Accelerated calculation method for combustion chemical kinetics process based on characteristic linear modulation

Abstract

The application particularly relates to a combustion chemical kinetics process acceleration calculation method based on characteristic linear modulation, which comprises the following steps: S1, obtaining complete trajectory data of a thermochemical state vector evolving over time; S2, extracting a thermochemical state vector at a current time and a thermochemical state vector after a time step, to form a plurality of training sample pairs; S3, based on the dimension of the thermochemical state vector in the normalized training sample pair, constructing a deep operator network model based on characteristic linear modulation; S4, training the deep operator network model through the normalized training sample pair; and S5, in an online calculation stage of combustion kinetics numerical simulation, replacing direct integral solution of a chemical reaction mechanism with the thermochemical state vector after the time step predicted by the trained deep operator network model, to realize acceleration calculation of the combustion kinetics process. The application can improve the calculation efficiency and wide-condition generalization prediction capability of combustion kinetics numerical simulation.

Description

Technical Field

[0001] This invention relates to the field of combustion numerical simulation and machine learning, specifically to a method for accelerating the computation of combustion chemical kinetics based on feature linear modulation. Background Technology

[0002] Combustion involves strong multi-physics coupling of flow, heat and mass transfer, and complex chemical reactions. High-fidelity numerical simulation of combustion processes based on detailed kinetic mechanisms is a key foundation for the design optimization and performance evaluation of efficient and clean combustion systems. However, the detailed kinetic mechanisms of real hydrocarbon fuels typically encompass hundreds or even thousands of components and their corresponding elementary reactions, with characteristic timescales for each component spanning a wide range of orders of magnitude. This results in extremely rigid sets of ordinary differential equations describing the combustion reaction flow process, with combustion kinetic simulation accounting for approximately 95% of the total time consumption. Therefore, significantly reducing the computational cost of combustion kinetic processes has become an urgent need in this field.

[0003] Currently, combustion dynamics acceleration algorithms are mainly divided into three categories: mechanism simplification, tabulation techniques, and AI-based acceleration algorithms. First, mechanism simplification involves eliminating intermediate components and elementary reactions that contribute little to the target macroscopic combustion characteristics (such as laminar flame velocity and ignition delay time) to construct a framework or simplified alternative mechanism, thereby reducing the dimensionality and rigidity of the ordinary differential equation system. Although this method can maintain the integrity of key reaction paths to some extent, over-simplification often leads to significant accuracy loss, and the simplified mechanism still requires implicit numerical iteration to solve rigid equations, making the computational speedup often insufficient for large-scale engineering simulations. Second, tabulation techniques avoid direct online integration by mapping the chemical reaction state space to a structured lookup table. However, the inherent contradiction between storage overhead and interpolation accuracy limits its applicability across a wide range of operating conditions.

[0004] The rapid development of artificial intelligence technology has provided new ideas for solving the aforementioned bottlenecks. These mainly include the following categories: Clustering and Partitioning Combined with Local Artificial Neural Networks (ANNs): This method divides the high-dimensional thermochemical state space into several sub-regions (clustering / partitioning), and trains a specialized local ANN model within each sub-region, which alleviates the difficulty of fitting the strongly nonlinear chemical space to some extent; however, this type of method often aims at predicting source terms or states at discrete time steps, making it difficult to strictly guarantee the numerical stability of long-term integrals. Physical Information Neural Networks (PINNs): This method embeds the residuals of the control equations into the loss function to constrain the network output to satisfy basic physical laws. Although PINNs have shown unique advantages in the field of combustion, their training stability and convergence still face significant challenges when dealing with complex reaction systems with high dimensions, strong rigidity, and multiple time scales. Combustion Dynamics Acceleration Algorithms Based on Neural Operators: This method learns the nonlinear operator mapping from the input function to the output function, thereby achieving rapid solutions for a class of problems rather than a single problem. However, it still faces the following key limitations: the backbone network's time encoding is fixed, making it unable to adaptively characterize time scale separation; and insufficient coupling between the input function and the time coordinate. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, the technical problem to be solved by this invention is: how to provide an accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation, which can extract high-density state transition sample pairs from the complete evolution trajectory through a sliding window sampling strategy, construct a deep operator network based on characteristic linear modulation to adaptively modulate time encoding and fuse operating parameters, and combine rigid numerical integral solutions that completely replace the chemical reaction mechanism through online forward inference to achieve a leapfrog acceleration of the combustion reaction process calculation, thereby improving the computational efficiency and wide-condition generalization prediction capability of combustion kinetic numerical simulation, as well as the numerical stability and state prediction accuracy of long-term recursive simulation.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] Accelerated computational methods for combustion chemical kinetics based on characteristic linear modulation include:

