Composite periodic physical sequence processing method based on architecture symmetry constraint

Abstract

The application discloses a composite material periodic physical sequence processing method based on architecture symmetry constraint, and comprises the following steps: S1, collecting an original sequence of a composite material layer, mapping by using a topological invariant embedding rule, extracting an initial embedding vector, and obtaining an embedding sequence; S2, padding the embedding sequence; S3, using a Transformer encoder to extract and process the padded embedding sequence, and obtaining a fixed-length vector; and S4, based on the fixed-length vector, using a pre-trained TED-Net model to solve, and obtaining an optimal layer sequence. The application makes the physical equivalent parameters strictly continuous in a feature space, fundamentally eliminates boundary discontinuity introduced by one-dimensional Euclidean mapping, and solves the problem of representing geometric misplacement.

Description

Technical Field

[0001] This invention relates to the field of materials data processing technology, and specifically to a method for processing periodic physical sequences of composite materials based on architectural symmetry constraints. Background Technology

[0002] In the fields of scientific computing and engineering optimization (such as composite laminate layup design and periodic metamaterial design), there exist a large number of physical sequences with strict periodicity and symmetry. These sequences differ from conventional time series; their parameters are typically defined on compact manifold spaces (such as circles and spheres) and are strictly constrained by physical laws (such as inversion equivalence). Utilizing deep learning for forward prediction and inverse design of these physical sequences represents a significant current direction in scientific machine learning.

[0003] The current mainstream technical approaches can be divided into the following three categories, but all of them have significant drawbacks.

[0004] One existing technique refers to a method of modeling periodic physical sequences using standard deep learning sequence models (such as standard Transformer, LSTM, CNN, etc.). Taking composite laminate layup design as a typical scenario, the technical solution is as follows: A laminate containing L layers is represented as a scalar sequence of fiber angles, where each element is the orientation angle of that layer relative to the reference axis (usually ranging from 0° to 180°). These angle values ​​are then simply linearly normalized (e.g., divided by 180° to scale to [0, 1]) and used as network input features without any transformation of the topology of the angle parameters themselves. Then, positional encodings are superimposed and fed into an encoder (Transformer) consisting of multi-head self-attention and feedforward layers, or the hidden states are recursively updated according to the layer order (LSTM), or local combined features of adjacent layups are extracted by sliding a one-dimensional convolutional kernel along the sequence dimension (CNN). Finally, through training with a large number of samples, the characteristics of periodic physical sequences are automatically summarized, such as sequence reversal equivalence and angle periodicity equivalence.

[0005] The disadvantages of the existing technology are: (1) It represents geometric misalignment and artificially creates discontinuous boundaries. Directly mapping periodic angles to one-dimensional Euclidean space will create physically equivalent but numerically far-distance boundaries: 0° and 180° are physically completely equivalent (period 180°), but the Euclidean distance is close to the maximum. The model is forced to consume a large number of parameters to smooth out the impact caused by the representation method. (2) High sample complexity and data hunger. Symmetry and periodicity can only be learned by the model itself. The model needs a large number of samples to approximately learn the invariance that should be guaranteed in the prior. In practice, such models often require tens of thousands of finite element samples to converge, and the cost of data acquisition and simulation is high. (3) It cannot guarantee physical consistency and is prone to non-physical predictions. Data augmentation can only make the predictions of the forward sequence and its reverse sequence roughly close. The model often gives inconsistent results for the two, which violates the laws of physics. Once used as a proxy model for reverse design, it will amplify the error.

[0006] To address the issue of Technique 1 completely ignoring physical laws, the industry has developed Physical Information Neural Networks (PINNs). As a second existing technology, its core is to incorporate physical laws as constraints into the training objective, guiding the network output towards physical plausibility. The implementation scheme is as follows: the network core remains a conventional multilayer perceptron or sequence network; the input is physical parameters, and the output is the physical field or property to be predicted. The key difference from Technique 1 lies in the loss function: PINNs construct an additional physical residual penalty term in addition to the data fitting term (the error between the predicted and true values). This type of method attempts to incorporate physical equations or symmetries as penalty terms into the training process through a soft loss function.

