Viscosity prediction method for composite materials based on physical information neural network

Abstract

The application discloses a composite material viscosity prediction method based on a physical information neural network, and belongs to the technical field of the cross of material information science and artificial intelligence. The method obtains the filler volume fraction, the shear rate and the temperature of a target composite material as input parameters, inputs the logarithmic transformation and the standardized processing into a trained physical information neural network model, the model outputs the predicted logarithmic viscosity, and the viscosity prediction result is obtained after the reverse standardization. The model is a fully connected multilayer perceptron, the training process adopts a total loss function containing rheological physical constraints, and at least contains an η0-φ global monotonicity constraint term which constrains the zero shear viscosity to be monotonically non-decreasing with the filler volume fraction. The application converts the rheological physical knowledge into a differentiable software constraint embedded neural network training, significantly improves the extrapolation accuracy of the unseen high filler content working condition under the small sample condition, the prediction result conforms to the rheological physical law, and the model training can obtain the physically consistent prediction result without a large amount of data.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of materials informatics and artificial intelligence, specifically to a method for predicting the viscosity of composite materials based on a physical information neural network, and more particularly to a method that embeds rheological physics knowledge into a neural network loss function to predict and extrapolate the viscosity of polymer composite materials within a parameter space of temperature, shear rate, and filler volume fraction. Background Technology

[0002] Polymer nanocomposites (PNCs) are a class of composite materials with polymers as the matrix and nanoscale fillers for reinforcement. Thanks to the high specific surface area and tunable interfacial interactions of nanofillers, polymer composites exhibit significant improvements in mechanical, thermal, electrical, and barrier properties compared to pure polymers, and have been widely used in aerospace, automotive, flexible electronics, and biomedical fields.

[0003] Among the many performance indicators that determine processability, melt viscosity plays a central role: it directly affects the stability of processing such as casting, extrusion, and injection molding, and determines the orientation and dispersion state of fillers in the final product. Therefore, accurately predicting the changes in viscosity with temperature T, shear rate γ, and filler volume fraction φ has direct scientific and engineering significance for the processing optimization and material design of polymer composites.

[0004] However, the viscosity behavior of polymer composites is far more complex than that of pure polymer melts. Nanofillers induce significant shear thinning, yield stress, and nonlinear viscoelasticity, and viscosity exhibits a strong nonlinear response to filler content, particle morphology, surface functionalization, and polymer-particle interactions. This results in a highly coupled and complex viscosity distribution within the φ-γ-T three-dimensional parameter space.

[0005] Existing viscosity prediction methods employ empirical or semi-empirical constitutive models with limited applicability, failing to cover the broad φ-γ-T parameter space and exhibiting poor portability to new systems. These limitations hinder their ability to accurately characterize the complex viscosity behavior of polymer composites as general-purpose tools. To obtain more reliable viscosity data, researchers have utilized non-equilibrium molecular dynamics simulations. However, while these simulations can physically accurately depict flow processes, their computational costs are enormous, data acquisition is expensive, and dense sampling in the three-dimensional parameter space is difficult, resulting in a severe scarcity of training data for modeling. Under this data scarcity constraint, researchers have introduced purely data-driven machine learning methods to learn the mapping relationship between input and output using limited samples. However, these methods themselves do not contain any physical constraints. Although they can fit shear thinning and filler content dependence well within the training distribution, they cannot guarantee physical consistency outside the training domain. When predicting new operating conditions beyond the calibration range, they often provide unreliable or even non-physical results, exhibiting poor extrapolation and generalization capabilities. While existing physical information neural network methods have explored solutions to fluid dynamics control equations and fitting of constitutive relations for non-Newtonian fluids, their design of physical constraints for viscosity prediction of polymer composites, especially for extrapolation of filler volume fraction, is still insufficient. There is still a lack of systematic solutions for how to replace data with physical knowledge and improve extrapolation capabilities under small sample conditions. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the viscosity of composite materials based on a physical information neural network, so as to solve the above-mentioned problems.