[0008] S1: Obtain complete trajectory data of the thermochemical state vector evolution over time;

[0009] S2: Using a sliding window strategy, extract the current thermochemical state vector and the thermochemical state vector after a time step from the complete evolution trajectory data of the thermochemical state vector over time, form several training sample pairs, and standardize each training sample pair.

[0010] S3: Based on the dimension of the thermochemical state vector in the standardized training sample pairs, construct a deep operator network model based on feature linear modulation;

[0011] S4: Train the deep operator network model using standardized training samples;

[0012] S5: In the online calculation stage of combustion dynamics numerical simulation, the thermochemical state vector, time step, and operating parameters at the current moment are input into the trained deep operator network model. After forward inference, the predicted thermochemical state vector after the time step is output, which replaces the direct integral solution of the chemical reaction mechanism and realizes accelerated calculation of the combustion dynamics process.

[0013] Preferably, in step S1, the thermochemical state vector includes temperature and the mass fraction of each component.

[0014] Preferably, in step S2, the standardization of the training sample pairs includes a fifth-order transformation and normalization.

[0015] Preferably, the initial working condition data corresponding to the complete trajectory data is obtained, and a corresponding working condition label is generated for each training sample pair.

[0016] Preferably, in step S3, the deep operator network model based on feature linear modulation includes:

[0017] Branching network, used to convert the current thermochemical state vector As input Layer-by-layer transformation of the hidden layers, using the hidden features of the Lth hidden layer as branch encoding. and will the The hidden features of the hidden layers are fed into the FiLM generator;

[0018] FiLM generator, used to generate the branch network's first branch. The hidden feature maps of the hidden layers are converted into modulation parameter vectors. And based on the total number of hidden layers in the backbone network modulation parameter vector Average score The groups correspond to the scaling and bias parameters of each hidden layer in the backbone network, respectively.

[0019] Displacement network, used to convert the thermochemical state vector at the current moment As input, generate displacement compensation amount;

[0020] The backbone network is used to take the logarithmic time step, after compensation by displacement compensation, as input. The layer-by-layer transformation of the hidden layer, and the 1st layer The hidden features of the hidden layers are used as the output of the dynamically modulated backbone network. In each hidden layer, the input features are first linearly transformed, and then the scaling and bias parameters corresponding to the hidden layer are used to perform FiLM modulation on the linearly transformed features. Finally, the output features of the hidden layer are obtained through nonlinear activation, so that the network can adaptively adjust the temporal encoding according to the input state.

[0021] A parameter network is used to convert the thermochemical state vector at the current moment. The corresponding working condition label code is the same as the branch code. Working condition parameter encoding with the same dimension ;

[0022] The operator product and state prediction module is used to convert branch codes. Operating Parameter Coding With backbone network output After fusion, a piecewise summation strategy is used to map the data to the state space, resulting in a thermochemical state vector after a time step.

[0023] Preferably, in step S3, the FiLM generator generates a modulation parameter vector. The calculation formula is:

[0024] ;

[0025] ;

[0026] In the formula: For the first linear layer through The output features after activation for Activation function For the branch network Hidden features of hidden layers , These are the weight matrix and bias vector of the first linear layer, respectively. , Let these be the weight matrix and bias vector of the second linear layer.

[0027] Preferably, in step S3, the FiLM generator modulates the modulation parameter vector. Average score The formula for calculating the group is:

[0028] ;

[0029] ;

[0030] In the formula: , These are the corresponding backbone network numbers. The scaling and bias parameters of the hidden layer. , The total number of hidden layers in the backbone network. This refers to the hidden layer dimension of the backbone network.

