dynamically adjusted based on course learning: epochs 1-50: The rest are 0 (pure data fitting stage); epochs 51-100: (Introducing physical constraints); epochs 101-150: Based on the above, add... (Multi-region consistency); epochs 151-200: Based on the above, add... (ELM Early Warning Fine-tuning); The equation weights in the physical residual loss are: .

[0123] The detailed configuration of the spectral neural operator core (basic configuration) is as follows: Number of Fourier layers: 3; Number of modes preserved: Anti-aliasing filter parameters: using a 2 / 3 cutoff rule, the cutoff frequency is... Local convolution kernel size: Activation function: GELU.

[0124] For high-precision applications, an enhanced configuration can be adopted: 4 Fourier layers, preserving the number of modes. To improve the frequency domain representation capability.

[0125] The total number of parameters in the model is approximately (28M). The total training time was approximately 120 hours (5 days), and the validation set loss after convergence was... .

[0126] Example 3: Model Export and Online Deployment After training, the model is compiled and exported to TorchScript format via PyTorch JIT. Optional quantization optimization uses dynamic quantization, quantizing the weights of linear layers from FP32 to INT8, reducing model size by approximately 60% and improving inference speed by approximately 30%, with an accuracy loss of less than 2%. The exported model file size is approximately 110MB (FP32) or 45MB (INT8).

[0127] The online reasoning phase includes the following steps: Step 1: Diagnostic Data Acquisition: Acquire raw signals (sampling frequency 10kHz) from the tokamak diagnostic system, perform low-pass filtering and downsampling to 1kHz, construct a diagnostic point cloud, and obtain actuator status and balance parameters. The delay is approximately 0.5ms.

[0128] Step 2: Model Inference: Call the TorchScript model to perform forward propagation, outputting the predicted physics, ELM hazard level, and remaining time. The latency is 2.7ms (FP32) or 1.9ms (INT8).

[0129] Step 3: Control Decision: When the ELM hazard level > 0.7 and the median remaining time < 30ms, an early warning is triggered. The predicted field is transmitted to the MPC controller to calculate the optimal actuator adjustment, and the command is issued through the fast control interface. The delay is approximately 0.8ms.

[0130] The end-to-end delay from diagnostic acquisition to actuator response is (FP32) or (INT8) meets the millisecond-level response requirement of the tokamak control system.

[0131] Example 4: Performance Verification and Comparison Experiment Validate dataset construction To verify the model's generalization ability and prediction accuracy, an independent test dataset was constructed. The test dataset contains 500 new simulated operating conditions, with parameter combinations generated through random sampling to ensure no overlap with the training set. In addition, 50 operating conditions (discharge numbers #60000 to #60050) were extracted from actual discharge data of the EAST tokamak device, covering different constraint modes such as L-mode, H-mode, and I-mode.

[0132] Field Reconstruction Accuracy Assessment On the synthetic test dataset, the average NRMSE for single-step predictions across the entire field is 5.3%; on the EAST real-world data, it is 12.7%. The cumulative error for 10-step rolling predictions is: 5.3% for step 1, 9.1% for step 5, and 14.8% for step 10.

[0133] ELM Early Warning Performance Evaluation On the synthetic test dataset, the accuracy was 92.3%, precision 88.7%, recall 91.5%, F1 score 90.1%, ROC-AUC 0.96, and mean advance time 24.6ms. On the EAST real-world dataset, the accuracy was 85.3%, recall 80.9%, mean advance time 18.2ms, and false positive rate approximately 10%.

[0134] Comparative experiment Compare with the following baseline methods: FNO-baseline: Standard Fourier neural operator, without anti-aliasing filtering and sheaf glue mechanism.

[0135] PINN: Physical Information Neural Network, based on MLP architecture.

[0136] ConvLSTM: Convolutional Recurrent Neural Network, used for time series prediction.

[0137] Comparison results (synthetic test dataset):

[0138] Compared with FNO-baseline, this invention improves field reconstruction accuracy by about 32%, reduces 10-step cumulative error by about 34%, and improves ELM F1 score by about 7%, verifying the effectiveness of anti-aliasing filtering and sheaf bonding mechanism.

[0139] ablation experiment To evaluate the contribution of each module, the following ablation experiments were conducted:

[0140] Removing the anti-aliasing filter reduced accuracy by 30%, removing the sheaf glued filter increased cumulative error by 19%, removing the projection repair filter increased cumulative error by 44% over 10 steps, and removing the balance conditionalization filter reduced the F1 score by 4.9%.

[0141] Example: Visual monitoring and configuration interface based on PySide6 To improve the operability of the system, this invention provides a graphical user interface based on the PySide6 framework for configuring model parameters, monitoring the training process, and verifying prediction results.

[0142] 1. System Architecture: The GUI system adopts the MVC architecture pattern. The data model layer encapsulates system configuration management (layer bonding parameters, anti-aliasing filter settings, energy limit configuration, etc.), the view layer builds graphical interface components based on PySide6, and the controller layer handles user interaction events and updates the interface through the Qt signal and slot mechanism.