[0007] The technical solution of this invention is: A method for predicting the viscosity of composite materials based on a physical information neural network includes the following steps: The filler volume fraction φ, shear rate γ, and temperature T of the target polymer composite material are obtained as input parameters. Taking the logarithm of the shear rate γ 10 γ, representing the filler volume fraction φ, log 10 γ and temperature T are standardized using the mean and standard deviation of the training set to obtain standardized input features; The standardized input features are input into a pre-trained physical information neural network model, which is a fully connected multilayer perceptron used to map the standardized input features to predicted log viscosity. The physical information neural network model is pre-trained with a total loss function that includes rheological physical constraints, and the total loss function includes at least an η0-φ global monotonicity constraint term that constrains zero shear viscosity to remain monotonically constant with the filler volume fraction. The physical information neural network model outputs the predicted log viscosity. The predicted logarithmic viscosity is denormalized using the mean and standard deviation of the training set to obtain and output the viscosity prediction result of the polymer composite material.

[0008] By transforming rheological physics knowledge into manageable constraints, the extrapolation accuracy for operating conditions with unseen high filler content is significantly improved under small sample conditions. The prediction results conform to the laws of rheology and physics, and have the advantages of high data efficiency, physical consistency and interpretability.

[0009] Furthermore, the training method for the physical information neural network model includes the following steps: With triples (φ, log 10 γ, T) as input features, with log viscosity log 10 η is used as the output target, and the input and output are standardized separately; A total loss function is constructed, which is the sum of the mean squared error loss term, the relative viscosity error regularization term weighted by the relative viscosity error coefficient, and the global monotonicity constraint term η0-φ and the shear thinning local constraint term whose weights are controlled by the preheating scheduling function. The global monotonicity constraint term η0-φ and the shear thinning local constraint term are weighted by the monotonicity constraint weight and the shear thinning constraint weight, respectively. The preheating scheduling function takes a value of zero when the training progress does not exceed the preheating ratio, and increases linearly from zero to one after the training progress exceeds the preheating ratio. The fully connected multilayer perceptron is trained on the training set using the total loss function, and the optimal model is retained based on the validation set using an early stopping strategy.

[0010] The total loss function consists of four terms: a data loss term, a relative viscosity error regularization term, an η0-φ global monotonicity constraint term, and a shear thinning local constraint term. These provide complementary supervision signals, among which the η0-φ monotonicity constraint term is the most critical constraint for extrapolating the unseen φ condition. Preheating scheduling suppresses physical constraints in the early stages of training and then linearly increases their weights from zero to one, preventing physical losses from disrupting convergence in the early stages of data fitting.

[0011] Furthermore, the fully connected multilayer perceptron includes one or more hidden layers. After each hidden layer, a ReLU activation function is applied and a dropout layer is added. By introducing the dropout layer, overfitting is alleviated, so that the model can still maintain stable generalization performance under small sample conditions.

[0012] Furthermore, the method for constructing the η0-φ global monotonicity constraint term includes the following steps: For each unique value of φ in a training batch, take the logarithm of its corresponding sample. 10The mean of the predicted log viscosity at the lowest quantile of γ is used as the zero-shear viscosity surrogate value under that φ. The φ values ​​are arranged in ascending order, and the difference between adjacent φ values ​​that violate the monotonically non-decreasing zero-shear viscosity surrogate value is penalized with a linear rectification function. The average of the penalty results is used to obtain the global monotonicity constraint term η0-φ.

[0013] The η0-φ global monotonicity constraint term anchors the network globally to the physics of filler content dependence, and is the most critical constraint for extrapolating to conditions where φ is not observed. Physically, this constraint corresponds to the following: as the filler volume fraction increases, the hydrodynamic interaction between particles strengthens, the particle network gradually forms, and the polymer chain conformation becomes more constrained, all of which jointly drive a monotonically increasing zero-shear viscosity.

[0014] Furthermore, the method for constructing the shear-thinning local constraint term includes the following steps: for each unique combination of filler volume fraction and temperature in a training batch, the samples within the combination are divided according to log... 10 Arranged in ascending order of γ, the predicted log viscosity varies with log. 10 The difference in the increase of γ is penalized by a linear rectified function. The penalty value of all its adjacent sample pairs in each combination is averaged, that is, divided by the number of samples in the combination minus one. The average penalty result of each combination is then averaged to obtain the shear thinning local constraint term.

[0015] The shear-thinning local constraint term locally forces a physically consistent shear rate ordering within each (φ, T) group. Physically, the shear-thinning local constraint term corresponds to the following: at a fixed composition and temperature, an increase in shear rate causes the polymer chains to untangle and orient along the flow direction, reducing intermolecular friction, and thus the viscosity decreases monotonically with the shear rate.

