A method for predicting magnetic core loss and multi-objective optimization

Abstract

This invention relates to the field of magnetic core loss prediction and optimization, and discloses a method for magnetic core loss prediction and multi-objective optimization. The method outputs multi-dimensional operating condition data of magnetic components. Based on this multi-dimensional operating condition data, a Fourier neural operator is used to perform a mapping from the operating condition field to the loss field, obtaining a physical encoding feature vector. During the mapping process, the Fourier neural operator introduces a progressive multi-layer physical constraint loss. Using the physical encoding feature vector as context information, a deep integrated neural process is used to perform distribution prediction, obtaining prediction distribution parameters and condition vectors, simultaneously completing magnetic core loss prediction and uncertainty quantification. Using the condition vector as input, a reversible flow model is used to perform multi-objective optimization, generating a Pareto optimal solution set. The Pareto optimal solution set is then subjected to physical consistency verification; if the verification fails, an iterative optimization instruction is generated to complete the closed-loop optimization.

Description

Technical Field

[0001] This invention relates to the field of magnetic core loss prediction and optimization, and specifically to a method for predicting magnetic core loss and multi-objective optimization. Background Technology

[0002] Magnetic components are the core components of power converters, and their loss characteristics directly affect the efficiency and reliability of the entire system. Accurate prediction of core losses is crucial to achieving high efficiency and high power density design goals.

[0003] Currently, electromagnetic field finite element simulation technology can accurately calculate the winding losses of copper conductors. However, the core loss problem in magnetic components is more complex. Core loss mainly refers to the power loss generated by magnetic materials under the action of high-frequency alternating magnetic flux. This loss is affected by various factors such as operating frequency, magnetic flux density, excitation waveform, operating temperature, and core material, exhibiting complex nonlinearity and interrelationships.

[0004] In existing technologies, the Steinmetz equation is a common method for predicting magnetic core losses. However, the Steinmetz equation is based on two variables: frequency and magnetic flux density. When the operating temperature changes significantly, the material's permeability, coercivity, and loss factor change nonlinearly with temperature, thus affecting the prediction accuracy. Traditional Steinmetz equations process the temperature field and corresponding changes through temperature corrections, but because they handle global scalar data, they struggle to reflect generalization capabilities. Direct optimization using machine learning models or multi-objective optimization algorithms also increases computational resource requirements. Therefore, how to achieve high-precision prediction, uncertainty quantification, and efficient multi-objective optimization of magnetic core losses under existing computational resource constraints has become an urgent problem to be solved. Summary of the Invention

[0005] Purpose of the invention: To address the problems mentioned in the background art, this invention discloses a method for predicting magnetic core loss and multi-objective optimization. By constructing a Fourier neural operator combined with multi-dimensional operating conditions of the magnetic core, a magnetic core loss prediction model is built based on a deep integrated neural process algorithm. Under resource constraints, this method achieves further optimization and prediction of magnetic core loss.

[0006] Technical solution:

[0007] This invention discloses a method for predicting magnetic core losses and performing multi-objective optimization, the method comprising the following steps:

[0008] S1 collects multi-dimensional operating condition data of magnetic components output by temperature sensor, frequency generator and magnetic flux density measurement device through standardized interface. The multi-dimensional operating condition data includes at least temperature, frequency, magnetic flux density, excitation waveform and material type.

[0009] S2 Based on the multidimensional working condition data, the working condition field is mapped to the loss field through the Fourier neural operator to obtain the physical coding feature vector; the Fourier neural operator introduces a progressive multi-layer physical constraint loss during the mapping process.

[0010] S3 uses the physical encoding feature vector as context information and performs distribution prediction through deep integrated neural processes to obtain the predicted distribution parameters and condition vector, and simultaneously completes the prediction of magnetic core loss and uncertainty quantification.

[0011] S4 takes the conditional vector as input, performs multi-objective optimization through the reversible flow model, and generates the Pareto optimal solution set;

[0012] S5 performs a physical consistency check on the Pareto optimal solution set. If the check fails, iterative optimization instructions are generated to complete the closed-loop optimization.