[0007] The disadvantages of the existing technology 2 are: (1) It heavily relies on explicit control equations, which limits its applicability. PINNs must know the exact partial differential equations (PDEs) or analytical symmetry relationships of the system in advance. However, high-dimensional systems such as macroscopic properties of composite materials and periodic metamaterials often lack simple and usable explicit control equations, making it difficult to construct penalty terms and implement this method on such black-box systems. (2) Symmetry is only a soft constraint and cannot fundamentally guarantee physical consistency. Symmetry only exists as a penalty term. Under limited training and multi-objective trade-offs, the network output can only approximately satisfy the constraints and cannot guarantee that the forward sequence is strictly equal to its reverse sequence. The residual physical inconsistency will be amplified in the reverse design optimization, causing the optimization to fall into a non-physical pseudo-optimal solution. (3) It only remedies the loss and does not touch the geometric essence of the representation. The input of PINNs still uses scalar representations that may have geometric misalignment, which does not reduce the complexity of the hypothesis space from the source, and the improvement in data efficiency is limited.

[0008] The third existing technology is geometric deep learning and high-dimensional physics embedding methods (such as SE(3)-Transformer and LayupFormer). In order to introduce physical priors at the input end, the industry has further proposed geometric deep learning and high-dimensional physics embedding methods, which mainly have two branches: Branch 1: Isovariant geometric deep learning (represented by SE(3)-Transformer): This method explicitly constructs operators that are equivariant to the three-dimensional spatial rotation and translation group SE(3) in the network. The input is the three-dimensional atom / node coordinates and their features. Through tools such as spherical harmonic functions and tensor products, equivariant attention and message passing mechanisms are constructed so that when the input as a whole undergoes three-dimensional rotation and translation, the network output is covariant according to the corresponding rules. This method has good results in the modeling of three-dimensional structures such as molecules and proteins. Branch 2: High-dimensional physical invariant embedding (represented by LayupFormer and methods using Tsai invariants): This method does not directly input the original angle, but first uses engineering empirical formulas to convert the angle into a set of physical invariant features (such as 6-dimensional Tsai triangular invariants or stiffness component combinations), and then inputs this set of high-dimensional features into networks such as Transformer to explicitly inject physical priors and improve prediction.

[0009] The disadvantages of the existing technology 3 are: (1) High-dimensional redundancy and high computational cost. The parameters are embedded in a redundant high-dimensional space by adopting methods such as 6-dimensional Tsai invariants. The dimension is much higher than the minimum dimension required to describe the topology (circular manifolds only require 2 dimensions), which increases the computation and storage overhead and does not achieve the theoretically optimal data efficiency. (2) Lack of hard guarantee of physical consistency at the architecture level. This type of method mainly works at the input feature level and does not force the injection of inversion invariance at the network architecture level, which is not reliable enough when used as a reverse design proxy model.

[0010] In summary, the fundamental bottleneck of existing technologies lies in the misalignment of representation geometry and the lack of hard physical constraints at the architectural level, resulting in extremely low model data utilization, poor cross-scale generalization ability, and inability to guarantee strict physical consistency, which seriously restricts the practical application of scientific machine learning in complex engineering sequence modeling. Summary of the Invention

[0011] To address the above problems, this invention proposes a method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints.

[0012] The technical solution of this invention is: a method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints, comprising the following steps: S1. Collect the original sequence of composite material layup, map it using topological isovariant embedding rules, extract the initial embedding vector, and obtain the embedding sequence; S2. Complete the embedded sequence; S3. Use the Transformer encoder to extract and process features from the padded embedding sequence to obtain a fixed-length vector. S4. Based on a fixed-length vector, the optimal layering sequence is obtained by using a pre-trained TED-Net model.

[0013] Furthermore, in S1, the elements of the original sequence are mapped to continuous manifold coordinates using the topologically equivariant embedding rule, and the initial embedding vector is extracted.