[0016] Furthermore, the relative viscosity error regularization term is calculated in the form of the mean square of the relative deviation between the predicted viscosity and the true viscosity. Since viscosity spans multiple orders of magnitude in the parameter space, the mean square error calculated in the normalized output space implicitly assigns a larger absolute gradient to high-viscosity samples; the relative viscosity error regularization term provides balanced supervision in the physical viscosity space, ensuring that low-viscosity (high shear rate) samples receive appropriate weights during the optimization process, consistent with the mean absolute percentage error objective.

[0017] Furthermore, the global monotonicity constraint term η0-φ is activated when the number of different φ values ​​within the batch is not less than 3; the local shear thinning constraint term is activated when the number of samples within the combination is not less than 3. By setting activation conditions, the constraints are ensured to take effect only when statistical stability is sufficient, avoiding constraint noise caused by insufficient sample size.

[0018] Furthermore, it also includes data partitioning, which employs a hybrid partitioning strategy and includes the following steps: The operating condition with the highest filler volume fraction is retained as an unseen test set. A portion of the remaining samples is randomly selected as the seen test set, and the remaining samples are used as the training set. A further portion of the training set is then used as the validation set. This hybrid partitioning strategy strictly excludes the operating condition with the highest filler content from the training, forming a strict external benchmark for evaluating the model's ability to extrapolate to higher filler loads. The seen test set evaluates interpolation ability, while the unseen test set evaluates generalization and extrapolation ability. A model with strong physical generalization ability should maintain similar accuracy on both test sets.

[0019] Furthermore, since the loss weight parameters span multiple orders of magnitude and their optimal values ​​are nontrivially coupled, manual grid search is impractical. Therefore, Bayesian optimization is employed to search for the relative viscosity error coefficient, monotonicity constraint weights, shear thinning constraint weights, and preheating ratio. This Bayesian optimization uses the root mean square error of the log-viscosity on the validation set as the objective and does not use any test set information during the search process. Bayesian optimization can efficiently identify the optimal hyperparameter combination within a finite number of trials, and the absence of test set information throughout the process ensures the objectivity of the evaluation results.

[0020] A composite material viscosity prediction system based on a physical information neural network includes: The parameter acquisition module obtains the filler volume fraction φ, shear rate γ, and temperature T of the target polymer composite material as input parameters. The preprocessing module takes the logarithm of the shear rate γ. 10 γ, representing the filler volume fraction φ, log 10 γ and temperature T are standardized using the mean and standard deviation of the training set to obtain standardized input features; The prediction module inputs the standardized input features into a trained physical information neural network model, which is a fully connected multilayer perceptron used to map the standardized input features to predicted log viscosity; it then obtains the predicted log viscosity output by the physical information neural network model. The physical information neural network model is pre-trained with a total loss function that includes rheological physical constraints, and the total loss function includes at least an η0-φ global monotonicity constraint term that constrains zero shear viscosity to remain monotonically constant with the filler volume fraction. The output module performs inverse standardization on the predicted logarithmic viscosity using the mean and standard deviation of the training set, and then outputs the viscosity prediction result of the polymer composite material.

[0021] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described above.

[0022] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0023] Compared with the prior art, the beneficial effects of the present invention are: This invention transforms established physical laws in polymer composite rheology—namely, the monotonically increasing zero-shear viscosity η0 with filler volume fraction φ and the shear-thinning law (viscosity monotonically decreasing with shear rate at fixed composition and temperature)—into differentiable soft constraints and embeds them into a neural network loss function. Simultaneously, a relative viscosity error regularization term is introduced to balance the supervision signal across samples over a wide dynamic range. This, along with limited NEMD data, drives network training. Preheating scheduling suppresses physical constraints in the early training phase and gradually increases their weights in the later phase to avoid disrupting early data fitting. This allows for the training of a physically consistent, interpretable, and highly extrapolation-capable viscosity prediction model under small sample conditions. Users only need to input the filler volume fraction, shear rate, and temperature of the target polymer composite material. After logarithmic transformation and standardization, the data is input into the trained model to quickly obtain physically reasonable viscosity prediction results. This effectively overcomes the technical problems of existing technologies, such as data scarcity, complex variable coupling, poor extrapolation and generalization capabilities, and a lack of physical consistency and interpretability. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the overall technical route of the present invention.