[0143] 2. Main Console Interface: The main window uses a vertical column layout, including a function tab container (occupying 85% of the space) and a bottom activity log area (occupying 15% of the space). The function tabs include: Data tab (plasma parameter configuration, ELM event modeling, data generation and preview), Training tab (model training configuration, totiology glue parameters, anti-aliasing filter settings, real-time training monitoring), Evaluation tab (model accuracy evaluation, physical consistency verification, totiology glue metric), and Deployment tab (model export and deployment).

[0144] 3. Core functions of the Training tab: The left-hand control panel provides model selection, basic training parameters (Epochs, Batch, Depth, Width, Modes), and loss function weight configuration. Configuration options include, etc., layer-based glue and collocation strategies (Risk frac, Colloc mode), anti-aliasing and regularization (Spectral filter, Liquid drop), energy stability control (Energy cap, Repair before eval), etc. The monitoring area on the right displays the training loss curve, validation loss curve, and ELM warning indicators (Hazard, TTE) in real time.

[0145] 4. Evaluation tab core functions: The left control panel provides checkpoint path selection, test dataset selection, and expansion step configuration. The right evaluation results area displays quantitative indicators such as MAE, RMSE, correlation coefficient, PDE residuals, as well as stratification cohesion measures (multi-region consistency loss, boundary flux deviation) and physical consistency verification diagrams (residual quantification of mass conservation, momentum conservation, and energy conservation).

[0146] 5. Technology Stack: The UI framework uses PySide6 6.5.0+, scientific computing uses NumPy 1.24+ and h5py 3.8+, data visualization uses Matplotlib 3.7+, and the communication mechanism uses Qt signal-slot mechanism. This interface system provides complete configuration, training, evaluation, and deployment interfaces for the core technologies of this invention, such as layer-theoretic topological constraints, anti-aliasing filtering, energy stability control, and ELM early warning, realizing full-process visualization operations from data preparation to model deployment.

[0147] 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.

[0148] 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 predicting turbulence in tokamak plasma based on layer-theoretic topology and spectral neural operators, characterized in that, Includes the following steps: S1. Collect diagnostic and control data of the tokamak device at time t and convert them into corresponding physical field vector sets, actuator vectors and equilibrium parameter vectors. The diagnostic data includes physical field measurement data collected by the diagnostic system, and the control data includes actuator state data read by the actuator control system and plasma equilibrium parameters obtained by the equilibrium reconstruction system. S2. Map the set of physical field vectors to the initial potential mesh representation, and map the actuator vector and equilibrium parameter vector to the corresponding condition vectors. Use the addition injection mechanism to fuse the condition vectors with the initial potential mesh representation to obtain the conditional potential mesh representation at time t. S3. The latent grid representation at time t+1 is obtained by performing time evolution on the conditional latent grid representation at time t using multi-layer Fourier neural operators; S4. Input the latent grid representation at time t+1 into the layer theory glue layer, and apply multi-region consistency constraints to the latent grid representation at time t+1 by restricting the mapping operator and the glue loss function to obtain the predicted latent grid representation after applying the constraints. S5. Input the predicted potential grid representation after applying constraints into the ELM early warning head, and output the predicted hazard level and remaining time of plasma turbulence in the tokamak device; S6. The predicted latent mesh representation after applying constraints is restored to the physical field prediction representation through the decoder, and physical constraints are applied to the restored physical field prediction representation using the projection and repair module to obtain the corrected physical field prediction representation.

2. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, In S2, the actuator vector and equilibrium parameter vector are mapped to corresponding condition vectors. The condition vectors are then fused with the initial latent mesh representation using an additive injection mechanism to obtain the final latent mesh representation at time t, which specifically includes: S21. Input the balance parameter vector into the balance encoder for encoding to obtain the balance condition vector. The balance encoder adopts a multilayer perceptron structure. S2-2. The actuator vector is input into the actuator encoder for encoding to obtain the actuator condition vector. The actuator encoder adopts a multilayer perceptron structure. S2-3. The conditional vector is incorporated into the initial latent mesh representation through an additive injection mechanism to obtain the conditional latent mesh representation. : in, This represents the initial potential mesh representation; Represents the equilibrium condition vector; Represents the executor condition vector; This represents a spatial broadcast operation, used to copy a condition vector across spatial dimensions.

3. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, In S3, a multi-layer Fourier neural operator is used to perform time evolution on the conditional latent grid representation at time t to obtain the latent grid representation at time t+1, specifically including: S31. Conditioned latent mesh representation The frequency domain representation is obtained by performing a three-dimensional Fourier transform. ; S32. Representation in the frequency domain Learnable weight tensors can be applied in this context. and anti-aliasing filter This yields a frequency domain representation that suppresses high-frequency aliasing; S33. Perform an inverse Fourier transform on the frequency domain representation of the suppressed high-frequency aliasing. We obtain the spatial domain representation after time evolution; S34. Compare the temporally evolved spatial domain representation with the latent grid representation. The convolutional results are concatenated, and the concatenated result is activated to obtain the latent mesh representation at time t+1. .