[0013] Furthermore, the Fourier neural operator sequentially maps the operating field to the loss field through the input layer, lifting layer, core layer, physical constraint unit, and projection layer. The specific process is as follows:

[0014] The input layer receives operating condition data corresponding to temperature, frequency, and magnetic flux density.

[0015] By using a fully connected network in the lifting layer, the input data is mapped to a high-dimensional feature space, expanding the input dimension to 64 dimensions;

[0016] Multi-scale frequency domain physical features are extracted through the core layer;

[0017] Physical consistency supervision is achieved by constructing a multi-layered progressive physical constraint loss through physical constraint units;

[0018] The 64-dimensional high-dimensional features are compressed to 1 dimension by using a fully connected network through the projection layer and output to the loss field output space, while also outputting the physical encoded feature vector.

[0019] The physical coding feature vector includes multi-scale frequency domain feature representation, local loss response information, frequency domain energy distribution information, and physical consistency residual signal.

[0020] Furthermore, the core layer comprises four cascaded Fourier layers, used to approximate the nonlinear integral operator in the core loss generation process, and to learn the operator-level mapping relationship from the operating field to the loss field. The execution process of each Fourier layer is as follows: the input features are transformed to the frequency domain through Fourier transform, the frequency domain features are filtered through a learnable complex weight kernel function, and the filtered results are restored to the time domain through inverse Fourier transform to obtain the updated feature representation.

[0021] Each Fourier layer introduces a learnable frequency-adaptive mask matrix in the frequency domain. The element values ​​of the frequency-adaptive mask matrix are dynamically generated by temperature, frequency, and peak magnetic flux density through two fully connected gating networks. The mask values ​​are restricted to the (0,1) interval by the sigmoid function, so that the filtering characteristics of the frequency domain convolution are adaptively adjusted according to the input conditions.

[0022] Furthermore, the multi-layer progressive physical constraint loss has a three-layer structure, including energy level constraint loss, path level constraint loss, and frequency domain consistency constraint loss, and the total physical constraint loss is the weighted sum of the three-layer losses;

[0023] Among them, the energy level constraint loss is determined based on the deviation between the physical loss corresponding to the hysteresis loop integral and the predicted loss, which is used to ensure the physical rationality of the total loss magnitude.

[0024] The path-level constraint loss is determined based on the point-by-point deviation of the magnetic field strength H and magnetic flux density B on the dynamically changing trajectory, and is used to ensure the physical authenticity of the dynamically changing trajectory of the hysteresis loop.

[0025] The frequency domain consistency constraint loss is determined based on the difference between the spectrum of the predicted loss signal and the spectrum corresponding to the hysteresis loop integral, and is used to ensure the physical interpretability of the spectral characteristics of the loss signal.

[0026] Furthermore, during the training process, the Fourier neural operator updates the model parameters based on a weighted sum of data loss and physical constraint loss;

[0027] The data loss is expressed as mean square error, which is used to characterize the deviation between the predicted loss and the measured loss.

[0028] The physical constraint loss is a weighted sum of three progressive physical constraint losses. The training process uses the Adam optimizer, and the learning rate decays with each iteration.

[0029] Furthermore, the execution process of the deeply integrated neural process is as follows:

[0030] A context encoder composed of a multilayer perceptron encodes the physical encoded feature vector to generate a context vector. An attention mechanism is used to fuse the working condition samples of the target material with the context vector to generate a task-related representation.

[0031] Task-related representations are encoded using a global shared encoder based on the Transformer architecture, and cross-task common features are extracted.

[0032] The mean and variance of a Gaussian distribution are output by K independent neural process heads, where K is an integer greater than 1;

[0033] The outputs of K neural process heads are aggregated to calculate the prediction mean and uncertainty parameters, and the task condition vector is obtained by sampling through reparameterization techniques.

[0034] Furthermore, the K neural process heads are 5 heterogeneous neural process heads that share a context encoder and use independent decoders; the encoder network depths of the 5 heterogeneous neural process heads are 2, 3, 4, 3, and 2 layers, respectively, and the number of attention heads are 4, 8, 16, 8, and 4, respectively.

