Dust particle charging fast algorithm based on deep learning

Abstract

The invention discloses a dust particle charging fast algorithm based on deep learning, and the algorithm comprises the following steps: 1, optimizing a neural network model; 2, generating an input data set; 3, generating an output data set; 4, generating a charging network model through machine learning; and utilizing the established charging network model to calculate the dust electric quantity under the real physical parameters. According to the algorithm disclosed by the invention, the network relationship between the input characteristic parameter and the to-be-solved output characteristic parameter is generated based on a deep learning method, and a calculation method based on a physical principle is replaced.

Description

Technical Field

[0001] The present invention belongs to the field of dust plasma, and in particular relates to a fast dust particle charging algorithm based on deep learning in this field, which can be used for multi-physics field coupling simulation related to weakly ionized dust plasma in space and laboratory. Background Art

[0002] Dust plasma is generally defined as a plasma system containing a large number of nanometer or micrometer dust particles. Most of the matter in the universe exists in the form of plasma, but dust is one of the ubiquitous components. Therefore, in most cases, plasma and dust particles coexist. The most important feature of dust plasma is that the dust particles immersed in it absorb electrons and ions and become highly charged. Charged dust particles have completely different dynamic behaviors from electrons and ions. They interact with plasma and can significantly change the properties of plasma and produce some physical phenomena unique to dust plasma. Restricted orbit theory is a commonly used numerical simulation method for dust plasma based on physical mechanisms. However, in practical applications, since the restricted orbit theory needs to be applied to dust particles one by one for charging calculation, a computer cluster needs to spend a lot of computing time to complete the simulation. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a fast dust particle charging algorithm based on deep learning.

[0004] The present invention adopts the following technical solution:

[0005] A fast dust particle charging algorithm based on deep learning, the improvement of which includes the following steps:

[0006] Step 1, neural network model optimization:

[0007] Preferably, a multi-layer perceptron MLP neural network is used as the neural network model to be used;

[0008] Step 2, input data set generation:

[0009] The physical parameters that determine the charge of dust particles are determined as the following seven input characteristic parameters: electron density, dust density, electron temperature, dust temperature, neutral gas temperature and dust particle size;

[0010] Randomly generate random arrays covering the range of physical parameter changes;

[0011] Use formula (1) to generate each input feature parameter:

[0012] X=randi(X min ,m,n)*zone (1)

[0013] In the above formula, X is the input feature parameter, randi is the random number generation function, and X min is the minimum value of the input characteristic parameter, X max is the maximum value of the input feature parameter, m is the number of rows in the generated array, n is the number of columns in the generated array, and zone is X max With X min The magnitude difference, X max =X min *zone;

[0014] Step 3, output data set generation:

[0015] The dust particle charge is determined as the output characteristic parameter, and the dust particle charge is solved by substituting the 7 randomly generated input characteristic parameters using the traditional physical model.

[0016] The traditional physical model refers to the use of restricted orbit theory to calculate the charging current I of the electron on the dust particles. e and the charging current I of the ions on the dust particles i , when I e =I i When , the dust particles are considered to reach a charge equilibrium state;

[0017] Charging cross sections of dust particles and charged particles for:

[0018]

[0019] Combining the law of conservation of angular momentum and the law of conservation of energy, we get:

[0020] m α v α b α =m α v gα r d (3)

[0021]

[0022] In the above formula, α represents electron e or ion i, m α represents the mass of the incident particle, v α represents the velocity of the incident particle, b α Represents the collision radius, v gα represents the velocity tangent to the dust particles, r d represents the radius of the dust particle, q α represents the charge of the charged particle, q d Indicates the charge of dust particles;

[0023] The relative dielectric constant of plasma is expressed as:

[0024]

[0025] In the above formula, ω p is the plasma frequency, ω is the angular frequency of the electromagnetic wave, v e is the effective collision frequency;

[0026] Combining equations (4) and (5), we can get the charging cross section related to particle velocity: for:

[0027]

[0028] In the above formula, φ d =q d / 4πε0r d , ε0 is the dielectric constant of vacuum;