[0031] Preferably, in step S3, the backbone network... The FiLM modulation of the hidden layer is represented as follows:

[0032] ;

[0033] In the formula: , They represent the first Layer and first Output features of hidden layers; Main backbone network The weight matrix of the hidden layer, , These are the corresponding backbone network numbers. The scaling and bias parameters of the hidden layer, ⊙ represents element-wise multiplication.

[0034] Preferably, in step S3, the processing steps of the operator product and state prediction module include:

[0035] S301: Branch coding Coding of operating parameters After adding element by element, then sum the results with the output of the backbone network. Element-wise multiplication yields a high-dimensional feature vector. ;

[0036] S302: Transform high-dimensional feature vectors Average score Each of the following segments corresponds to a basis function combination for a state component, and each basis function combination contains... One basis function;

[0037] S303: For each state component, sum all elements in its corresponding segment to obtain the predicted value of the state component at the next time step.

[0038] The calculation formula is:

[0039] , ;

[0040] In the formula: For the first Each state component in the next time step The predicted value, For base function index, , Let be the dimension of the thermochemical state vector. High-dimensional feature vectors Dimensions The number of basis functions for each state component;

[0041] S304: Concatenate the predicted values ​​of all state components at the next time step to obtain the predicted state vector;

[0042] S305: After inverse transformation of the predicted state vector, the thermochemical state vector at the next moment is obtained.

[0043] Preferably, in step S4, training the deep operator network model using standardized training samples includes: using the thermochemical state vector at the current moment in the standardized training sample pair as the model input, the thermochemical state vector after the time step as the supervision label, using the mean squared error as the loss function, and using the backpropagation algorithm to train the deep operator network model end-to-end.

[0044] Compared with existing technologies, the accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation in this invention has the following advantages:

[0045] Traditional accelerated combustion dynamics calculation methods typically use a single initial state as the starting point for samples, resulting in training data that only covers a limited number of reaction path initiations, making it difficult to characterize the differentiated kinetic features of the same reaction trajectory at different evolution stages. To address this issue, this invention employs a sliding window strategy to densely extract state vectors from the complete evolution trajectory at different starting times and their corresponding time steps. This allows a single trajectory under the same operating condition to generate a large number of sample pairs covering different chemical timescales, such as ignition delay, rapid reaction, and equilibrium approach. The deep operator network trained in this way can learn the differentiated mapping patterns corresponding to different regions of the thermochemical state space. Therefore, even when faced with initial conditions not seen in the training set or extrapolated operating conditions, it can still maintain high prediction accuracy, significantly enhancing the model's adaptability to a wide range of operating conditions in practical engineering applications. Meanwhile, this invention allows for the flexible construction of input-output mapping relationships under different time increments based on trajectory data with a fixed storage time step through a sliding window, avoiding the computational overhead of repeated numerical integration. Furthermore, the input-output sample pairs contain the mapping relationship from the current state to the future state, enabling the model to directly learn the state transition operator instead of conventional derivative fitting, thereby improving the model's ability to represent rigid chemical systems.

[0046] Traditional deep operator networks use only a fixed time coordinate as input, and their time encoding remains unchanged under different input states, failing to characterize the drastic changes in the reaction process timescale under different temperatures, equivalence ratios, and component concentrations in combustion reactions. To address this issue, this invention uses a FiLM generator to map the thermochemical state features extracted by the branch networks into modulation parameters, and performs feature linear modulation on the intermediate features of each hidden layer in the backbone network. This allows the same time-step input to exhibit differentiated time encoding representations after forward propagation through the backbone network under different chemical states. The network can adaptively adjust the expression of time features according to the current chemical stage of the reaction, thereby accurately characterizing the time progression characteristics of different stages such as low-temperature oxidation, thermal ignition, and high-temperature equilibrium, significantly improving the model's fitting ability for rigid chemical systems. Simultaneously, this invention sets up an independent parameter network to encode operating parameters into feature vectors with the same dimension as the branch encoding, and fuses this with the branch encoding and backbone network output. This allows the model to handle changes in kinetic behavior caused by variations in operating conditions such as initial temperature, equivalence ratio, and initial pressure within the same network framework, improving the model's operating condition generalization ability. Furthermore, the operator product and state prediction module adopts a piecewise summation strategy instead of the traditional single fully connected layer mapping. Each state component corresponds to a set of independent basis function combinations. Through summation operations, high-dimensional features are interpretably reduced to the state space, which greatly reduces the number of trainable parameters, lowers the risk of overfitting, and at the same time gives the state prediction a clear physical meaning of basis function expansion.