[0035] When aggregating the outputs of each neural process head, random uncertainty, cognitive uncertainty, and total uncertainty are simultaneously decomposed and calculated. Random uncertainty is used to characterize the inherent noise of the data, cognitive uncertainty is used to characterize the cognitive boundary of the model, and total uncertainty is determined by both random uncertainty and cognitive uncertainty.

[0036] Based on the predicted mean and total uncertainty, the task latent variables are sampled as the task condition vector by introducing a reparameterization technique using standard Gaussian noise.

[0037] Furthermore, the multi-objective optimization execution process of the reversible flow model is as follows:

[0038] Combine task latent variables, optimize the objective vector, and generate an uncertainty budget to generate a conditional input vector;

[0039] The FiLM conditional injection mechanism generates element-wise scaling and offset parameters based on the conditional input vector.

[0040] By performing a conditional invertible transformation through an invertible neural network, noise vectors are sampled from a standard Gaussian distribution and then transformed inversely to generate candidate solutions.

[0041] Based on the Pareto dominance relation, non-dominated solutions are selected from the candidate solutions, a Pareto optimal solution set is constructed, and the optimal combination of operating parameters and the corresponding generation probability are output.

[0042] Furthermore, the reversible neural network adopts a structure of alternating 8 coupling layers and substitution layers;

[0043] Each coupling layer adopts an affine coupling structure. The execution process is as follows: the input features are divided into two parts along the channel dimension. Based on one part of the features, a scaling parameter and a translation parameter are generated by a multilayer perceptron. An affine transformation is performed on the other part of the features. An exponential function is used to ensure that the scaling factor is positive. Each permutation layer uses a fixed random permutation matrix to rearrange the channel order to enhance the feature mixing capability.

[0044] Furthermore, the physical consistency verification uses a preset physical model to verify the consistency between the loss prediction results corresponding to the Pareto optimal solution set and the physical calculation results of the hysteresis loop integral.

[0045] If the verification fails, uniformly sample neighborhood samples within the preset range of the optimal solution parameters, expand the training set with neighborhood samples, and re-execute the deep ensemble neural process distribution prediction and reversible flow model multi-objective optimization steps until the verification passes.

[0046] Beneficial effects:

[0047] The Fourier neural operator mapping unit learns integral operators in the frequency domain to handle field mapping problems under varying temperature and frequency conditions, and embeds hysteresis loop integrals as soft constraints to prevent purely data-driven models from deviating from physical laws. The deep integrated neural process unit uses physically encoded feature vectors as contextual information and aggregates the distribution of multiple heterogeneous neural process heads to output the prediction mean, random uncertainty, cognitive uncertainty, and total uncertainty, achieving stepwise quantification of uncertainty. The reversible multi-objective optimization unit uses task latent variables as conditions to guide the reversible neural network to generate Pareto optimal solutions. It replaces the traditional evolutionary algorithm with an inverse transformation sampling mechanism, outputting the optimal combination of operating parameters under objective constraints such as core loss, transmitted magnetic energy density, and uncertainty budget, and quickly verifies physical consistency through Fourier neural operators. Thus, it achieves high-precision prediction, uncertainty quantification, and multi-objective collaborative optimization under varying temperature conditions within the constraints of existing computing resources. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the method framework of the present invention;

[0049] Figure 2 This is a schematic diagram of the data flow structure of the Fourier neural operator mapping unit of the present invention;

[0050] Figure 3 This is a schematic diagram of the context learning structure of the deeply integrated neural process unit of the present invention;

[0051] Figure 4 This is a schematic diagram of the reversible network structure of the reversible multi-objective optimization unit of the present invention;

[0052] Figure 5 This is a bar chart showing the cross-condition prediction performance of the Fourier neural operator in this embodiment of the invention.

[0053] Figure 6 This is a scatter plot of the Pareto front generated by reversible multi-objective optimization in an embodiment of the present invention.