[0029] The charge currents for electrons and ions are the integrals of the charge cross section and the rate distribution function:

[0030]

[0031] In the above formula, represents the minimum collision rate, f α represents the particle velocity distribution function, assuming it satisfies the Maxwell distribution:

[0032]

[0033] In the above formula, n α is the number density distribution of particle α, k B is the Boltzmann constant, T α is the particle temperature, and the charging current of electrons and ions is:

[0034]

[0035] Step 4: Machine learning generates a charging network model:

[0036] The input data set of step 2 and the output data set of step 3 are divided into a training set and a test set, and the sets are fed into the neural network model selected in step 1 to generate a charging network model capable of describing the relationship between each input feature parameter and the output feature parameter;

[0037] Step 5: Use the established charging network model to calculate the dust charge under real physical parameters:

[0038] Based on the established charging network model, the physical scene to be simulated is substituted to solve the dust charge under real physical parameters.

[0039] Furthermore, in step 4, the residual RMSE is used as a criterion to measure whether the generated charging network model meets the calculation accuracy requirements:

[0040]

[0041] In the above formula, x represents the output data set of step 3, x net is the predicted value of the charging network model, M is the total number of data;

[0042] When RMSE≤0.05, the generated charging network model meets the calculation accuracy requirements.

[0043] The beneficial effects of the present invention are:

[0044] The algorithm disclosed in the present invention generates a network relationship between input feature parameters and output feature parameters to be solved based on deep learning methods, replacing the calculation method based on physical principles. On the one hand, it saves a lot of time for technical developers, and more importantly, it enables complex loop nested calculations of dust charging and other physical scenes to be quickly implemented on ordinary computers.

[0045] The algorithm disclosed in the present invention can realize the rapid simulation of the charge calculation of dust particles in the plasma environment. It is of great significance to the coupled simulation modeling research of multi-physics scenarios of dusty plasmas, such as interplanetary physics, polar mid-layer summer echoes, solid rocket tail flames, and dust plasma sheaths formed by ablation, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the flow chart of the algorithm of the present invention;

[0047] Figure 2 is the random array of electron density of the input data set;

[0048] Figure 3 is the random array of dust density of the input dataset;

[0049] Figure 4 is a random array of temperatures of the input data set;

[0050] Figure 5 It is the dust charge of the output data set obtained based on the restricted orbit theory;

[0051] Figure 6 It is a demonstration of the convergence performance of the charging network model between input and output data sets established using random numbers;

[0052] Figure 7 This is a comparison chart of the prediction results of the training set of the charging network model;

[0053] Figure 8This is a comparison chart of the prediction results of the test set of the charging network model;

[0054] Fig. 9 This is a diagram showing the calculation results of the charge in a real physical scenario based on the restricted orbit theory;

[0055] Fig.10 This is a diagram of the charge calculation results based on the algorithm of the present invention in the same real physical scenario. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0057] Example 1, this example discloses a fast algorithm for charging dust particles based on deep learning, such as Figure 1 As shown, the following steps are included:

[0058] Step 1, neural network model optimization:

[0059] The optimization of the neural network model refers to optimizing the neural network model that can solve the physical problem to be calculated and is easy to calculate.

[0060] Neural network models can be simply divided into three main types: feedforward neural network, feedback neural network and graph neural network. Among them, the feedforward neural network is also called multi-layer perceptron (MLP). In this network, different neurons belong to different layers, which are composed of input layer-hidden layer-output layer. The signal is transmitted from the input layer to the output layer in one direction without feedback in the middle. Its purpose is to fit a certain function. This kind of neural network meets the scene calculation requirements of the present invention. Therefore, the multi-layer perceptron MLP neural network is preferably used as the neural network model to be used;

[0061] Step 2, input data set generation:

[0062] The physical parameters that determine the charge of dust particles are determined as the following seven input characteristic parameters: electron density, dust density, electron temperature, dust temperature, neutral gas temperature and dust particle size;

[0063] Randomly generate random arrays covering the range of physical parameter changes;

