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CN-121997765-A - Porous medium seepage field rapid prediction method based on random nerve operator efficient training

CN121997765ACN 121997765 ACN121997765 ACN 121997765ACN-121997765-A

Abstract

The invention discloses a porous medium seepage field rapid prediction method based on principal component analysis and a random neural network. Firstly, performing principal component analysis and dimension reduction on a permeability field and a pressure field to construct an encoder and a decoder, and then constructing a random neural network, wherein the hidden layer weight and bias of the random neural network are fixed after initialization, and the output layer weight is trained only by solving a linear least square problem so as to learn a potential space mapping relation. Preferably, the stability and the precision of prediction can be improved by integrating a plurality of networks, and further, a conformal prediction method can be utilized to provide a prediction interval with statistical assurance for an integrated model, so as to quantify the prediction uncertainty. The invention shortens the training time to the second level, remarkably reduces the calculation cost while maintaining high prediction precision, has strong robustness, and provides an efficient tool for real-time simulation and quick decision of scenes such as oil gas exploitation, groundwater simulation and the like.

Inventors

  • WANG FEI
  • DENG ZIRUI

Assignees

  • 西安交通大学

Dates

Publication Date
20260508
Application Date
20260203

Claims (10)

  1. 1. A porous medium seepage field rapid prediction method based on random nerve operator efficient training is characterized by comprising the following steps: step 1, obtaining a plurality of groups of known porous medium permeability fields and corresponding pressure field data thereof to form a training sample set; Step 2, respectively carrying out principal component analysis on the permeability field sample set and the pressure field sample set, and extracting respective principal component substrates; constructing an encoder and a decoder based on the principal component bases, wherein the encoder is configured to project an input physical field to a corresponding principal component base to obtain projection coefficients as potential encoding vectors, and the decoder is configured to linearly combine the principal component bases to reconstruct the physical field using the potential encoding vectors as coefficients; Step 3, constructing a random neural network comprising hidden layers, which is used for learning the potential space mapping defined in the step 2, wherein all weights and bias parameters of the hidden layers are randomly initialized before training and then fixed, and when the number of the hidden layers is greater than 1, the output of each hidden layer except the last hidden layer is directly connected to an output layer through an independent jump path; step 4, training the random neural network by using the training sample potential coding vector obtained in the step 2; And 5, for a new permeability field to be predicted, firstly mapping the new permeability field into a low-dimensional potential vector by using the encoder in the step 2, then inputting the random neural network trained in the step 4 to obtain a predicted output potential vector, and finally reconstructing the predicted output potential vector into a complete predicted pressure field by using the decoder in the step 2.
  2. 2. The rapid prediction method for porous medium seepage field based on efficient training of random nerve operators according to claim 1, wherein in step 2, the number of principal components is selected by setting a cumulative variance contribution rate threshold value, and the threshold value is more than or equal to 90%.
  3. 3. The method for rapidly predicting the porous medium seepage field based on efficient training of random nerve operators according to claim 1, wherein in the step 3, a non-linear activation function is adopted for a hidden layer of the random nerve network, and the non-linear activation function is selected from one of hyperbolic tangent function, sigmoid function, gaussian function, triangular sine function, triangular cosine function, polynomial function, reLU function, leakyReLU function or ELU function.
  4. 4. The rapid prediction method for porous medium seepage field based on efficient training of random nerve operators according to claim 1 is characterized in that in step 3, an energy matching strategy is adopted for parameter initialization of the hidden layers, and when the number of the hidden layers is larger than 1, a layered energy matching strategy is adopted, specifically, for a first hidden layer, an initialization range parameter of a weight is calculated based on total sample energy of input potential codes and output potential codes, and for each subsequent hidden layer, the initialization range parameter of the weight of the layer is calculated based on total sample energy of output of a previous hidden layer and total sample energy of output potential codes.
  5. 5. The rapid prediction method for porous medium seepage field based on efficient training of random nerve operators according to claim 4, wherein the layered energy matching strategy is realized by the following modes: The overall sample energy of the input potential code is recorded as Outputting the total sample energy of the potential codes as For the random neural network A hidden layer whose weight initializes the range parameter Is determined by the following formula: Wherein, the In the formula, Is the first The total sample energy output by each hidden layer is defined ; Is the first The width of the hidden layer; And Is a preset super parameter used for restricting the initialization range; Is the first Layer-set energy matching coefficients for outputting target energy Is distributed to each layer in proportion and meets Wherein Is the total number of hidden layers; The overall sample energy is defined as, for a set of sample vectors Data matrix The overall sample energy of (2) is Wherein Representing vectors Norms.
  6. 6. The rapid prediction method of porous medium seepage field based on efficient training of random nerve operators according to claim 1 is characterized by further comprising the following step 4 and the preceding step 5, and further comprising the following step 4-1, integrated learning enhancement; The integrated learning enhancement specifically comprises the steps of independently and repeatedly executing the step 3 and the step 4 for a plurality of times to construct a plurality of random neural networks with different random initialization parameters, respectively inputting low-dimensional potential vectors to be predicted into the plurality of random neural networks when predicting in the step 5, carrying out arithmetic average on output potential vectors of all the random neural networks, and obtaining final predicted output potential vectors in an integrated mode.
  7. 7. The method according to claim 1, wherein in step 4, the training sample potential coding vector obtained in step 2 is input into the random neural network, forward propagation is carried out to obtain output feature matrixes of all hidden layers, a global optimal solution of all weight matrixes connecting the hidden layers to the output layers is obtained through one-time calculation by solving a linear least square problem taking the feature matrixes as design matrixes and target output potential codes as observation values, and network training is completed, wherein the linear least square problem is solved through a numerical method, and the numerical method is selected from one of Moore-Penrose generalized inverse, QR decomposition, singular value decomposition, cholesky decomposition or normal equation solving of the output feature matrixes is calculated.
  8. 8. The rapid prediction method for porous medium seepage field based on efficient training of stochastic nerve operators according to claim 6, wherein after the step 4-1, the method further comprises the step 6 of uncertainty quantization, wherein the uncertainty quantization provides a prediction interval with statistical assurance for the prediction pressure field based on a conformal prediction method by utilizing the plurality of stochastic neural network models, and specifically comprises the following steps: Step 6-1, predicting and reconstructing the pressure field of each calibration sample through the plurality of random neural network models by using a calibration data set, and calculating the prediction mean value and standard deviation of each calibration sample on the discrete grid points of the solving domain; step 6-2, constructing a calibration score set for the calibration data set based on the prediction mean, the standard deviation and the corresponding real pressure field; Step 6-3, determining the quantiles of the calibration score set according to a preset confidence level ; Step 6-4, for the permeability field to be predicted, calculating the average value of the predicted pressure field on the discrete grid points of the solving domain And standard deviation of And carrying out numerical stabilization treatment on the standard deviation to obtain Wherein A preset positive number threshold value is set, and then a prediction interval is generated 。
  9. 9. The method for rapid prediction of porous media seepage field based on efficient training of stochastic nerve operators according to claim 9, wherein the constructing the calibration score set in the step 6-2 comprises calculating the calibration score point by point on the solution domain discrete grid points for each sample in the calibration data set Wherein Is the first The samples are at grid points Is used for the actual pressure value of (a), And (3) with Respectively a prediction mean value and a standard deviation, To pair(s) The value after the numerical stabilization treatment is carried out, A preset positive number threshold value, and then all grid points of all calibration samples are used for the calibration Value collection as a set of calibration scores Wherein In order to calibrate the number of samples, Points for the grid.
  10. 10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor performs the steps of the porous medium seepage field fast prediction method based on efficient training of stochastic nerve operators according to any one of claims 1 to 9.