[0054] Figure 7 This is a line graph showing the three-stage information gain and reliability improvement in this embodiment of the invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] like Figure 1 As shown, this invention discloses a method for predicting magnetic core losses and performing multi-objective optimization. The method steps are as follows:

[0057] Step 1: Collect multi-dimensional operating condition data of the magnetic components. The multi-dimensional operating condition data includes at least temperature field, frequency and magnetic flux density field data, as well as waveform type and material type.

[0058] Step two, as Figure 2 As shown, a Fourier neural operator network is constructed, using the hysteresis loop integral as a physical constraint, to learn the mapping relationship from the operating field to the loss field and output the physical encoding feature vector.

[0059] The Fourier neural operator network consists of a lifting layer, a core layer, a physical layer, and a projection layer, which learns the mapping relationship from the operating field to the loss field.

[0060] The lifting layer is used to map the input data to a high-dimensional feature space; the core layer is used to perform frequency domain convolution operations through multiple Fourier layers to approximate the nonlinear integral operator in the magnetic core loss generation process; the physical layer is used to construct a multi-layer progressive physical constraint loss; the projection layer is used to project the high-dimensional features to the loss field output space and output the physical encoded feature vector.

[0061] The physical coding feature vector includes multi-scale frequency domain feature representation, local loss response information, frequency domain energy distribution information, and physical consistency residual signal; the lifting layer uses a fully connected network to expand the input dimension to 64 dimensions, the core layer contains 4 Fourier layers, and the projection layer uses a fully connected network to compress the 64 dimensions to a 1-dimensional output.

[0062] During training, the model parameters are updated using a weighted average of data loss and physical constraint loss. The data loss is used to characterize the deviation between the predicted loss and the measured loss, while the physical constraint loss is the squared difference between the hysteresis loop integral and the predicted loss. The parameters are updated using the Adam optimizer and a learning rate that decays with iteration, providing input for subsequent deep ensemble neural process models.

[0063] The physical layer constructs a multi-layered progressive physical constraint loss, including energy conservation constraints, path consistency constraints, and frequency domain consistency constraints;

[0064] The mathematical expression for the total physical constraint loss is:

[0065]

[0066] in, This represents the total physical constraint loss; Energy level constraint loss characterizes the deviation between the physical loss corresponding to the hysteresis loop integral and the predicted loss. The path-level constraint loss characterizes the point-by-point deviation of the dynamic trajectory of the magnetic field strength H and magnetic flux density B. The frequency domain consistency constraint loss characterizes the difference between the spectrum of the predicted loss signal and the spectrum corresponding to the hysteresis loop integral. , , These are the preset weighting coefficients for each constraint term;

[0067] Energy level constraint loss:

[0068]

[0069] in, This represents the hysteresis loop integral per unit volume of magnetic core over one magnetization period. For switching frequency, The core loss is predicted by the network.

[0070] The path-level constraint loss:

[0071]

[0072] Where N is the number of sampling points on the hysteresis loop. For the magnetic flux density output by the network in Predicted value at time, For magnetic flux density at The measured values ​​at time t are consistent with the physical measurements in the point-by-point predictions of the loss term-constrained network on the hysteresis loop path.

[0073] The frequency domain consistency constraint loss:

[0074]

[0075] Where FFT stands for Fast Fourier Transform. Representing the power spectral density, this loss term constrains the predicted loss signal to have the same energy distribution in the frequency domain as the physical loss signal;

[0076] The three-layer progressive constraints achieve physical consistency supervision from three levels: total energy, dynamic path trajectory, and frequency domain energy distribution, respectively, ensuring that the output physical coding feature vector conforms to the electromagnetic physical mechanism of the magnetic core.

[0077] The core layer module contains four Fourier layers. The Fourier layers transform the input features to the frequency domain through Fourier transform, filter the frequency domain features through a learnable complex weight kernel function, and restore the filtering result to the time domain through inverse Fourier transform to obtain the updated feature representation.

