A method and system for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential

Abstract

The present invention discloses a method and system for calculating the refrigeration performance of a two-dimensional electrocaloric material based on machine learning potential, and the method comprises the following steps: firstly, based on first-principles calculation and machine learning deep neural network, a molecular dynamics potential function having both the calculation efficiency of classical dynamics and the calculation accuracy of first-principles is trained; then, the trained potential function is used to calculate the polarizability of the system by using the definition of Born effective charge, and the influence of the external electric field on the system simulation is considered; then, molecular dynamics is used to simulate the curve of polarization changing with electric field, the curve of polarization changing with temperature, and the hysteresis loop of ferroelectricity; finally, the electrocaloric performance of the two-dimensional ferroelectric material including adiabatic temperature change and isothermal entropy change is calculated by a direct method with the help of molecular dynamics data, so as to provide a theoretical basis and guiding basis for the actual experimental preparation of two-dimensional ferroelectric electrocaloric materials.

Description

Technical Field

[0001] The present invention relates to the field of new energy material calculation technology, and in particular to a method and system for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential. Background Art

[0002] Energy is a major pillar of social development today. Focusing on new energy technologies is an important part of developing and strengthening strategic emerging industries. Finding new refrigeration technologies and refrigeration materials is crucial.

[0003] Solid-state refrigeration materials and technologies based on external field-induced phase change are a promising solution for future refrigeration feasibility technologies. The development of new solid-state refrigeration materials and technologies that are green, environmentally friendly, energy-saving, efficient, stable and reliable has become the focus and challenge of countries around the world; in particular, electric card refrigeration is easier to implement and more cost-effective than magnetic card refrigeration, spring card refrigeration and pressure card refrigeration because the electric field is more controllable and easy to obtain; ferroelectric materials are ideal candidates for electric refrigeration because they exhibit spontaneous polarization that can be modulated near the ferroelectric phase transition temperature under the action of an external electric field.

[0004] However, the performance of traditional electrocaloric cooling is usually not enough to meet the needs of practical applications. With the advancement of miniaturization and integration technology, people are increasingly studying micron or nanoscale chip cooling, which has great potential. Therefore, there is an urgent need for a calculation method that can quickly determine the electrocaloric performance of a material. Summary of the invention

[0005] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a method that combines efficiency and accuracy to calculate the refrigeration properties of two-dimensional electrocaloric materials including isothermal entropy change and adiabatic temperature change. The method is based on first-principles calculations, deep potential energy training, and molecular dynamics simulation of the phase change law of ferroelectric materials under an external field, and induces electrocaloric refrigeration.

[0006] In order to solve the above technical problems, the present invention provides a method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential, comprising:

[0007] Step S1: Calculate the energy, force and virial particles of the initial data set to generate first principle structure data, wherein the first principle structure data includes: energy, atomic force and virial force data of the first principle structure;

[0008] Step S2: Perform machine learning training based on first principle structural data to generate a deep potential energy model;

[0009] Step S3: performing molecular dynamics simulation exploration according to the deep potential energy model, generating error data of the deep potential energy model, and then marking the error data;

[0010] Step S4: performing molecular dynamics simulation according to the deep potential energy model evaluated by a preset test method to simulate the phase change process of the two-dimensional electrocaloric material;

[0011] Step S5: simulating the polarization dynamics of the two-dimensional electrocaloric material under an external electric field, and then calculating the refrigeration performance of the two-dimensional electrocaloric material.

[0012] As a preferred embodiment of the present invention, in step S1, the energy, force and virial particles are calculated using the Vienna ab initio simulation package and the Perdew-Burke-Ernzerhof generalized gradient approximation for the initial data set;

[0013] Among them: the projected enhanced wave pseudopotential is used to represent the effect of ion nuclei, and in order to achieve the convergence of energy and atomic forces, an energy cutoff of 400 eV and a K-point spacing of 3×3×1 are used. -6 When the self-consistent field iteration stops, the energy, atomic force, and dimensional data of the first-principles structure are generated.

[0014] As a preferred embodiment of the present invention, in step S2, the method comprises the following steps:

[0015] Step S20: using deep potential training software to train four dynamic programming models based on the energy, atomic force, and dimensional force data of the first principle structure;

[0016] Step S20: Using the stochastic gradient descent method to control the weights of energy and force losses in the total loss function, four deep potential energy models with different initial random seeds are generated.