4. The tokamak plasma turbulence prediction method as described in claim 3, characterized in that, In step S32, the anti-aliasing filter In the frequency domain representation In each spatial dimension, the first 2 / 3 of the frequency modes are retained, and high-frequency modes exceeding the cutoff frequency are directly set to zero.

5. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, In S4, the layer-theoretic glue layer applies multi-region consistency constraints to the latent mesh representation at time t+1 by restricting the mapping operator and the glue loss function, thereby obtaining the predicted latent mesh representation after applying the constraints. Specifically, this includes the following steps: S41. Spatial domain in the latent grid representation at time t+1 Divided evenly along the circumference into overlapping subdomains ; S42. For circumferential grid size Determine the first The circular index range occupied by each subdomain; Each subdomain It covers the entire space radially and longitudinally, but is localized only in the circumferential direction; Interconnect adjacent subdomains through overlapping regions Establish an association with an overlap width of 2. 4 grid points; S43. For adjacent subfield pairs Using restricted mapping Subdomain The potential mesh on the surface is limited to the overlapping region: Similarly, using constraint mapping Subdomain The potential mesh on the surface is limited to the overlapping region: S44. Define the glue loss according to the constraint mapping: ， in For the set of adjacency relations of subdomains, Represents a restriction mapping Subdomain The region obtained after limiting the potential mesh to the overlapping area, Represents a restriction mapping Subdomain The region obtained after limiting the potential mesh to the overlapping area; S45. By minimizing the cementation loss, a prediction pattern that maintains a smooth and continuous physical field across different regions is learned, outputting a predicted latent mesh representation with constraints applied. .

6. The tokamak plasma turbulence prediction method as described in claim 5, characterized in that, In S43, the restricted mapping is implemented through sparse matrix indexing or interpolation operators.

7. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, In S5, the ELM early warning head outputs the hazard level and remaining time prediction values ​​of plasma turbulence in the tokamak device, specifically including: Predicted latent grid representation from adhesive layer Perform global pooling to compress the spatial dimension into a single pooled feature vector; The pooled feature vectors are mapped to risk levels using a multilayer perceptron, and the risk levels are converted into probability values ​​using a sigmoid function. The remaining time prediction head maps pooled feature vectors to non-negative time values. The remaining time prediction head adopts a two-layer fully connected network structure, with the middle layer using the GELU activation function and the output layer using the Softplus activation function to ensure that the predicted value is non-negative.

8. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, In S6, the predicted latent mesh representation after applying constraints is restored to the physical field prediction representation by the decoder, specifically including: The predicted latent mesh representation obtained from S4 is input into the decoder module, and the predicted latent representation is restored to the physical field prediction representation using the learnable 3D convolutional layer in the decoder.

9. The tokamak plasma turbulence prediction method as described in claim 1, characterized in that, In S6, the projection and repair module applies physical constraints to the restored physical field prediction representation, specifically including: Positive projection: Corrects negative values ​​in the physical field prediction representation to zero through clamping operations; Divergence free projection: A scalar potential is obtained by solving the Poisson equation, and then the gradient of the scalar potential is subtracted from the original vector field to obtain the corrected field, such that the corrected vector field... satisfy ; Energy target projection: When a specified target energy is projected in the physical field prediction representation. Once determined, the total energy represented by the predicted physical field is first calculated. Then through the scaling factor Rescale the state field to match the target value with the corrected total energy; Boundary condition projection: When the physics prediction representation provides a boundary mask, the predicted values ​​for the boundary regions are forcibly replaced with the specified boundary condition values.

10. A tokamak plasma turbulence prediction system based on layer-theoretic topology and spectral neural operators, used to execute the tokamak plasma turbulence prediction method according to any one of claims 1-9, characterized in that, include: The diagnostic subsystem collects diagnostic and control data of the tokamak device at time t and converts them into corresponding physical field vector sets, actuator vectors, and equilibrium parameter vectors. The diagnostic data includes physical field measurement data collected by the diagnostic system, and the control data includes actuator state data read by the actuator control system and plasma equilibrium parameters obtained by the equilibrium reconstruction system. The data processing unit receives the data output by the diagnostic subsystem and executes steps S2-S6, outputting the hazard level of plasma turbulence in the tokamak device, the predicted value of remaining time, and the corrected physical field prediction. The actuator control unit determines whether the pre-approval control threshold is met based on the hazard level and remaining time prediction value output by the data processing unit. If the control threshold is met, the corrected physical field prediction representation is transmitted to the MPC controller. The MPC controller calculates the optimal actuator adjustment amount based on the predicted field and sends the actuator command formed based on the adjustment amount to the actuator mechanism of the tokamak device through the control interface.

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