[0078] The mathematical expression for the Fourier layer is:

[0079]

[0080] Where F is the Fourier positive transform operator from the spatial domain to the frequency domain; It is the inverse Fourier transform operator from the frequency domain to the spatial domain; The learnable complex weight kernel function of the l-th layer represents the nonlinear integral operator of core loss. Here is the frequency adaptive mask matrix for the l-th layer; ⊙ represents the element-wise multiplication operation of the matrix. The input spatial feature field is the l-th layer of the network; It is a non-linear activation function; The weight matrix is ​​the linear mapping matrix for the l-th layer.

[0081] The frequency adaptive mask matrix It is dynamically generated by the gating network based on the input condition characteristics of the current layer, and its mathematical expression is:

[0082]

[0083] in, The gating network corresponding to layer l is implemented using a two-layer fully connected network. For inputting temperature parameters of the operating conditions, For input operating conditions, frequency parameters, The peak value of the magnetic flux density under the input operating condition. The function restricts the mask value to the (0,1) interval, enabling the network to adaptively learn the importance weights of each frequency component under different operating conditions during training.

[0084] Through the above frequency domain convolution operation and frequency adaptive mask adjustment, operator-level mapping learning from the operating field to the loss field is realized, providing effective feature support for subsequent physical constraint loss calculation.

[0085] Step 3, as Figure 3 As shown, a deep integrated neural process model is constructed using the physical encoding feature vector as context information. The model outputs prediction distribution parameters and uncertainty quantification through the distribution aggregation of multiple neural process heads, and samples to obtain the task condition vector.

[0086] The deep integrated neural process unit includes a context encoder, a context aggregation module, a global shared encoder, an ensemble prediction module, a distribution aggregation module, and a sampling module;

[0087] The context aggregation module receives the working condition samples of the target material and the physical encoding feature vector, and fuses them through an attention mechanism to generate task-related representations. The global shared encoder receives the task-related representations and extracts cross-task common features. The integrated prediction module contains five heterogeneous neural process heads with encoder network depths of 2, 3, 4, 3, and 2 layers, and attention heads of 4, 8, 16, 8, and 4, respectively. The shared context encoder adopts a Transformer architecture. The distribution aggregation module aggregates the outputs of the five neural process heads and calculates the prediction mean, random uncertainty, cognitive uncertainty, and total uncertainty. The sampling module obtains the task condition vector based on the prediction mean and total uncertainty through reparameterization techniques. The context encoder uses a multilayer perceptron to provide feature support for subsequent uncertainty quantification and multi-objective optimization.

[0088] The distribution aggregation module aggregates data based on the mean and variance of the outputs from multiple neural process heads, and performs the following operations in conjunction with the uncertainty decomposition module:

[0089] Integrated Predicted Mean:

[0090]

[0091] Random uncertainty:

[0092]

[0093] Cognitive uncertainty:

[0094]

[0095] Total uncertainty, reparameterized sampling:

[0096] , .

[0097] in, To integrate the predicted mean, Indicates the first The average output of each neural process head Indicates the first The variance of the head output of a neural process Due to chance and uncertainty, To understand uncertainty, For total uncertainty, The noise is standard Gaussian noise; the integrated prediction mean reflects the model's central estimate of core loss; the random uncertainty reflects the inherent noise of the data; the cognitive uncertainty reflects the model's knowledge boundary; and the reparameterized sampling achieves differentiable sampling of latent variables by introducing standard Gaussian noise, providing task condition vector input for subsequent conditional invertible neural networks.

[0098] Step four, as Figure 4 As shown, a conditional invertible neural network is constructed using the task condition vector as the condition input, and the Pareto optimal solution set is generated through inverse transformation sampling.

[0099] The reversible flow multi-objective optimization unit includes a condition vector module, a FiLM condition injection module, a reversible network module, an inverse transform sampling module, and an output module;

[0100] The conditional vector module is used to combine task latent variables, target vector, and uncertainty budget. The FiLM conditional injection module is used to receive the output of the conditional vector module and generate scaling and offset parameters. The reversible network module contains an alternating structure of 8 coupling layers and permutation layers. The coupling layers use an affine coupling structure to perform reversible transformations on different parts of the input features. The permutation layers are used to rearrange the channel order. The inverse transformation sampling module is used to sample noise vectors from a standard Gaussian distribution and generate candidate solutions through reversible transformation. The output module is used to output the Pareto optimal solution set from the candidate solutions to provide optimized solution samples for subsequent physical consistency verification.