[0017] As a preferred embodiment of the present invention, in step S3, the method comprises the following steps:

[0018] Step S30: using four deep potential energy models to perform molecular dynamics simulation exploration to obtain energy errors and force errors of the four deep potential energy models;

[0019] Step S31: marking the energy error and force error that fall between the first preset trust level and the second preset trust level, and then generating a machine learning potential function.

[0020] As a preferred embodiment of the present invention, in step S30, during exploration, isothermal and isobaric deep potential molecular dynamics simulations are used to sample relevant configurations of a set of thermodynamic states spanning a phase diagram region, and the initial configuration used in the simulation includes a supercell of 5×5×1 Pnma and Cmcm phases, a temperature range of 100K-700K, a pressure range of 1atm-1GPa, and a time range of 2ps-20ps.

[0021] As a preferred embodiment of the present invention, in step S4, the method comprises the following steps:

[0022] Step S400: Calculate the energy error and the mean absolute error of the energy error between the deep potential model and the first principle results, evaluate the fitting performance, use the R square factor to measure the consistency between the two, calculate the atomic force error and its mean absolute error, and evaluate the fitting performance;

[0023] Step S401: using the Vienna ab initio simulation method to perform first-principles calculations of energy and force, using the Perdew-Burke-Ernzerhof generalized gradient approximation method to describe the electron exchange correlation, and using the projected enhanced wave pseudopotential to simulate the ion-nuclear effect;

[0024] Step S402: Calculate energy and force for the potential function of the deep potential energy model, and then compare the calculated energy and atomic force with the first principle results;

[0025] Step S403: comparing the non-harmonic double-well potential of the ferroelectric material obtained by dynamic programming and first-principles calculation, and evaluating the difference error between the two;

[0026] Step S404: Calculate the phonon spectra of the materials respectively and compare them, and then accurately calculate the phonon dispersion.

[0027] As a preferred embodiment of the present invention, in step S4, the method further comprises the following steps:

[0028] Step S405: Calculate the polarization using the first definition of Born's effective charge:

[0029]

[0030] Where P is the polarization intensity, Z * is the Born effective charge tensor, V is the volume of the unit cell, e is the electron charge, and δd is the displacement of the polarized phase atoms relative to the non-polarized phase;

[0031] Step S406: Use the second definition of Born's effective charge:

[0032]

[0033] The influence of the external electric field is obtained:

[0034] F=-eZ * ×E,or,

[0035] Where E is the external electric field and F is the additional force exerted on the atom by the external electric field.

[0036] As a preferred embodiment of the present invention, in step S4, the method further comprises the following steps:

[0037] Step S407: using force field parameters to perform temperature rise simulation;

[0038] Step S408: after the temperature reaches thermodynamic equilibrium, the polarization intensity is calculated according to the polarization method of the first definition of Born's effective charge, and a curve of polarization intensity versus temperature is generated;

[0039] Step S409: setting a preset external electric field, repeating the molecular dynamics simulation at different temperatures, and generating a curve of polarization intensity changing with the electric field under different electric fields;

[0040] Step S410: keeping the temperature constant at a preset temperature, performing a simulation of the cyclic variation of the electric field within a preset interval, and generating a hysteresis loop at the preset temperature.

[0041] As a preferred embodiment of the present invention, in step S5, the method comprises the following steps:

[0042] Step S50: During the initial adiabatic polarization stage, an external electric field is applied while keeping the total entropy constant, thereby undergoing a transition from initial non-polarized / disordered to polarized / ordered, resulting in heating of the electrocaloric material;

[0043] Step S51: Keep the electric field unchanged, exchange heat with the surrounding environment under the electric field, and use the isobaric and isothermal ensemble to reduce the temperature to the initial temperature, thereby experiencing a transition from polarization / order to polarization / order phase;

[0044] Step S52: removing the electric field while maintaining a constant system entropy, using an isobaric and isoenthalpic ensemble, thereby experiencing a transition from a polarized / ordered phase to a non-polarized / disordered phase, causing the temperature of the material to drop;

[0045] Step S53: Keep the electric field at zero, make the system exchange heat with the outside, and use an isobaric and isothermal ensemble to experience the process from the non-polarized / disordered phase back to the non-polarized / disordered phase;

[0046] Step S54: Repeat steps S50 to S53 to obtain the adiabatic temperature change and isothermal entropy change under the required temperature and electric card, and then obtain the refrigeration performance of the two-dimensional electric card material based on the adiabatic temperature change and isothermal entropy change.