[0014] Furthermore, continuous manifold coordinates The expression is: ; in, This represents the i-th element in the original sequence. Represents topologically equivariant embedding. It represents the set of real numbers.

[0015] Furthermore, the initial embedding vector The expression is: ; in, Represents a learnable embedding matrix. This represents a learnable embedding bias vector. express 3D real vector space, Indicates the total length of the sequence. Represents the coordinates of a continuous manifold.

[0016] Furthermore, S3 includes the following sub-steps: S31. Superimpose standard sinusoidal position codes onto the padded embedded sequence and input it into the dual-path shared weight sequence encoder; S32. Use a dual-path shared-weight sequence encoder to extract features from the original sequence and the reversed sequence; S33. Element-wise average pooling is performed on the extracted features using a symmetric fusion layer to obtain the context feature sequence. S34. Generate a fixed-length vector based on the context feature sequence.

[0017] Furthermore, the characteristics of the original sequence The expression is: ; in, Represents the original sequence. Represents topologically equivariant embedding. Indicates Transformer encoder; Features of reversed sequences The expression is: ; in, Indicates the reverse sequence; Context feature sequence The expression is: .

[0018] Furthermore, fixed-length vectors The expression is: ; in, This represents the feature vector at the i-th position in the context feature sequence. Indicates the total length of the sequence. express A real vector space.

[0019] Furthermore, in S4, the expression for the objective function solved using the pre-trained TED-Net model is: ; in, This represents the forward prediction function of the pre-trained TED-Net. Represents an angle vector. Let the objective function be the one to be minimized. This represents topologically equivariant embeddings.

[0020] The beneficial effects of this invention are: (1) Completely eliminate the boundary influence caused by human intervention and ensure the continuity of the representation topology: This invention makes the physical equivalent parameters strictly continuous in the feature space (1° and 179° are adjacent), fundamentally eliminating the boundary discontinuity introduced by the one-dimensional Euclidean mapping and solving the problem of geometric misalignment in representation.

[0021] (2) Data efficiency: This invention reduces the conditional entropy to the theoretical lower bound by using the minimum complete representation, which reduces the total data requirement by more than 90% compared with traditional methods, and significantly alleviates data hunger.

[0022] (3) High-precision physical consistency: The dual-path shared weight and symmetric fusion layer architecture of this invention have hard constraints, which can achieve an error of less than 10 without data augmentation. -15 The strict inversion remains unchanged, eliminating non-physical predictions and providing an absolutely reliable surrogate model for reverse engineering.

[0023] (4) Eliminating dependence on explicit equations and adapting to black-box systems: The physical priors of this invention are injected through representation and architecture rather than partial differential equation constraints, enabling the method to be directly applied to high-dimensional systems such as composite materials and metamaterials that lack explicit governing equations.

[0024] (5) Strong generalization across scales and tasks: The single model of this invention can uniformly process variable-length sequences from 1 to 20 layers, and has the ability to perform zero-sample cross-scale extrapolation and few-sample cross-task transfer.

[0025] (6) Approaching the theoretical optimality of the bottleneck of reverse design: This invention benefits from the smoothness of the continuous topological manifold space and the fact that the boundary has no effect, and the reverse design effectively avoids the local optimal trap. Attached Figure Description

[0026] Figure 1 This is a flowchart of a method for processing periodic physical sequences of composite materials based on architectural symmetry constraints. Figure 2 This is a schematic diagram illustrating the principle of continuous topological manifold mapping and boundary elimination. Detailed Implementation

[0027] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0028] like Figure 1 As shown, this invention provides a method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints, comprising the following steps: S1. Collect the original sequence of composite material layup, map it using topological isovariant embedding rules, extract the initial embedding vector, and obtain the embedding sequence; S2. Complete the embedded sequence; S3. Use the Transformer encoder to extract and process features from the padded embedding sequence to obtain a fixed-length vector. S4. Based on a fixed-length vector, the optimal layering sequence is obtained by using a pre-trained TED-Net model.