[0101] The reversible network module includes multiple alternating coupling layers and permutation layers. Each coupling layer employs an affine coupling structure to perform reversible transformations on different parts of the input features. Each permutation layer rearranges the channel order to enhance feature mixing capabilities. Each layer of the reversible network module performs the following operations:

[0102] ; ;

[0103] Here, `split` represents the channel splitting function. and This represents the features of the two parts after segmentation. This represents element-wise multiplication. Represents an exponential function. This indicates scaling the network output. This indicates the output of the translation network. and The transformed features are represented by the channel segmentation function, which divides the input features into two parts along the channel dimension. The scaling and translation networks are multilayer perceptrons. The element-wise multiplication implements the scaling transformation of the features, and the exponential function ensures that the scaling factor is positive, providing a differentiable feature representation for subsequent inverse transformation sampling.

[0104] Step 5: Verify the physical consistency of the Pareto optimal solution set using a preset physical model. If the verification fails, expand the training set with neighborhood samples of the optimal solution and return to Step 3. The physical consistency verification compares the prediction loss of the Fourier neural operator output. Integral with hysteresis loop If the calculated physical reference value fails the verification, the training set is expanded by uniformly sampling in the neighborhood of the optimal solution, and the deep integrated neural process stage and the reversible multi-objective optimization stage are re-executed.

[0105] The verification process compares the deviation between the prediction results and the calculation results of the physical model to ensure the physical rationality and engineering feasibility of the optimized solution set, and completes the closed-loop control of the core loss prediction and multi-objective optimization method.

[0106] This embodiment uses a PC95 manganese-zinc ferrite core as the test object, such as Figure 5 As shown, the curves comparing the measured values ​​and model predictions of core loss under multiple combined operating conditions cover a wide range of temperature, frequency, and magnetic flux density operating ranges. The prediction curves closely match the measured true values, with no significant deviations or jumps throughout. This invention relies on Fourier neural operators combined with multi-layered progressive physical constraints to characterize the magnetization energy transfer and loss evolution of the core from the frequency domain mechanism level, effectively solving the problems of insufficient nonlinear characterization, weak generalization ability across operating conditions, and high-frequency prediction distortion in traditional models. The prediction accuracy and stability are significantly improved under all operating conditions. The model accuracy index and the curves showing the changes in the quantification of double uncertainties are shown in the figure. Figure 7 As shown, the model's coefficient of determination converges rapidly and maintains a high steady-state level, while the prediction error continues to decrease. At the same time, random uncertainty and cognitive uncertainty are decomposed through multi-heterogeneous neural process head integration. Both types of quantitative indicators are within a controllable and reasonable range, breaking through the limitations of traditional methods that only output single-point predictions and lack result confidence assessment. This is the core innovation of this invention and provides a reliable quantitative basis for setting subsequent multi-objective optimization constraints.

[0107] The distribution of the Pareto optimal front solution set obtained by multi-objective optimization is as follows: Figure 6 As shown, the solution front is complete and smooth, with uniform and moderate distribution, and there are no front breakages, local accumulations, or gaps. It can achieve a reasonable trade-off between the two major objectives of core loss and magnetic flux transmission density, providing multiple sets of directly selectable compromise optimal solutions for core material selection, operating frequency matching, and operating parameter configuration in engineering.

[0108] Table 1 shows the convergence changes of loss indicators and physical deviations during the physical consistency closed-loop iteration process. In the early stage of iteration, the physical deviation was large and the loss indicator did not reach the optimum. As the neighborhood samples of the optimal solution were expanded and the model parameters were reversed, the physical consistency deviation rapidly decreased and tended to stabilize, and the core loss indicator gradually converged to the optimal steady-state value. This result fully verifies that the physical consistency verification and closed-loop iteration mechanism added in this invention can effectively compensate for the modeling deviation caused by limited measured samples, so that the optimized operating parameters not only have theoretical optimality, but also fully conform to the electromagnetic physical mechanism and the feasibility of actual engineering.