[0064] Use formula (1) to generate each input feature parameter:

[0065] X=randi(X min,m,n)*zone (1)

[0066] In the above formula, X is the input feature parameter, randi is the random number generation function, and X min is the minimum value of the input characteristic parameter, X max is the maximum value of the input feature parameter, m is the number of rows in the generated array, n is the number of columns in the generated array, and zone is X max With X min The magnitude difference, X max =X min *zone;

[0067] Figure 2 is the random array of electron density of the input data set; Figure 3 is the random array of dust density of the input dataset; Figure 4 is a random array of temperatures of the input data set;

[0068] Step 3, output data set generation:

[0069] The dust particle charge is determined as the output characteristic parameter, and the dust particle charge is solved by substituting the 7 randomly generated input characteristic parameters using the traditional physical model.

[0070] The traditional physical model refers to the use of restricted orbit theory to calculate the charging current I of the electron on the dust particles. e and the charging current I of the ions on the dust particles i , when I e =I i When , the dust particles are considered to reach a charge equilibrium state;

[0071] Charging cross sections of dust particles and charged particles for:

[0072]

[0073] Combining the law of conservation of angular momentum and the law of conservation of energy, we get:

[0074] m α v α b α =m α v gα r d (3)

[0075]

[0076] In the above formula, α represents electron e or ion i, m α represents the mass of the incident particle, v α represents the velocity of the incident particle, b αrepresents the collision radius, that is, the distance from the incident velocity to the axis parallel to the velocity direction and passing through the center of the dust particle when the incident particle is tangent to the surface of the dust particle; v gα represents the velocity tangent to the dust particles, r d represents the radius of the dust particle, q α represents the charge of the charged particle, q d Indicates the charge of dust particles;

[0077] The relative dielectric constant of plasma is expressed as:

[0078]

[0079] In the above formula, ω p is the plasma frequency, ω is the angular frequency of the electromagnetic wave, v e is the effective collision frequency;

[0080] Combining equations (4) and (5), we can get the charging cross section related to particle velocity: for:

[0081]

[0082] In the above formula, φ d =q d / 4πε0r d , ε0 is the vacuum dielectric constant; the thermal motion of charged particles in the plasma will charge the dust particles. Because the electrons move fast, the dust particles are generally negatively charged. At this time, the electrons will be repelled but the ions will be attracted, making the ion current on the surface of the dust particles larger but the electron current smaller, and the particle surface is positively charged. In this case, the dust particles will repel ions and attract electrons, so that the electron current will increase and the ion current will decrease. The charging current of electrons and ions is the integral of the charging cross section and the rate distribution function:

[0083]

[0084] In the above formula, represents the minimum collision rate, f α represents the particle velocity distribution function, assuming it satisfies the Maxwell distribution:

[0085]

[0086] In the above formula, n α is the number density distribution of particle α, k B is the Boltzmann constant, T α is the particle temperature, and the charging current of electrons and ions is:

[0087]

[0088] Figure 5 It is the dust charge of the output data set obtained based on the restricted orbit theory;

[0089] Step 4: Machine learning generates a charging network model:

[0090] The input data set of step 2 and the output data set of step 3 are divided into a training set and a test set, and the sets are fed into the neural network model selected in step 1 to generate a charging network model with high calculation accuracy and capable of describing the relationship between each input characteristic parameter and the output characteristic parameter;

[0091] The residual error (RMSE) is used as a criterion to measure whether the generated charging network model meets the calculation accuracy requirements:

[0092]

[0093] In the above formula, x represents the output data set of step 3, x net is the predicted value of the charging network model, M is the total number of data;

[0094] When RMSE≤0.05, the generated charging network model meets the calculation accuracy requirements.

[0095] Step 5: Use the established charging network model to calculate the dust charge under real physical parameters:

[0096] Based on the established charging network model, the restricted orbit theory calculation module in the original dust particle charging model is replaced, and the physical scene to be simulated is substituted to solve the dust charge under real physical parameters.