[0025] Figure 2 This is a flowchart of the method of the present invention.

[0026] Figure 3 This is a schematic diagram illustrating the structure and loss function of the physical information neural network of the present invention.

[0027] Figure 4 This is a schematic diagram of the Hybrid Split data partitioning strategy of the present invention. Detailed Implementation

[0028] The following is combined with Figures 1 to 4 The specific embodiments of the present invention will be described in detail below.

[0029] Example like Figure 1 and Figure 2 As shown, the construction and training of the physical information neural network model in this embodiment includes the following steps: Nonequilibrium molecular dynamics simulations were used to generate viscosity data for polymer composites under different combinations of temperature, shear rate, and filler volume fraction. Nonequilibrium molecular dynamics introduces external perturbations into classical molecular dynamics to directly explore nonequilibrium states related to flow processing. The simulations employed Lees-Edwards boundary conditions and the SLLOD equations of motion to describe the dynamics of shear flow, applying shear deformation at a constant shear rate γ in the xy-plane, with the shear rate range, for example, taken from γ=10. −5 Up to γ=1; temperature and pressure are controlled by a Nosé–Hoover thermostat and a pressure regulator, respectively, to ensure thermodynamic equilibrium. Viscosity η is determined by equation (1) from the steady-state shear stress σ. xy The ratio to the shear rate γ is calculated and recorded in steady state.

[0030] Viscosity η is calculated based on the ratio of shear stress to shear rate: (1) In one embodiment, a total of 358 data points were used after preprocessing, covering nine different filler content levels with filler volume fraction φ∈[0, 0.461], temperature T∈[0.4, 2.5], and logarithmic shear rate log. 10 γ∈[−5,0].

[0031] With triples (φ, log 10 γ, T) as input features, with log viscosity log 10 η is used as the output target, and both the input and output are standardized. To facilitate convergence, all input features and the output target are standardized using StandardScaler, i.e., the mean is subtracted and the standard deviation is divided. The standardization uses the mean and standard deviation of the training set. During the prediction phase, the network output is de-standardized to restore the log-viscosity. The de-standardization uses the mean and standard deviation of the training set.

[0032] To strictly distinguish between interpolation and extrapolation, this embodiment adopts a hybrid partitioning strategy with explicit extrapolation semantics, such as... Figure 4 As shown. Since the viscosity of the polymer composite material exhibits a strong nonlinear dependence on the filler volume fraction, φ is chosen as the extrapolation dimension.

[0033] Specifically, the operating condition with the highest filler volume fraction (e.g., φ=0.461, corresponding to 58 data points) is retained as an unseen test set. These samples are never used in training and constitute a strict distributional extrapolation baseline. A portion of the remaining samples is randomly selected as the seen test set to evaluate the model's prediction accuracy in the same parameter domain as the training data. The remaining samples are used as the training set, and a portion of the training set is further divided as the validation set. This results in a training set of 240 samples, a seen test set of 60 samples, and an unseen test set of 58 samples, for a total of 358 samples.

[0034] The observed test set evaluates interpolation capability: samples fall within the parameter space covered by training but do not participate in optimization, thus providing an unbiased assessment of prediction accuracy within the training domain; the unseen test set evaluates generalization and extrapolation capability: the entire highest filler content scenario never appears in training, constituting a strict external benchmark for evaluating the model's ability to extrapolate to higher filler loads. Models with strong physical generalization capability should maintain similar accuracy on both test sets, while purely data-driven models often exhibit significant performance degradation on the unseen test set.

[0035] like Figure 3 As shown, the physical information neural network of this embodiment continuously maps the three-dimensional parameter space to scalar logarithmic viscosity according to equation (2): (2) The network employs a fully connected multilayer perceptron, preferably comprising three hidden layers with 256 neurons per layer. A ReLU activation function is applied after each hidden layer, and a dropout rate of 0.1 is added after each layer to alleviate overfitting. It should be noted that the number of hidden layers and neurons can be configured according to the data scale; for example, each layer can also have 128 neurons, which does not constitute a limitation of the invention.