[0029] To address the problem that existing technologies directly map periodic angles to one-dimensional Euclidean space, resulting in extremely large distances between physically equivalent parameters such as 1° and 179° in the feature space, this invention aims to provide an input representation that mathematically guarantees the topological continuity of physically equivalent parameters, thereby eliminating the influence of human intervention on the boundary from the source of representation.

[0030] To address the problem that existing technologies rely on massive samples (often requiring tens of thousands of finite metadata records) to approximate the learning of symmetry and periodicity, this invention aims to transform physical priors from data-driven learning to representation and hardware architecture guarantees, thereby reducing conditional entropy to the theoretical lower bound and significantly reducing the training data requirements.

[0031] To address the problem that existing technologies (such as data augmentation and soft loss penalty) can only make the predictions of forward and reverse sequences approximately equal and cannot fundamentally guarantee the equivalence of forward and reverse sequences, this invention requires the forced injection of inversion invariance at the network function level to achieve strict physical consistency at the machine accuracy level and eliminate non-physical predictions.

[0032] To address the problem that existing technologies (PINNs) require precise partial differential equations and are difficult to apply to systems such as composite materials / metamaterials that lack explicit governing equations, this invention injects physical priors through architectural constraints rather than equation constraints, enabling the method to be directly applied to black-box systems.

[0033] To address the problems of existing technologies (such as 6-dimensional Tsai invariants) being in redundant high-dimensional feature spaces, having high computational costs, and not achieving optimal data efficiency, this invention aims to complete the representation with the minimum dimension required to characterize the topology (such as a circular manifold which is only 2-dimensional).

[0034] In this embodiment of the invention, in S1, the elements of the original sequence are mapped to continuous manifold coordinates using the topological isovariant embedding rule, and the initial embedding vector is extracted.

[0035] For those with periodicity and Physical parameters of multisymmetry This invention does not directly input scalars. Instead, the following mapping rules are executed: ; Taking composite materials as an example (period) ,symmetry ), mapped to This rule maps a one-dimensional discontinuous linear homeomorphism to a two-dimensional continuous circular manifold (see [link]). Figure 2 This ensures that physically equivalent angles (such as 0° and 180°) are identical in the feature space, and that the dimension reaches the minimum complete state required by topology, avoiding high-dimensional redundancy (such as traditional 6DTsai invariants) and minimizing conditional entropy from the data source.

[0036] In S2, sequences of different lengths within a batch are padded to the maximum length S, and a mask is generated so that the padded bits do not participate in attention calculation and subsequent aggregation.

[0037] In this embodiment of the invention, continuous manifold coordinates The expression is: ; in, This represents the i-th element in the original sequence. Represents topologically equivariant embedding. It represents the set of real numbers.

[0038] Topologically equivariant embeddings (TEEs) independently map each element in a sequence to coordinates of a continuous manifold of fixed dimensions, the dimensions of which are determined only by the topology of the parametric symmetric group and are independent of the total length L of the sequence.

[0039] In this embodiment of the invention, the initial embedding vector The expression is: ; in, Represents a learnable embedding matrix. This represents a learnable embedding bias vector. express 3D real vector space, Indicates the total length of the sequence. Represents the coordinates of a continuous manifold.

[0040] In this embodiment of the invention, S3 includes the following sub-steps: S31. Superimpose standard sinusoidal position codes onto the padded embedded sequence and input it into the dual-path shared weight sequence encoder; S32. Use a dual-path shared-weight sequence encoder to extract features from the original sequence and the reversed sequence; S33. Element-wise average pooling is performed on the extracted features using a symmetric fusion layer to obtain the context feature sequence. S34. Generate a fixed-length vector based on the context feature sequence.

[0041] Since TED embedding independently maps each physical element to a fixed-dimensional (e.g., 2D) manifold space, and combines a symmetric fusion mechanism to aggregate the sequence length, this invention breaks the limitation of the fixed input dimension of traditional models. Specifically, it is achieved through the structure of independent embedding for each element and average pooling along the sequence length mask.