[0109] Table 1

[0110]

[0111] The foregoing description of the embodiments enables those skilled in the art to make or use the present invention. Various modifications to the embodiments will be readily apparent to those skilled in the art. The general principles of the invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention should not be limited to the embodiments shown herein, but should cover the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting magnetic core loss and performing multi-objective optimization, characterized in that, Includes the following steps: S1 collects multi-dimensional operating condition data of magnetic components output by temperature sensor, frequency generator and magnetic flux density measurement device through standardized interface. The multi-dimensional operating condition data includes at least temperature, frequency, magnetic flux density, excitation waveform and material type. S2 Based on the multidimensional working condition data, the working condition field is mapped to the loss field through the Fourier neural operator to obtain the physical coding feature vector; the Fourier neural operator introduces a progressive multi-layer physical constraint loss during the mapping process. S3 uses the physical encoding feature vector as context information and performs distribution prediction through deep integrated neural processes to obtain the predicted distribution parameters and condition vector, and simultaneously completes the prediction of magnetic core loss and uncertainty quantification. S4 takes the conditional vector as input, performs multi-objective optimization through the reversible flow model, and generates the Pareto optimal solution set; S5 performs a physical consistency check on the Pareto optimal solution set. If the check fails, iterative optimization instructions are generated to complete the closed-loop optimization.

2. The core loss prediction and multi-objective optimization method according to claim 1, characterized in that, The Fourier neural operator sequentially maps the operating field to the loss field through the input layer, lifting layer, core layer, physical constraint unit, and projection layer. The specific process is as follows: The input layer receives operating condition data corresponding to temperature, frequency, and magnetic flux density. By using a fully connected network in the lifting layer, the input data is mapped to a high-dimensional feature space, expanding the input dimension to 64 dimensions; Multi-scale frequency domain physical features are extracted through the core layer; Physical consistency supervision is achieved by constructing a multi-layered progressive physical constraint loss through physical constraint units; The 64-dimensional high-dimensional features are compressed to 1 dimension by using a fully connected network through the projection layer and output to the loss field output space, while also outputting the physical encoded feature vector. The physical coding feature vector includes multi-scale frequency domain feature representation, local loss response information, frequency domain energy distribution information, and physical consistency residual signal.

3. The core loss prediction and multi-objective optimization method according to claim 2, characterized in that, The core layer contains four cascaded Fourier layers, which are used to approximate the nonlinear integral operator in the core loss generation process and learn the operator-level mapping relationship from the operating field to the loss field. The execution process of each Fourier layer is as follows: the input features are transformed to the frequency domain through Fourier transform, the frequency domain features are filtered through a learnable complex weight kernel function, and the filtered results are restored to the time domain through inverse Fourier transform to obtain the updated feature representation. Each Fourier layer introduces a learnable frequency-adaptive mask matrix in the frequency domain. The element values ​​of the frequency-adaptive mask matrix are dynamically generated by temperature, frequency, and peak magnetic flux density through two fully connected gating networks. The mask values ​​are restricted to the (0,1) interval by the sigmoid function, so that the filtering characteristics of the frequency domain convolution are adaptively adjusted according to the input conditions.

4. The core loss prediction and multi-objective optimization method according to claim 2, characterized in that, The multi-layered progressive physical constraint loss has a three-layer structure, including energy-level constraint loss, path-level constraint loss, and frequency-domain consistency constraint loss. The total physical constraint loss is the weighted sum of the three-layer losses. Among them, the energy level constraint loss is determined based on the deviation between the physical loss corresponding to the hysteresis loop integral and the predicted loss, which is used to ensure the physical rationality of the total loss magnitude. The path-level constraint loss is determined based on the point-by-point deviation of the magnetic field strength H and magnetic flux density B on the dynamically changing trajectory, and is used to ensure the physical authenticity of the dynamically changing trajectory of the hysteresis loop. The frequency domain consistency constraint loss is determined based on the difference between the spectrum of the predicted loss signal and the spectrum corresponding to the hysteresis loop integral, and is used to ensure the physical interpretability of the spectral characteristics of the loss signal.