[0036] The total loss function in this embodiment consists of four terms according to Equation (6), where the data loss term is the mean square error of the standardized output space, the relative viscosity error regularization term is calculated according to Equation (5), the global monotonicity constraint term η0-φ is calculated according to Equation (3), and the shear thinning local constraint term is calculated according to Equation (4).

[0037] The total loss function consists of four terms: (6) Where L data The mean square error loss term for the standardized output space; α is the relative viscosity error coefficient; λ mono and λ stThese are the monotonicity constraint weights and shear thinning constraint weights, respectively; ω(t) is the warm-up scheduling function, used to suppress physical constraints in the early stages of training, and then linearly increase their weights from 0 to 1 to avoid physical loss disrupting convergence in the early stages of data fitting. The four terms provide complementary supervision signals: the data loss term drives the overall regression accuracy; the relative viscosity error regularization term balances the contribution of each sample over a wide dynamic range; the η0-φ monotonicity constraint term globally anchors the network to filler content-dependent physics, and is the most critical constraint for extrapolating to conditions without φ; the shear thinning constraint term locally forces a physically consistent shear rate ranking within each (φ, T) group.

[0038] The aforementioned physical constraints are superimposed on the standard data loss in the form of soft constraints. The main network is still a conventional fully connected multilayer perceptron. There is no need to design a special network structure for the physical constraints, which makes it easy to combine with the existing training framework and extend to viscosity prediction of other material systems.

[0039] The η0-φ global monotonicity constraint term is constructed as follows: for each unique φ value in a training batch, take the logarithm of the corresponding sample. 10 The mean of the predicted log viscosity at the lowest quantile (e.g., the lowest 10th quantile) of γ is used as the surrogate value η0(φ) for zero shear viscosity at that φ; φ within the batch is sorted in ascending order, and any adjacent differences that violate monotonically non-decreasing are penalized using a linear rectified (ReLU) function: (3) Where M is the number of different φ values ​​within the batch; this constraint is activated only when M≥3 to ensure statistical stability. Physically, this constraint corresponds to the following: as the filler volume fraction increases, the hydrodynamic interaction between particles strengthens, the particle network gradually forms, and the polymer chain conformation becomes more restricted, all of which jointly drive the monotonically increasing zero-shear viscosity.

[0040] The shear-thinning local constraint term is constructed as follows: for each unique combination of filler volume fraction and temperature in a training batch, the samples within that combination are processed according to log... 10 Arranged in ascending order of γ, the predicted log viscosity varies with log. 10 The upward trend of γ is penalized using a linear rectified function: (4) Where G is the number of (φ, T) combinations in this batch, B g For samples within group g (in logarithmic order) 10 The set of indices after γ is sorted in ascending order, |B g | represents the number of samples in the set, yi (g) For group g, log 10The i-th predicted log viscosity after ascending order of γ; when |B g This constraint is activated only when |≥3. Physically, this constraint corresponds to the following: at a fixed composition and temperature, an increase in shear rate causes the polymer chains to untangle and orient along the flow direction, reducing intermolecular friction, thus causing the viscosity to decrease monotonically with the shear rate, i.e., ∂log 10 η / ∂log 10 γ≤0.

[0041] Since viscosity spans multiple orders of magnitude in the parameter space, the mean squared error calculated in the normalized output space implicitly assigns a larger absolute gradient to high-viscosity samples; therefore, a relative viscosity error regularization term is introduced to provide balanced supervision in the physical viscosity space: (5) Where ŷ and y are the predicted and true logarithmic viscosities, respectively, and the viscosity is given by η = 10^y. The relative viscosity error regularization term is calculated in the mean square form of the relative deviation between the predicted and true viscosities. This term penalizes the relative deviation in the physical viscosity space in a differentiable manner, consistent with the mean absolute percentage error objective, ensuring that low-viscosity (high shear rate) samples receive appropriate weights during the optimization process.

[0042] One implementation of the warm-up scheduling function ω(t) is as follows: Let the training progress be progress (the ratio of the current training round to the total number of rounds), and the warm-up ratio be f. warmup When progress ≤ f warmup When ω(t) = 0, that is, no physical constraints are applied in the early stages of training; when progress > f warmup At that time, ω(t)=min(1,(progress−f) warmup ) / (1−f warmup The physical constraint weights are linearly increased from 0 to 1. This scheduling allows the network to first learn the global data manifold before applying physical regularization, thus avoiding physical loss that could ruin the early data fit.