[0042] In this embodiment of the invention, the characteristics of the original sequence The expression is: ; in, Represents the original sequence. Represents topologically equivariant embedding. Indicates Transformer encoder; Features of reversed sequences The expression is: ; in, Indicates the reverse sequence; Context feature sequence The expression is: .

[0043] This design transforms the physical inversion invariance from "data augmentation or soft loss" into an "architectural-level hard constraint," forcibly guaranteeing it at the model function level. This achieves machine precision level (error) The strict inversion invariance of the ) eliminates the generation of non-physical predictions and provides an absolutely reliable surrogate model for subsequent reverse design.

[0044] In this embodiment of the invention, the features of each element output by the encoder are subjected to masked average pooling along the sequence length dimension and aggregated into a fixed-length vector that is independent of the sequence length.

[0045] Fixed-length vector The expression is: ; in, This represents the feature vector at the i-th position in the context feature sequence. Indicates the total length of the sequence. express A real vector space.

[0046] regardless What value should be taken? The dimension is constant Therefore, a single network model can directly handle physical sequence inputs of arbitrary length (such as 1 to N layers) without modifying its architecture. This mechanism enables the model to learn the underlying mechanical superposition laws regardless of the number of layers, thereby achieving extreme data efficiency across scales (predicting thicker layers with zero samples) and across tasks (predicting different physical properties with few samples).

[0047] In this embodiment of the invention, in S4, the expression for the objective function solved using the pre-trained TED-Net model is: ; in, This represents the forward prediction function of the pre-trained TED-Net. Represents an angle vector. Let the objective function be the one to be minimized. This represents topologically equivariant embeddings.

[0048] This invention transforms reverse design into a constrained optimization problem on a continuous topological manifold space. A pre-trained TED-Net is used as the fitness surrogate model, and a differential evolution algorithm is employed to directly perform population evolution search on the topological manifold. After convergence, truth verification is performed using classical laminate theory (CLT). The specific details are as follows: Optimization problem modeling: Let the angle vector of the L-layer sequence to be designed be θ=(θ_1,...,θ_L), and map it to two-dimensional circular manifold coordinates through topological isovariant embedding.

[0049] Taking maximizing the inflationary effect (a more negative Poisson's ratio is better) as an example, the optimization objective is to minimize the predicted value of the surrogate model. This applies to approximating a specified target attribute. In general, it is advisable to take Because the inversion-invariant fusion layer guarantees... The fitness of each candidate individual is naturally and physically consistent, without the need to evaluate the forward and reverse sequences separately.

[0050] Sobol quasi-Monte Carlo sequence generation An initial individual is then mapped to manifold coordinates via topologically isovariant embedding: .

[0051] The evolutionary search of the population can employ any swarm intelligence / evolutionary optimization algorithm. This embodiment uses the differential evolution algorithm to search for the first... For each individual implement: Mutation: Randomly select three distinct individuals r_1, r_2, r_3, different from p, to generate a mutation vector; since the individuals are located on a continuous circular manifold, after mutation, normalize and project back to the unit circle according to the following formula to ensure that they are still valid topological coordinates. (for scaling factors) ; Crossover: Based on crossover probability (generally) Perform a binary crossover between the mutant and the original individual, ensuring that at least one dimension comes from the mutant: ; Selection: Evaluate fitness using a pre-trained TED-Net agent and retain the better one: ; When the maximum number of generations is reached, or the improvement in optimal fitness over several consecutive generations is less than a threshold. When the iteration stops, output the manifold coordinates corresponding to the best individual. Reversing this to a physical perspective: .

[0052] The optimal layup sequence is then input into classical laminate theory (CLT) to calculate the actual physical properties, eliminating surrogate model bias and obtaining the final verification solution.

[0053] The system corresponding to this invention consists of four core modules connected in sequence, with the data flow as follows: original physical sequence → topological equivariant embedding and preprocessing module → shared weight dual-path feature extraction module → symmetric fusion and attribute prediction module → output physical attributes. During reverse engineering, the prediction module is used as a surrogate model and is cyclically called by the fourth module.