5. The method for predicting magnetic core loss and multi-objective optimization according to claim 1, characterized in that, During training, the Fourier neural operator updates the model parameters based on a weighted sum of data loss and physical constraint loss. The data loss is expressed as mean square error, which is used to characterize the deviation between the predicted loss and the measured loss. The physical constraint loss is a weighted sum of three progressive physical constraint losses. The training process uses the Adam optimizer, and the learning rate decays with each iteration.

6. The method for predicting magnetic core loss and performing multi-objective optimization according to claim 1, characterized in that, The execution process of the deep integrated neural process is as follows: A context encoder composed of a multilayer perceptron encodes the physical encoded feature vector to generate a context vector. An attention mechanism is used to fuse the working condition samples of the target material with the context vector to generate a task-related representation. Task-related representations are encoded using a global shared encoder based on the Transformer architecture, and cross-task common features are extracted. The mean and variance of a Gaussian distribution are output by K independent neural process heads, where K is an integer greater than 1; The outputs of K neural process heads are aggregated to calculate the prediction mean and uncertainty parameters, and the task condition vector is obtained by sampling through reparameterization techniques.

7. The method for predicting magnetic core loss and performing multi-objective optimization according to claim 6, characterized in that, The K neural process heads consist of 5 heterogeneous neural process heads that share a context encoder and use independent decoders; the encoder network depths of the 5 heterogeneous neural process heads are 2, 3, 4, 3, and 2 layers, respectively, and the number of attention heads are 4, 8, 16, 8, and 4, respectively. When aggregating the outputs of each neural process head, random uncertainty, cognitive uncertainty, and total uncertainty are simultaneously decomposed and calculated. Random uncertainty is used to characterize the inherent noise of the data, cognitive uncertainty is used to characterize the cognitive boundary of the model, and total uncertainty is determined by both random uncertainty and cognitive uncertainty. Based on the predicted mean and total uncertainty, the task latent variables are sampled as the task condition vector by introducing a reparameterization technique using standard Gaussian noise.

8. The method for predicting magnetic core loss and performing multi-objective optimization according to claim 1, characterized in that, The multi-objective optimization execution process of the reversible flow model is as follows: Combine task latent variables, optimize the objective vector, and generate an uncertainty budget to generate a conditional input vector; The FiLM conditional injection mechanism generates element-wise scaling and offset parameters based on the conditional input vector. By performing a conditional invertible transformation through an invertible neural network, noise vectors are sampled from a standard Gaussian distribution and then transformed inversely to generate candidate solutions. Based on the Pareto dominance relation, non-dominated solutions are selected from the candidate solutions, a Pareto optimal solution set is constructed, and the optimal combination of operating parameters and the corresponding generation probability are output.

9. The method for predicting magnetic core loss and multi-objective optimization according to claim 8, characterized in that, The reversible neural network adopts a structure with 8 alternating coupling layers and substitution layers; Each coupling layer adopts an affine coupling structure. The execution process is as follows: the input features are divided into two parts along the channel dimension. Based on one part of the features, a scaling parameter and a translation parameter are generated by a multilayer perceptron. An affine transformation is performed on the other part of the features. An exponential function is used to ensure that the scaling factor is positive. Each permutation layer uses a fixed random permutation matrix to rearrange the channel order to enhance the feature mixing capability.

10. The method for predicting magnetic core loss and performing multi-objective optimization according to claim 1, characterized in that, The physical consistency verification uses a preset physical model to verify the consistency between the loss prediction results corresponding to the Pareto optimal solution set and the physical calculation results of the hysteresis loop integral. If the verification fails, uniformly sample neighborhood samples within the preset range of the optimal solution parameters, expand the training set with neighborhood samples, and re-execute the deep ensemble neural process distribution prediction and reversible flow model multi-objective optimization steps until the verification passes.

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