[0043] The performance of the total loss function depends critically on four scalar hyperparameters: the relative viscosity error coefficient α, the monotonicity constraint weight λ, and so on. mono Shear thinning constraint weight λ st and preheating ratio f warmup Since these parameters span multiple orders of magnitude and their optimal values ​​are non-trivially coupled, manual grid search is impractical. Therefore, this embodiment employs the Optuna framework combined with a tree-structured Parzen estimator (TPE) sampler for Bayesian optimization.

[0044] The objective function evaluates a single training iteration on the validation set (randomly partitioned from the training set by 10%) and returns the optimal root mean square error of the validation set (log-viscosity space) achieved before early stopping; no test set information is used during the search process. The search space and the identified optimal value are shown below:

[0045] λ st Logarithmically uniform distribution, range [10^−4,1], optimal value 0.0254; λ mono Logarithmically uniform distribution, range [10^−4,1], optimal value 0.0680; α: Logarithmically uniform distribution, range [0.01, 0.1], optimal value 0.0110; f warmup Uniform distribution, range [0, 0.5], optimal value 0.485.

[0046] The three loss weight parameters are logarithmically uniformly distributed because their effective range spans three to four orders of magnitude; the preheating ratio is uniformly distributed because it is a bounded fraction without natural scale separation. The code includes a weight validity check; if α + λ st +λ mono A hyperparameter value ≥1.0 will result in the experiment being pruned and discarded. Therefore, the search upper limit is manually set to 0.45 to avoid invalid trial calculations. After the search is completed, the final model is retrained on the complete training set using the optimal hyperparameters (the same validation subset is retained for early stopping), thus ensuring that test data does not participate in hyperparameter selection at any stage.

[0047] Preferably, the AdamW optimizer is used for training, with a learning rate of 2×10^−4, weight decay of 5×10^−5, and batch size of 128. The training is conducted for a maximum of 3000 epochs, and an early stopping strategy is employed based on the root mean square error of the log viscosity of the validation set (e.g., evaluation every 10 epochs, with a patience value of 800 evaluation periods). The checkpoint with the optimal validation metric is retained as the final model. The above training hyperparameters are exemplary values ​​and can be adjusted without departing from the concept of this embodiment.

[0048] Using the trained model, viscosity predictions are performed on the seen test set, the unseen test set, and the overall test set, and evaluated using the following metrics: Root mean square error in logarithmic viscosity space:

[0049] (7) (8) (9) Where y = log 10η is the true logarithmic viscosity, ŷ is the predicted value, and ȳ is the mean of all true values. The mean absolute percentage error is calculated in the physical viscosity space (η=10^y) and used as the main evaluation index because it directly reflects the prediction accuracy of physically relevant quantities.

[0050] In contrast, four machine learning baselines were trained on the same data partition: XGBoost (learning rate 0.2, maximum depth 2, number of estimators 1000), support vector regression (penalty coefficient C=50, using radial basis kernel), decision tree (maximum depth 12), and linear regression.

[0051] In one embodiment, the physical information neural network of this embodiment achieves a coefficient of determination of 0.9908 and a mean absolute percentage error (MAE) of 10.91% on the overall test set (a total of 118 samples, both seen and unseen), outperforming all comparative methods. On the unseen test set consisting only of samples with the highest filler content φ=0.461, the MAE of this embodiment is 12.11%, a reduction of approximately 30.7% compared to XGBoost's 17.48% and a reduction of approximately 36.7% compared to Support Vector Regression's 19.12%. Meanwhile, the MAE of this embodiment on the seen test set is 9.75%, with a small and stable difference from the 12.11% on the unseen test set, indicating that its accuracy comes from true generalization rather than data memorization.

[0052] Furthermore, sparsity experiments were conducted in this embodiment: The highest filler content φ=0.461 was fixed as the unseen test set. While keeping other hyperparameters constant, the proportion of training data was gradually increased from 25% to 100%, resulting in different training scales of approximately 60, 96, 120, 144, 168, 192, and 240 samples. The results show that the determination coefficient of this embodiment on the unseen test set remains at a high level (e.g., greater than 0.97) across all training scales, even in the extreme case of only 60 training samples; while XGBoost and decision trees experience a sharp performance drop when data is scarce. The determination coefficient advantage of this embodiment relative to XGBoost reaches approximately 0.149 with only 60 training samples, and gradually decreases as the training data increases, directly demonstrating the data substitution effect of physical constraints.