Description

Porous medium seepage field rapid prediction method based on random nerve operator efficient training Technical Field The invention relates to the technical field of computational fluid mechanics and industrial numerical intelligent simulation, in particular to a porous medium seepage field rapid prediction method based on efficient training of random nerve operators, which is used for realizing efficient and high-precision rapid prediction of the porous medium seepage field. Background The porous medium seepage problem, the mathematical model of which is usually described by Darcy's law or its derivative form, is a core physical process in many industrial fields such as oil gas exploitation, groundwater, environmental engineering and chemical separation. The high-precision and high-efficiency numerical simulation of the problems is a key for realizing scientific prediction and engineering optimization. At present, the main flow numerical method for solving the porous medium seepage field mainly comprises a finite difference method, a finite element method, a finite volume method and the like, and the methods are used for directly dispersing and solving through a physical equation, so that the method has a firm mathematical basis and higher universality. However, this type of approach is extremely computationally expensive when faced with strong non-linearity problems or "multi-query" scenarios where extensive parameterization studies (e.g., for different permeability fields) are required. Every parameter change needs to carry out complete mesh division, matrix assembly and equation solving again, the single simulation time is different from hours to days, and urgent requirements of industrial real-time prediction and quick optimization cannot be met. Particularly in the fields of oil and gas field development scheme optimization, groundwater pollutant migration emergency assessment and the like, rapid simulation is often required to be carried out on tens to hundreds of different geological models (represented by permeability field changes) in a period of hours or even less so as to evaluate development risks or pollution ranges. In face of the engineering requirement of such "multi-scheme, fast decision", the computational efficiency of the conventional numerical method has become a key bottleneck restricting its application. In order to overcome the bottleneck of the traditional method, in recent years, an operator learning method based on deep learning has been developed, aiming at directly learning the mapping relation from an input parameter field to an output solution field. Representative methods include depth operator networks, fourier nerve operators, and the like. Once training is complete, prediction of new inputs by such models can be done quickly. However, the method generally relies on a deep neural network to perform end-to-end gradient optimization training, and has two inherent defects that firstly, the training process involves non-convex optimization of millions or billions of parameters, the calculation cost is huge, and usually, the calculation cost is required to be several hours to several days on high-performance calculation equipment, and secondly, the model performance is extremely sensitive to the selection of an optimization algorithm, super-parameter setting and initialization, the training process is unstable and is easy to fall into local optimization, so that the generalization capability of the model fluctuates. In addition, attempts have been made to combine the dimensionality reduction methods such as principal component analysis with shallow stochastic neural networks (e.g., extreme learning machines) to improve efficiency. However, the method generally adopts a single hidden layer network, has limited nonlinear expression capability, is difficult to accurately describe complex multi-scale features in a seepage field, and meanwhile, the random initialization of network parameters lacks guidance adaptive to specific data distribution, so that the model performance is unstable, and the prediction precision still has a larger improvement space on complex problems. Therefore, how to further improve the prediction accuracy and stability of the data driving method to the complex nonlinear seepage problem while ensuring extremely high calculation efficiency is still a technical problem to be solved in the art. Disclosure of Invention Aiming at the problems that in industrial scenes such as oil and gas reservoir simulation, groundwater environment evaluation and the like, the traditional numerical simulation method for the porous medium seepage field is too long in calculation time and cannot meet the requirements of real-time analysis and multi-scheme quick selection, and the existing data driving agent model is high in training cost and insufficient in prediction stability under complex heterogeneous conditions, the invention aims to provide the quick prediction method for the