[0047] The present invention also provides a system for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential, comprising:

[0048] A model training module is used to calculate the energy, force and virial particles of the initial data set to generate first principle structure data, which includes: energy, atomic force and virial force data of the first principle structure; perform machine learning training based on the first principle structure data to generate a deep potential energy model; perform molecular dynamics simulation exploration based on the deep potential energy model to generate error data of the deep potential energy model, and then mark the error data;

[0049] A polarization calculation module is used to perform molecular dynamics simulation based on a deep potential energy model evaluated by a preset test method to simulate the phase change process of the two-dimensional electrocaloric material;

[0050] The performance calculation module is used to simulate the polarization dynamics of two-dimensional electrocaloric materials under an external electric field, and then calculate the refrigeration performance of two-dimensional electrocaloric materials.

[0051] Beneficial effects of the present invention:

[0052] The present invention can train a force field for two-dimensional electrocaloric materials, which combines the efficiency of classical methods with the accuracy of first-principles molecular dynamics simulation. By using this precise force field, the slow temperature rise simulation can successfully capture the change of the polarization intensity of the two-dimensional electrocaloric material with temperature. Above a specific temperature, the polarization intensity instantly changes to 0, that is, the ferroelectric-paraelectric phase transition process is generated. The slow electric field simulation can successfully capture the change law of the polarization intensity of the two-dimensional electrocaloric material with the external electric field, revealing its polarization dynamics under the external electric field, including the temperature dependence and hysteresis loop of polarization under different electric fields. And directly simulate the isothermal entropy change and adiabatic temperature change of electrocaloric performance parameters. The trained machine learning potential function will be widely used by others in thermodynamic analysis and phase field simulation to predict phase transitions, domain structure evolution, ferroelectric properties and material design in low-dimensional systems. The present invention also provides a paradigm for predicting the electrothermal properties of materials based on machine learning potential functions, and provides a feasible direction for the electrothermal community to find materials with high electrothermal properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0054] Figure 1 It is a schematic diagram of a method for calculating the refrigeration performance of a two-dimensional electrocaloric material provided in an embodiment of the present invention.

[0055] Figure 2It is a flow chart of calculating the refrigeration performance of a two-dimensional electrocaloric material provided in an embodiment of the present invention.

[0056] Figure 3 It is a flow chart of an error marking method provided by an embodiment of the present invention.

[0057] Figure 4 is a schematic diagram of a change curve provided by an embodiment of the present invention; wherein, Figure 4 (a) is a schematic diagram of the energy and DFT result comparison curve. Figure 4 (b) is a schematic diagram of the change curve of atomic force and DFT results. Figure 4 (c) is a schematic diagram of the energy calculation comparison change curve. Figure 4 (d) is a schematic diagram of the molecular dynamics simulation change curve.

[0058] Figure 5 It is a flow chart of a method for calculating the refrigeration performance of a two-dimensional electrocaloric material provided in an embodiment of the present invention.

[0059] Figure 6 It is a schematic diagram of a hysteresis loop variation curve provided by an embodiment of the present invention.

[0060] Figure 7 It is a schematic diagram of a curve of polarization intensity varying with temperature provided in an embodiment of the present invention.

[0061] Figure 8 It is a schematic diagram of module connections of a system for calculating the refrigeration performance of two-dimensional electrocaloric materials provided in an embodiment of the present invention.

[0062] Description of the Figures in the Specification:

[0063] 100. Model training module, 101. Polarization calculation module, 102. Performance calculation module. DETAILED DESCRIPTION

[0064] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0065] refer to Figure 1 and Figure 2 As shown, in some embodiments, a method for calculating the refrigeration performance of a two-dimensional electrocaloric material based on machine learning potential is involved, and the method includes the following steps:

[0066] Step S1: Calculate the energy, force and virial particles of the initial data set to generate first principle structure data, wherein the first principle structure data includes: energy, atomic force and virial force data of the first principle structure.