[0053] Ablation experiments further demonstrate that the contribution of the global monotonicity constraint term η0-φ is significantly greater than that of the shear-thinning local constraint term, revealing a transferable constraint design principle: the effectiveness of the constraint increases with its coverage and information density in the input space.

[0054] Based on the above-mentioned method for constructing and training a physical information neural network model, this embodiment also provides a polymer composite material viscosity prediction system, which can be used to deploy the trained model in actual prediction scenarios.

[0055] A composite material viscosity prediction system based on a physical information neural network includes: The parameter acquisition module obtains the filler volume fraction φ, shear rate γ, and temperature T of the target polymer composite material as input parameters. The preprocessing module takes the logarithm of the shear rate γ. 10 γ, representing the filler volume fraction φ, log 10 γ and temperature T are standardized using the mean and standard deviation of the training set to obtain standardized input features; The prediction module inputs the standardized input features into a trained physical information neural network model, which is a fully connected multilayer perceptron used to map the standardized input features to predicted log viscosity; it then obtains the predicted log viscosity output by the physical information neural network model. The physical information neural network model is pre-trained with a total loss function that includes rheological physical constraints, and the total loss function includes at least an η0-φ global monotonicity constraint term that constrains zero shear viscosity to remain monotonically constant with the filler volume fraction. The output module performs inverse standardization on the predicted logarithmic viscosity using the mean and standard deviation of the training set, and then outputs the viscosity prediction result of the polymer composite material.

[0056] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described above.

[0057] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0058] The method for predicting the viscosity of polymer composites using the trained physical information neural network model includes the following steps: The filler volume fraction φ, shear rate γ, and temperature T of the target polymer composite material are obtained as input parameters. Taking the logarithm of the shear rate γ 10 γ, representing the filler volume fraction φ, log 10 γ and temperature T are standardized using the mean and standard deviation of the training set to obtain standardized input features; The standardized input features are input into a pre-trained physical information neural network model, which is a fully connected multilayer perceptron used to map the standardized input features to predicted log viscosity. The physical information neural network model is pre-trained with a total loss function that includes rheological physical constraints, and the total loss function includes at least an η0-φ global monotonicity constraint term that constrains zero shear viscosity to remain monotonically constant with the filler volume fraction. The physical information neural network model outputs the predicted log viscosity. The predicted logarithmic viscosity is denormalized using the mean and standard deviation of the training set to obtain and output the viscosity prediction result of the polymer composite material.

[0059] By transforming rheological physics knowledge into manageable constraints, the extrapolation accuracy for operating conditions with unseen high filler content is significantly improved under small sample conditions. The prediction results conform to the laws of rheology and physics, and have the advantages of high data efficiency, physical consistency and interpretability.

[0060] For example, when it is necessary to predict the viscosity of a polymer composite material under given processing conditions, the user only needs to input the filler volume fraction, processing temperature and shear rate into the computer system. The system will automatically execute the above steps and quickly obtain the predicted viscosity value of the material under the working conditions without having to repeat NEMD simulation or rheological experiments.

[0061] The above-disclosed embodiments are merely preferred embodiments of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A method for predicting the viscosity of composite materials based on a physical information neural network, characterized in that, Includes the following steps: The filler volume fraction φ, shear rate γ, and temperature T of the target polymer composite material are obtained as input parameters. Taking the logarithm of the shear rate γ 10 γ, representing the filler volume fraction φ, log 10 γ and temperature T are standardized using the mean and standard deviation of the training set to obtain standardized input features; The standardized input features are input into a pre-trained physical information neural network model, which is a fully connected multilayer perceptron used to map the standardized input features to predicted log viscosity. The physical information neural network model is pre-trained with a total loss function that includes rheological physical constraints, and the total loss function includes at least an η0-φ global monotonicity constraint term that constrains zero shear viscosity to remain monotonically constant with the filler volume fraction. The physical information neural network model outputs the predicted log viscosity. The predicted logarithmic viscosity is denormalized using the mean and standard deviation of the training set to obtain and output the viscosity prediction result of the polymer composite material.

2. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 1, characterized in that, The training method for the physical information neural network model includes the following steps: With triples (φ, log 10 γ, T) as input features, with log viscosity log 10 η is used as the output target, and the input and output are standardized separately; A total loss function is constructed, which is the sum of the mean squared error loss term, the relative viscosity error regularization term weighted by the relative viscosity error coefficient, and the global monotonicity constraint term η0-φ and the shear thinning local constraint term whose weights are controlled by the preheating scheduling function. The global monotonicity constraint term η0-φ and the shear thinning local constraint term are weighted by the monotonicity constraint weight and the shear thinning constraint weight, respectively. The preheating scheduling function takes a value of zero when the training progress does not exceed the preheating ratio, and increases linearly from zero to one after the training progress exceeds the preheating ratio. The fully connected multilayer perceptron is trained on the training set using the total loss function, and the optimal model is retained based on the validation set using an early stopping strategy.

3. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 1, characterized in that, The fully connected multilayer perceptron includes one or more hidden layers, after which a ReLU activation function is applied and a dropout layer is added.

4. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 2, characterized in that, The method for constructing the η0-φ global monotonicity constraint term includes the following steps: For each unique value of φ in a training batch, take the logarithm of its corresponding sample. 10 The mean of the predicted log viscosity at the lowest quantile of γ is used as the zero-shear viscosity surrogate value under that φ. The φ values ​​are arranged in ascending order, and the difference between adjacent φ values ​​that violate the monotonically non-decreasing zero-shear viscosity surrogate value is penalized with a linear rectification function. The average of the penalty results is used to obtain the global monotonicity constraint term η0-φ.

5. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 2, characterized in that, The method for constructing the shear-thinning local constraint term includes the following steps: for each unique combination of filler volume fraction and temperature in a training batch, the samples within the combination are divided according to log... 10 Arranged in ascending order of γ, the predicted log viscosity varies with log. 10 The difference in γ as it increases is penalized using a linear rectified function. The penalty values ​​of all adjacent sample pairs within each combination are averaged, and then the average penalty results of each combination are averaged to obtain the shear thinning local constraint term.

6. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 2, characterized in that, The relative viscosity error regularization term is calculated in the mean square form of the relative deviation between the predicted viscosity and the true viscosity.

7. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 2, characterized in that, The global monotonicity constraint term η0-φ is activated when the number of different φ values ​​in the batch is not less than 3; the local shear thinning constraint term is activated when the number of samples in the combination is not less than 3.

8. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 1, characterized in that, It also includes data partitioning, which employs a hybrid partitioning strategy and includes the following steps: The operating condition with the highest filler volume fraction is retained as the unseen test set. A portion of the remaining samples is randomly selected as the seen test set, and the remaining samples are used as the training set. A portion of the training set is then divided as the validation set.

9. The method for predicting the viscosity of composite materials based on a physical information neural network according to claim 2, characterized in that, It also includes: using Bayesian optimization to search for the relative viscosity error coefficient, monotonicity constraint weight, shear thinning constraint weight, and preheating ratio, wherein the Bayesian optimization uses the root mean square error of log viscosity on the validation set as the objective and does not use any test set information during the search process.

10. A composite material viscosity prediction system based on a physical information neural network, characterized in that, include: The parameter acquisition module obtains the filler volume fraction φ, shear rate γ, and temperature T of the target polymer composite material as input parameters. The preprocessing module takes the logarithm of the shear rate γ. 10 γ, representing the filler volume fraction φ, log 10 γ and temperature T are standardized using the mean and standard deviation of the training set to obtain standardized input features; The prediction module inputs the standardized input features into a trained physical information neural network model, which is a fully connected multilayer perceptron used to map the standardized input features to predicted log viscosity; it then obtains the predicted log viscosity output by the physical information neural network model. The physical information neural network model is pre-trained with a total loss function that includes rheological physical constraints, and the total loss function includes at least an η0-φ global monotonicity constraint term that constrains zero shear viscosity to remain monotonically constant with the filler volume fraction. The output module performs inverse standardization on the predicted logarithmic viscosity using the mean and standard deviation of the training set, and then outputs the viscosity prediction result of the polymer composite material.

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