[0047] This invention, during the online computation phase, only requires inputting the current thermochemical state vector and time step into a trained deep operator network for a single forward inference step to directly obtain the predicted state vector value after that time step. This completely bypasses the core time-consuming steps of rigid solvers, such as Jacobian matrix calculation, nonlinear iteration, and matrix decomposition. Since forward inference only involves matrix multiplication and nonlinear activation operations in a few fully connected layers, its floating-point operands are far lower than the single-step computation of traditional numerical integration. This allows for a one to three-order-of-magnitude acceleration of chemical reaction calculations while maintaining high prediction accuracy, providing a practical technical path for large-scale high-fidelity combustion numerical simulation. Because the model directly learns state transition mappings rather than derivative fitting, its single-step prediction is not limited by the stable step size in rigid equation numerical analysis. Compared to the exponential error amplification caused by the rigidity of traditional rigid solvers during time-step progression, the error growth of this model in the training domain is more gradual. This enables the model to stably complete the full-time evolution prediction from the initial state to the equilibrium state, providing a reliable numerical stability guarantee for accelerating chemical reactions in engineering-grade combustion chamber simulations. Attached Figure Description

[0048] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0049] Figure 1 This is a logic block diagram of an accelerated computational method for combustion chemical kinetics based on characteristic linear modulation.

[0050] Figure 2 This is a network structure diagram of a deep operator network model. Detailed Implementation

[0051] 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0052] The following detailed explanation illustrates the specific implementation methods:

[0053] Example:

[0054] This embodiment discloses an accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation.

[0055] like Figure 1 As shown, an accelerated computational method for combustion chemical kinetics based on characteristic linear modulation includes:

[0056] S1: Based on detailed chemical reaction mechanisms, the combustion process under various preset initial mixing conditions within the target application domain, using a zero-dimensional homogeneous constant-pressure reactor model, is numerically solved to obtain complete trajectory data of the thermochemical state vector evolution over time; where the thermochemical state vector includes temperature and the mass fraction of each component.

[0057] In this embodiment, the representative thermochemical scalars in the thermochemical state vector are determined by path flux analysis (PFA) from all species of the complete chemical mechanism. The representative thermochemical scalars include temperature and the mass fraction of characteristic components on key reaction pathways. The remaining thermochemical scalars are reconstructed by a lightweight artificial neural network.

[0058] S2: Using a sliding window strategy, the thermochemical state vector at the current moment and the thermochemical state vector after a time step are extracted from the complete evolution trajectory data of the thermochemical state vector over time, forming several training sample pairs. Each training sample pair is then standardized; the standardization includes a fifth-order transformation and normalization. The training sample pairs also include the operating condition data corresponding to the complete trajectory data.

[0059] S3: Based on the dimension of the thermochemical state vector in the standardized training sample pairs, construct a deep operator network model based on feature linear modulation, such as... Figure 2 As shown.

[0060] S4: Train the deep operator network model using standardized training samples;

[0061] S5: In the online calculation stage of combustion dynamics numerical simulation, the thermochemical state vector, time step, and operating parameters (operating condition labels) at the current moment are input into the trained deep operator network model. After forward inference, the predicted thermochemical state vector after the time step is output, which replaces the direct integral solution of the (detailed) chemical reaction mechanism, thereby accelerating the calculation of the combustion dynamics process.

[0062] To better illustrate the technical solution of the present invention, this embodiment will be described in more detail through the following parts.