[0097] Figure 6 It is a demonstration of the convergence performance of the charging network model between input and output data sets established using random numbers; Figure 7 This is a comparison chart of the prediction results of the training set of the charging network model; Figure 8 This is a comparison chart of the prediction results of the test set of the charging network model; Fig. 9 This is a diagram showing the calculation results of the charge in a real physical scenario based on the restricted orbit theory; Fig.10 This is a diagram of the charge calculation results based on the algorithm of the present invention in the same real physical scenario.

[0098] In summary, the algorithm disclosed in the present invention saves a lot of time for technical developers. More importantly, it enables the loop nested calculation of dust charging and other physical fields in physical scenarios such as interplanetary physics, polar mid-spheric summer echoes, solid rocket tail flames, and dust plasma sheaths formed by ablation to be quickly implemented on ordinary computers.

Claims

1. A fast dust particle charging algorithm based on deep learning, characterized in that: The steps include: Step 1, neural network model optimization: Preferably, a multi-layer perceptron MLP neural network is used as the neural network model to be used; Step 2, input data set generation: The physical parameters that determine the charge of dust particles are determined as the following seven input characteristic parameters: electron density, dust density, electron temperature, dust temperature, neutral gas temperature and dust particle size; Randomly generate random arrays covering the range of physical parameter changes; Use formula (1) to generate each input feature parameter: X =randi(X min ,m,n)*zone (1) In the above formula, X is the input feature parameter, randi is the random number generation function, and X min is the minimum value of the input characteristic parameter, X max is the maximum value of the input feature parameter, m is the number of rows in the generated array, n is the number of columns in the generated array, and zone is X max With X min The magnitude difference, X max =X min *zone; Step 3, output data set generation: The dust particle charge is determined as the output characteristic parameter, and the dust particle charge is solved by substituting the 7 randomly generated input characteristic parameters using the traditional physical model. The traditional physical model refers to the use of restricted orbit theory to calculate the charging current I of the electron on the dust particles. e and the charging current I of the ions on the dust particles i , when I e =I i When , the dust particles are considered to reach a charge equilibrium state; Charging cross sections of dust particles and charged particles for: Combining the law of conservation of angular momentum and the law of conservation of energy, we get: m α v α b α =m α v gα r d (3) In the above formula, α represents electron e or ion i, m α represents the mass of the incident particle, v α represents the velocity of the incident particle, b α Represents the collision radius, v gα represents the velocity tangent to the dust particles, r d represents the radius of the dust particle, q α represents the charge of the charged particle, q d Indicates the charge of dust particles; The relative dielectric constant of plasma ε r The expression is: In the above formula, ω p is the plasma frequency, ω is the angular frequency of the electromagnetic wave, v e is the effective collision frequency; Combining equations (4) and (5), we can get the charging cross section related to particle velocity: for: In the above formula, φ d =q d / 4πε0r d , ε0 is the dielectric constant of vacuum; The charge currents for electrons and ions are the integrals of the charge cross section and the rate distribution function: In the above formula, represents the minimum collision rate, f α represents the particle velocity distribution function, assuming it satisfies the Maxwell distribution: In the above formula, n α is the number density distribution of particle α, k B is the Boltzmann constant, T α is the particle temperature, and the charging current of electrons and ions is: Step 4: Machine learning generates a charging network model: The input data set of step 2 and the output data set of step 3 are divided into a training set and a test set, and the sets are fed into the neural network model selected in step 1 to generate a charging network model capable of describing the relationship between each input characteristic parameter and the output characteristic parameter; Step 5: Use the established charging network model to calculate the dust charge under real physical parameters: Based on the established charging network model, the physical scene to be simulated is substituted to solve the dust charge under real physical parameters.

2. The deep learning-based fast dust particle charging algorithm according to claim 1 is characterized in that: In step 4, the residual RMSE is used as a criterion to measure whether the generated charging network model meets the calculation accuracy requirements: In the above formula, x represents the output data set of step 3, x net is the predicted value of the charging network model, M is the total number of data; When RMSE≤0.05, the generated charging network model meets the calculation accuracy requirements.

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