[0067] In step S1, the Vienna ab initio simulation package (VASP) and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) were used to perform ab initio calculations of energy, force, and virial particles. The projected augmented wave (PAW) pseudopotential was used to represent the effects of the ion nucleus. To achieve convergence of energy and atomic force, an energy cutoff of 400 eV and a K-point spacing of 3 × 3 × 1 were used. When the difference in total energy was less than 10 -6 When eV, the self-consistent field iteration stops, thereby obtaining the energy, atomic force, and virial force data of the first-principles structure of a large number of structures.

[0068] Step S2: Perform machine learning training based on first-principles structural data to generate a deep potential energy model.

[0069] In step S2, machine learning training is performed using the energy, atomic force, and dimensional force data of the above-mentioned first-principles structure; in the training step, four dynamic programming (DP) models are trained using the DeePMD suite software package. These models share the same set of hyperparameters, but the random seeds used to initialize the parameters are different for each model.

[0070] Among them, the size of the embedding grid is set to: 25, 50, 100, while the size of the fitting grid is: 240, 240, 240; a cutoff radius of 9A and a smoothing parameter of 0.5A are used, and the stochastic gradient descent scheme Adam is adopted. There are usually 1 million training steps. The hyperparameters start-pref_e, start-pref_f, start-pref_v, limit-pref_e, limit-pref_f and limit-pref_v are set to 0.01, 100, 0.01, 1.0, 1.0 and 1.0 respectively to control the weights of energy and force losses in the total loss function; the starting learning rate is 10 -3 , decays exponentially to 10 at the end of training -8 , and finally four deep potential training models with different initial random seeds are obtained.

[0071] Step S3: Perform molecular dynamics simulation exploration according to the deep potential energy model to generate error data of the deep potential energy model, and then mark the error data.

[0072] refer to Figure 3 As shown, in step S3, the method further includes the following steps:

[0073] Step S30: Use the above four deep potential energy training models to perform molecular dynamics simulation exploration. In the exploration step, the Large-scale Atomic / Molecular Massively Parallel Simulator (LAMMPS) uses isothermal isobaric (NPT) deep potential molecular dynamics (DPMD) to simulate and sample relevant configurations of the set of thermodynamic states spanning the phase diagram region.

[0074] Among them, a set of initial configurations used in the simulation includes Pnma and Cmcm phases with a supercell of 5×5×1, a temperature range of 100K to 700K, a pressure range of 1atm to 1GPa, and a time range of 2ps to 20ps, obtaining more structures than the data in step S1, as well as the energy errors, force errors, etc. of the four models.

[0075] Step S31: Mark the energy error and force error in step S30: Only when the model uncertainty of the configuration on the DPMD trajectory (i.e., the energy error and the force error) falls between two customized confidence levels (given by σ lo and σ hi ), the configuration along the DPMD trajectory is selected for marking.

[0076] The uncertainty of the model is quantified as the maximum standard deviation of the force predicted by a set of DP models. These models are trained using the same data set and hyperparameters, but initialized using different random seeds. After obtaining the labeled data structure, the above steps S1 to S3 are repeated until the energy error and force error of 99% of the structures are less than σ lo When the iteration is stopped, the machine learning potential function with excellent performance can be obtained; for all iterations, the trust level is set to σ lo = 0.07 and σ hi =0.25eVA -1 ,This trust level can be modified according to the specific system.

[0077] Step S4: performing molecular dynamics simulation according to the deep potential energy model evaluated by a preset test method to simulate the phase change process of the two-dimensional electrocaloric material.

[0078] In step S4, after the deep potential model is successfully trained, a series of tests are performed to ensure its consistency with the density functional theory (DFT) results to verify the accuracy of the machine learning model. The following are the detailed verification steps:

[0079] 1. Energy and atomic force error analysis:

[0080] Calculate the energy error between the deep potential model (DP) and the first principles results (DFT) results, as well as the mean absolute error of the energy error.

[0081] To evaluate the fitting performance, the R-squared factor was used to measure the consistency between the two.

[0082] Likewise, the atomic force errors and their mean absolute errors were calculated and the fitting performance was evaluated.

[0083] 2. DFT calculation settings:

[0084] Accurate DFT calculations of energies and forces were performed using the Vienna Ab Initio Simulation Package (VASP).