[0063] This embodiment illustrates the technical solution of the present invention through two examples:

[0064] Example 1: A FiLM-React-DeepONet model was constructed and online inference predictions were performed on the hydrogen mechanism involving 10 components and 21 elementary reactions. The results were compared and analyzed with those of Cantera / CVODE. This example provides a detailed explanation of the present invention.

[0065] Example 2: A FiLM-React-DeepONet model was constructed and online inference predictions were performed on the n-heptane mechanism, which includes 160 components and 1540 elementary reactions. The results were compared and analyzed with those of Cantera / CVODE. This example provides a detailed explanation of the present invention.

[0066] I. Constructing complete trajectory data

[0067] 1. Example 1:

[0068] Numerical solutions were obtained using a zero-dimensional homogeneous isobaric reactor model in Cantera software. The reaction pressure was fixed at 1 atm, the initial temperature range was T0 ∈ [980, 1240] K, and the equivalence ratio range was Φ ∈ [0.60, 1.30]. The operating condition space was constructed using the Cartesian product of the initial temperature and the equivalence ratio, resulting in a total of 210 initial operating conditions, covering a wide range of combustion conditions from lean to rich and from medium to high temperatures. From the aforementioned operating condition space, ignition process data for 99 operating conditions with T0 = 1000, 1020, 1040, 1060, 1080, 1100, 1120, 1140, 1160, 1180 and 1200 K and Φ = 0.75, 0.80, 0.85, 0.90, 0.95, 1.00, 1.05, 1.10, and 1.15 were selected to form a training set. The remaining operating conditions were used as an extrapolation test set. To fully capture the transient evolution characteristics before and after ignition, the total simulation duration was set to 0.5 ms, and data was stored with a fixed time step of 1 μs.

[0069] 2. Example 2:

[0070] Numerical simulations were performed using a zero-dimensional homogeneous isobaric reactor model in Cantera software. The reaction pressure was fixed at 40 atm, the initial temperature range was T0 ∈ [800, 930] K, and the equivalence ratio range was Φ ∈ [0.75, 1.15]. The operating condition space was constructed using the Cartesian product of the initial temperature and the equivalence ratio, resulting in a total of 12 × 9 = 108 training operating conditions. Extrapolated operating conditions were constructed using combinations of temperatures T0 = 780 K and 790 K with equivalence ratios Φ = 0.6, 0.65, 0.7, 1.2, and 1.3, covering the main combustion region of n-heptane from low-temperature oxidation to high-temperature ignition. The total simulation duration was set to 4 ms, and data was stored with a fixed time step of 0.5 μs.

[0071] II. Constructing Training Samples

[0072] 1. Example 1:

[0073] Combining the PFA algorithm, five representative thermochemical scalars, including temperature and the mass fractions of H2, H, H2O, and O2, are extracted from the complete solution vector containing 10 components. The remaining components are reconstructed using a lightweight ANN network. A sliding window strategy is employed to generate the training sample pairs required for FiLM-React-DeepONet training. Let the total trajectory length be N, the sliding window duration be Δt = 40 μs, and the corresponding number of steps within the window be K = Δt / dt = 40 (dt = 1 μs). For the i-th initial time step, downsampling is performed with a fixed step size, traversing all time increments j ∈ [1, K] (j is an integer) within the window to construct sample data pairs. A fifth-order transformation is applied to their evolution curves. The transformed variables are linearly scaled based on their global minimum and maximum values, normalized to the [-1, 1] interval.

[0074] 2. Example 2:

[0075] Based on the path flux method (PFA), six representative thermochemical scalars, including temperature and nC7H, were screened from 160 species. 16 The mass fractions of O2, CO2, HO2, and H2O2 are used to construct the state vector, and the remaining components are reconstructed using a lightweight ANN network. Based on the above trajectory data, a sliding window strategy is used to generate the training sample pairs required for FiLM-React-DeepONet training. Let the total trajectory length be N, the sliding window duration be Δt = 80 μs, and the corresponding number of steps within the window be K = Δt / dt = 160 (dt = 0.5 μs). For the i-th starting time, downsampling is performed with a fixed step size, traversing all time increments j∈ [1, K] (j is an integer) within the window to construct sample data pairs. Similar to Example 1, a fifth-order transformation is applied to the evolution curves of the components, which may span multiple orders of magnitude. The transformed variables are linearly scaled based on their global minimum and maximum values ​​and normalized to the interval [-1, 1].