[0054] Topological isovariant embedding and preprocessing module: Maps each element of the original sequence to continuous manifold coordinates according to the topological isovariant embedding rules, and superimposes position encoding to output a manifold coordinate sequence of fixed length dimension.

[0055] Shared-weight dual-path feature extraction module: This module contains a Transformer encoder with shared parameters. It simultaneously encodes the original sequence and its inverse sequence, extracting features from both paths in parallel using the same set of weights. This captures bidirectional physical interaction information while halving the number of parameters compared to a dual-encoder approach.

[0056] The symmetric fusion and attribute prediction module consists of a parameterless symmetric fusion layer (element-wise average pooling) and a multilayer perceptron (MLP) regression head. The fusion layer aggregates the outputs of both paths, forcing complete consistency between the forward and reverse feature representations; the regression head maps the fused global features to target physical attributes (such as Poisson's ratio, stiffness matrix components, etc.).

[0057] The inverse design optimization module based on continuous manifolds uses a pre-trained TED-Net as a surrogate model and combines heuristic / evolutionary or gradient optimization algorithms to iteratively search for the optimal sequence in the continuous topological manifold space, and verifies the truth value by classical laminate theory (CLT).

[0058] Relationship between modules: The first three modules together constitute the forward prediction surrogate model; the fourth module does not contain a neural network, but is an optimizer wrapped outside the first three modules. Each time it generates a candidate sequence, it feeds it back to modules one to three to evaluate the fitness, and reuses the continuous topological manifold constructed by module one as both the feature space and the search space; the inversion invariant hard constraint of module three ensures the physical reliability of the surrogate model.

[0059] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for processing periodic physical sequences of composite materials based on architectural symmetry constraints, characterized in that, Includes the following steps: S1. Collect the original sequence of composite material layup, map it using topological isovariant embedding rules, extract the initial embedding vector, and obtain the embedding sequence; S2. Complete the embedded sequence; S3. Use the Transformer encoder to extract and process features from the padded embedding sequence to obtain a fixed-length vector. S4. Based on a fixed-length vector, the optimal layering sequence is obtained by using a pre-trained TED-Net model.

2. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 1, characterized in that, In S1, the elements of the original sequence are mapped to continuous manifold coordinates using topologically equivariant embedding rules, and the initial embedding vector is extracted.

3. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 2, characterized in that, The continuous manifold coordinates The expression is: ； in, This represents the i-th element in the original sequence. Represents topologically equivariant embedding. It represents the set of real numbers.

4. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 2, characterized in that, The initial embedding vector The expression is: ； in, Represents a learnable embedding matrix. This represents a learnable embedding bias vector. express 3D real vector space, Indicates the total length of the sequence. Represents the coordinates of a continuous manifold.

5. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 1, characterized in that, S3 includes the following sub-steps: S31. Superimpose standard sinusoidal position codes onto the padded embedded sequence and input it into the dual-path shared weight sequence encoder; S32. Use a dual-path shared-weight sequence encoder to extract features from the original sequence and the reversed sequence; S33. Element-wise average pooling is performed on the extracted features using a symmetric fusion layer to obtain the context feature sequence. S34. Generate a fixed-length vector based on the context feature sequence.

6. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 5, characterized in that, The characteristics of the original sequence The expression is: ； in, Represents the original sequence. Represents topologically equivariant embedding. Indicates Transformer encoder; The characteristics of the reverse sequence The expression is: ； in, Indicates the reverse sequence; The context feature sequence The expression is: 。 7. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 5, characterized in that, The fixed-length vector The expression is: ； in, This represents the feature vector at the i-th position in the context feature sequence. Indicates the total length of the sequence. express A real vector space.

8. The method for processing the periodic physical sequence of composite materials based on architectural symmetry constraints according to claim 1, characterized in that, In step S4, the expression for the objective function solved using the pre-trained TED-Net model is: ； in, This represents the forward prediction function of the pre-trained TED-Net. Represents an angle vector. Let the objective function be the one to be minimized. This represents topologically equivariant embeddings.

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