[0085] The Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) was used to describe the electron exchange correlation.

[0086] The projector augmented wave (PAW) pseudopotential is used to simulate ion nuclear effects to improve computational efficiency and accuracy.

[0087] To ensure the convergence of energy and atomic forces, the energy cutoff was set to 400 eV and a 3 × 3 × 1 K-point grid was used.

[0088] The total energy difference is less than 10 -6 eV to ensure the convergence of the results.

[0089] 3. Energy and force calculation of DP model:

[0090] The potential function of the DP model was loaded using LAMMPS software to calculate energy and force.

[0091] Compare the energy and atomic forces calculated by the DP model with the DFT results, see Figure 4 (a) and Figure 4 (b) as shown.

[0092] 4. Comparison of non-harmonic double-well potentials:

[0093] The anharmonic double-well potentials of ferroelectric materials calculated by DP and DFT are compared to evaluate the difference error between the two.

[0094] This comparison is a key indicator in the study of ferroelectric phase transitions and reflects the accuracy of the deep potential energy model.

[0095] The structure changes from a non-polarized state to a polarized state, and a series of structures with different polarization values ​​are obtained, and then the energy is calculated and compared. Figure 4 (c) as shown.

[0096] 5. Accurate calculation of phonon dispersion:

[0097] The phonon spectra of the materials were calculated using DFT-Phonopy software and LAMMPS-Phonopy for comparison, which is a strict standard for testing the accuracy of the deep potential energy method.

[0098] Through the accurate calculation of phonon dispersion, it is proved that the trained DP potential model can be used for molecular dynamics simulation with DFT accuracy. Figure 4 (d) as shown.

[0099] Through the above validation steps, the performance of the deep potential energy model can be comprehensively evaluated and its reliability in the prediction of physical and chemical properties can be ensured.

[0100] After confirming that the machine learning potential function is accurate, it is used to perform molecular dynamics simulations to simulate the phase transition process of two-dimensional electrocaloric materials and simulate their polarization dynamics under an external electric field. The specific steps are as follows:

[0101] First, the principles of calculating polarization intensity and applied electric field are introduced, and the first definition of Born's effective charge in modern polarization theory is used to calculate the polarization of the system.

[0102]

[0103] Where P is the polarization intensity, Z * is the Born effective charge tensor, V is the volume of the unit cell, e is the electron charge, and δd is the displacement of the polarized phase atoms relative to the non-polarized phase;

[0104] Then, using Born's second definition of effective charge:

[0105]

[0106] The effect of the external electric field on the system is obtained as follows:

[0107] F=-eZ * ×E,or,

[0108] Where E is the external electric field and F is the additional force exerted on the atom by the external electric field.

[0109] The above-mentioned fine-tuned molecular dynamics (MD) model was used, combined with the proposed electric field application and polarization calculation principles, to carry out molecular dynamics simulation experiments. These simulation experiments aim to deeply analyze how temperature and electric field jointly drive the polarization transition phenomenon of materials.

[0110] Experimental setup:

[0111] A polarimetric phase supercell with a supercell size of 25 × 25 × 1 consisting of 2500 atoms was chosen to ensure representativeness and reliability of the simulations.

[0112] The simulations were performed at atmospheric pressure using an NPT ensemble and the temperature was controlled using a Nose-Hoover thermostat to ensure the physical authenticity of the simulated environment.

[0113] Periodic boundary conditions are used to simulate infinitely extended crystal structures in real materials.

[0114] Simulation parameters:

[0115] The time step of the simulations was set to 1 femtosecond (fs) to capture subtle changes in the polarization dynamics.

[0116] The total simulation time was set to 50 picoseconds (ps), which is long enough to ensure adequate convergence and stability assessment of the structure.

[0117] Simulation process:

[0118] Using precise force field parameters, a slow heating simulation is first performed to observe how the polarization intensity of the two-dimensional electrocaloric material changes with temperature.

[0119] Above a certain temperature threshold, a sharp drop in the polarization intensity to zero is observed, marking the ferroelectric to paraelectric phase transition.

[0120] Calculation of polarization intensity:

[0121] Using the LAMMPS software, we calculated the polarization intensity according to the first definition of Born effective charge mentioned above after reaching thermodynamic equilibrium, and obtained a detailed curve of the polarization intensity varying with temperature.