[0076] III. Deep Operator Network Model

[0077] In this embodiment, the deep operator network model based on characteristic linear modulation (FiLM-React-DeepONet) includes:

[0078] Branching network, used to convert the current thermochemical state vector As input Layer-by-layer transformation of the hidden layers, using the hidden features of the Lth hidden layer as branch encoding. and will the The hidden features of the hidden layers are fed into the FiLM generator;

[0079] FiLM generator, for fully connected networks, is used to generate the branch network's first branch. The hidden feature maps of the hidden layers are converted into modulation parameter vectors. And based on the total number of hidden layers in the backbone network modulation parameter vector Average score The groups correspond to the scaling and bias parameters of each hidden layer in the backbone network, respectively.

[0080] Displacement network, used to convert the thermochemical state vector at the current moment As input, generate displacement compensation amount;

[0081] The backbone network is used to take the logarithmic time step, after compensation by displacement compensation, as input. The layer-by-layer transformation of the hidden layer, and the 1st layer The hidden features of the hidden layers are used as the output of the dynamically modulated backbone network. In each hidden layer, the input features are first linearly transformed, and then the scaling and bias parameters corresponding to the hidden layer are used to perform FiLM modulation on the linearly transformed features. Finally, the output features of the hidden layer are obtained through nonlinear activation, so that the network can adaptively adjust the temporal encoding according to the input state.

[0082] A parameter network is used to convert the thermochemical state vector at the current moment. The corresponding working condition label code is the same as the branch code. Working condition parameter encoding with the same dimension ;

[0083] The operator product and state prediction module is used to convert branch codes. Operating Parameter Coding With backbone network output After fusion, a piecewise summation strategy is used to map the data to the state space, resulting in a thermochemical state vector after a time step.

[0084] Preferably, in step S3, the FiLM generator generates a modulation parameter vector. The calculation formula is:

[0085] ;

[0086] ;

[0087] In the formula: For the first linear layer through The output features after activation for Activation function For the branch network Hidden features of hidden layers , These are the weight matrix and bias vector of the first linear layer, respectively. , Let these be the weight matrix and bias vector of the second linear layer.

[0088] Specifically, the FiLM generator modulates the parameter vector. Average score The formula for calculating the group is:

[0089] ;

[0090] ;

[0091] In the formula: , These are the corresponding backbone network numbers. The scaling and bias parameters of the hidden layer. , The total number of hidden layers in the backbone network. This refers to the hidden layer dimension of the backbone network.

[0092] Specifically, the backbone network... The FiLM modulation of the hidden layer is represented as follows:

[0093] ;

[0094] In the formula: , They represent the first Layer and first Output features of hidden layers; Main backbone network The weight matrix of the hidden layer, , These are the corresponding backbone network numbers. The scaling and bias parameters of the hidden layer, ⊙ represents element-wise multiplication.

[0095] Specifically, the processing steps of the operator product and state prediction module include:

[0096] S301: Branch coding Coding of operating parameters After adding element by element, then sum the results with the output of the backbone network. Element-wise multiplication yields a high-dimensional feature vector. ;

[0097] S302: Transform high-dimensional feature vectors Average score Each of the following segments corresponds to a basis function combination for a state component, and each basis function combination contains... One basis function;

[0098] S303: For each state component, sum all elements in its corresponding segment to obtain the predicted value of the state component at the next time step.

[0099] The calculation formula is:

[0100] , ;

[0101] In the formula: For the first Each state component in the next time step The predicted value, For base function index, , Let be the dimension of the thermochemical state vector. High-dimensional feature vectors Dimensions The number of basis functions for each state component;

[0102] S304: Concatenate the predicted values ​​of all state components at the next time step to obtain the predicted state vector;

[0103] S305: After inverse transformation of the predicted state vector, the thermochemical state vector at the next moment is obtained.

[0104] IV. Model Training

[0105] In this embodiment, training the deep operator network model using standardized training samples includes: using the current thermochemical state vector from the standardized training sample pair as the model input, the thermochemical state vector after a time step as the supervision label, and employing the mean squared error (MSE) as the loss function, performing end-to-end training of the deep operator network model using the backpropagation algorithm. The training loss and validation loss are ultimately reduced to 1×10⁻ 7 The magnitude of the two values ​​is similar, and they remain highly consistent, with no obvious overfitting, indicating that the network has fully learned the intrinsic evolutionary laws of chemical kinetics.

[0106] 1. Example 1:

[0107] The network structures and training parameters are as follows: FiLMBranchNet structure: (5, 50, 50, 50, 200); FiLMTrunkNet structure: (1, 50, 50, 50, 200); FiLMNet structure: (50, 8, 300); ParamNet structure: (1, 50, 200); the network parameter count is 42k, and the training iterations are 2×10^6. 5 The initial learning rate is 1×10⁻², with a step size of 5000 and an exponential decay rate of 0.9. The operator product output vector q ∈ R² 00 It is divided into Ns = 5 segments (corresponding to 5 state components), each segment P per = 40 elements. The high-dimensional vector is mapped to the state space by piecewise summation.

[0108] 2. Example 2:

[0109] The network structures and training parameters are as follows: FiLMBranchNet structure: (6, 80, 80, 80, 240); FiLMTrunkNet structure: (1, 80, 80, 80, 240); FiLMNet structure: (80, 10, 480); ParamNet structure: (1, 80, 120); the number of network parameters is 91k, and the number of training iterations is 2×10^6. 5 The initial learning rate is 1×10⁻², with an exponential decay of 0.9 in step sizes of 5000. The operator product output vector q ∈ R² 40 It is divided into Ns = 6 segments (corresponding to 6 state components), each segment P per = 40 elements. The high-dimensional vector is mapped to the state space by piecewise summation.

[0110] V. Online Calculation Stage

[0111] 1. Example 1:

[0112] The prediction results of the trained FiLM-React-DeepONet model were compared with the Cantera reference solution based on detailed hydrogen hydration kinetics over time at normalized temperature, H2, and H mass fraction. Both models showed good consistency throughout the entire time history. Within the training set, FiLM-React-DeepONet had a mean absolute error (MAE) of 0.09%, and an MAE of 1.6% in the extrapolated case, demonstrating good generalization ability even outside the training data distribution. In terms of computational efficiency, FiLM-React-DeepONet achieved a 13.4x speedup compared to Cantera.

[0113] 2. Example 2:

[0114] The prediction results of the FiLM-React-DeepONet model trained for the n-heptane oxidation process were compared with the calculation results of Cantera. The mean absolute error (MAE) in the training set was 0.58%, and the MAE in the extrapolated operating condition was 2%. In terms of computational efficiency, FiLM-React-DeepONet achieved a speedup of 732 times compared to Cantera.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. An accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation, characterized in that, include: S1: Obtain complete trajectory data of the thermochemical state vector evolution over time; S2: Using a sliding window strategy, the thermochemical state vector at the current moment and the thermochemical state vector after the time step are extracted from the complete evolution trajectory data of the thermochemical state vector over time, forming several training sample pairs, and each training sample pair is standardized. S3: Based on the dimension of the thermochemical state vector in the standardized training sample pairs, construct a deep operator network model based on feature linear modulation; S4: Train the deep operator network model using standardized training samples; S5: In the online calculation stage of combustion dynamics numerical simulation, the thermochemical state vector and time step of the current moment are input into the trained deep operator network model. After forward inference, the predicted thermochemical state vector after the time step is output, which replaces the direct integral solution of the chemical reaction mechanism and realizes the accelerated calculation of the combustion dynamics process.

2. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 1, characterized in that: In step S1, the thermochemical state vector includes temperature and the mass fraction of each component.

3. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 1, characterized in that: In step S2, the standardization of the training sample pairs includes a fifth-order transformation and normalization.

4. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 1, characterized in that: Obtain the initial working condition data corresponding to the complete trajectory data, and generate corresponding working condition labels for each training sample pair.

5. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 1, characterized in that: In step S3, the deep operator network model based on characteristic linear modulation includes: Branching network, used to convert the current thermochemical state vector As input Layer-by-layer transformation of the hidden layers, using the hidden features of the Lth hidden layer as branch encoding. and the first The hidden features of the hidden layers are fed into the FiLM generator; FiLM generator, used to generate the branch network's first branch. The hidden feature maps of the hidden layers are converted into modulation parameter vectors. And based on the total number of hidden layers in the backbone network modulation parameter vector Average score The groups correspond to the scaling and bias parameters of each hidden layer in the backbone network, respectively. Displacement network, used to convert the thermochemical state vector at the current moment As input, generate displacement compensation amount; The backbone network is used to take the logarithmic time step, after compensation by displacement compensation, as input. The layer-by-layer transformation of the hidden layer, and the first layer The hidden features of the hidden layers are used as the output of the dynamically modulated backbone network. In each hidden layer, the input features are first linearly transformed, then FiLM modulation is performed on the linearly transformed features using the scaling and bias parameters corresponding to the hidden layer, and finally the output features of the hidden layer are obtained through nonlinear activation. A parameter network is used to convert the thermochemical state vector at the current moment. The corresponding working condition label code is the same as the branch code. Working condition parameter encoding with the same dimension ; The operator product and state prediction module is used to convert branch codes. Operating Parameter Coding With backbone network output After fusion, a piecewise summation strategy is used to map the data to the state space, resulting in a thermochemical state vector after a time step.

6. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 5, characterized in that: In step S3, the FiLM generator generates the modulation parameter vector. The calculation formula is: ； ； In the formula: For the first linear layer through The output features after activation for Activation function For the branch network Hidden features of hidden layers , These are the weight matrix and bias vector of the first linear layer, respectively. , Let these be the weight matrix and bias vector of the second linear layer.

7. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 6, characterized in that: In step S3, the FiLM generator modulates the modulation parameter vector. Average score The formula for calculating the group is: ； ； In the formula: , These are the corresponding backbone network numbers. The scaling and bias parameters of the hidden layer. , The total number of hidden layers in the backbone network. This refers to the hidden layer dimension of the backbone network.

8. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 5, characterized in that: In step S3, the backbone network... The FiLM modulation of the hidden layer is represented as follows: ； In the formula: , They represent the first Layer and first Output features of hidden layers; Main backbone network The weight matrix of the hidden layer, , These are the corresponding backbone network numbers. The scaling and bias parameters of the hidden layer, ⊙ represents element-wise multiplication.

9. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 5, characterized in that: In step S3, the processing steps of the operator product and state prediction module include: S301: Branch coding Coding of operating parameters After adding element by element, then sum the results with the output of the backbone network. Element-wise multiplication yields a high-dimensional feature vector. ; S302: Transform high-dimensional feature vectors Average score Each of the following segments corresponds to a basis function combination for a state component, and each basis function combination contains... One basis function; S303: For each state component, sum all elements in its corresponding segment to obtain the predicted value of the state component at the next time step. The calculation formula is: ， ； In the formula: For the first Each state component in the next time step The predicted value, For base function index, , Let be the dimension of the thermochemical state vector. High-dimensional feature vectors Dimensions The number of basis functions for each state component; S304: Concatenate the predicted values ​​of all state components at the next time step to obtain the predicted state vector; S305: After inverse transformation of the predicted state vector, the thermochemical state vector at the next moment is obtained.

10. The accelerated calculation method for combustion chemical kinetics based on characteristic linear modulation as described in claim 9, characterized in that: In step S4, training the deep operator network model using standardized training samples includes: using the thermochemical state vector at the current moment in the standardized training sample pair as the model input, the thermochemical state vector after the time step as the supervision label, using the mean squared error as the loss function, and using the backpropagation algorithm to train the deep operator network model end-to-end.

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