[0122] By changing the temperature and repeating the above calculations, it is possible to plot the polarization intensity variation curve at different temperatures.

[0123] Simulation of electric field effects:

[0124] According to the formula in the second definition of Born's effective charge, a specific external electric field (eg, 0.001) is set, and the molecular dynamics simulation is repeated at different temperatures.

[0125] In this way, a curve showing the change of polarization intensity with temperature under different electric fields is obtained.

[0126] Obtaining the hysteresis loop:

[0127] Keeping the temperature constant (eg, 300 K), a simulation of cyclically changing the electric field from -300 MV / cm to 300 MV / cm and back is performed.

[0128] The polarization intensity is recorded at each electric field value, so that a curve of polarization changing with electric field at a specific temperature, i.e., a hysteresis loop, can be plotted.

[0129] Results:

[0130] refer to Figure 6 and Figure 7 As shown, the temperature dependence of polarization intensity under different electric field conditions, as well as the hysteresis loop and the curve of polarization intensity changing with temperature are demonstrated, providing an intuitive perspective for understanding the polarization behavior of materials.

[0131] Step S5: simulating the polarization dynamics of the two-dimensional electrocaloric material under an external electric field, and then calculating the refrigeration performance of the two-dimensional electrocaloric material.

[0132] In step S5, solid-state refrigeration involves a total of four transformation processes, and heat absorption and heat release are achieved in these four processes, which is used as an example to illustrate the use of the optimized DP model to calculate isothermal entropy change and adiabatic temperature change:

[0133] Step S50: In the initial adiabatic polarization stage, an external electric field is applied while keeping the total entropy of the system constant. The system undergoes a transition from initial non-polarized / disordered (state A) to polarized / ordered (state B), resulting in heating of the electrocaloric material. The adiabatic temperature change during the heating process is defined as: ΔT 0→E =T A -T B ; Note that the Lammps ensemble selects the isobaric and isoenthalpic ensemble (NPH) to ensure that the system is in an adiabatic state and achieves a constant total entropy. When the electric field is applied, the rate of change of the electric field must be very small, for example To ensure that the system undergoes a reversible phase transition.

[0134] Step S51: The second stage involves an isofield process, i.e., the electric field is kept constant, and the system exchanges heat with the surrounding environment under the electric field using an isobaric isothermal (NPT) ensemble to reduce the temperature to the initial temperature; during this process, the system transitions from polarized / ordered (state B) to polarized / ordered phase (state C), showing a slightly enhanced polarization. The isothermal entropy change during heating is determined using the following formula: ΔS 0→E =Q BC / T; Note that the lammps ensemble selects NPT to ensure that the system is in heat exchange with the outside world.

[0135] Step S52: In the third stage, i.e., the adiabatic depolarization stage, the electric field is removed while maintaining a constant system entropy. Using the NPH ensemble, the system transitions from the polarized / ordered phase (state C) to the non-polarized / disordered phase (state D), causing the temperature of the material to drop; the adiabatic temperature change during cooling is defined as: ΔT E→0 =T D –TA ; Note that the Lammps ensemble selects NPH to ensure that the system is in an adiabatic state and achieves a constant total entropy, and when the electric field is removed, the rate of change of the electric field must be very small, for example To ensure that the system undergoes a reversible phase transition.

[0136] Step S53: The whole process forms a closed loop, called the equal field depolarization stage. The electric field is kept at zero, and the system is allowed to exchange heat with the outside world. Using the NPT ensemble, since the working electrocaloric material is colder than the target environment, heat is transferred to the electrocaloric material; at the same time, the system returns from the non-polarized / disordered phase (state D) to the non-polarized / disordered (state A). The isothermal entropy change during the cooling process may be given by the following formula ΔS E→0 =Q DA' / T.

[0137] Step S54: Finally, only steps S50 to S53 are needed to obtain the adiabatic temperature change and isothermal entropy change under any temperature and electric card.

[0138] In some embodiments, reference Figure 8 As shown, the present application also relates to a calculation system for the refrigeration performance of a two-dimensional electrocaloric material based on machine learning potential, using the above-mentioned calculation method for the refrigeration performance of a two-dimensional electrocaloric material based on machine learning potential, including:

[0139] The model training module is used to calculate the energy, force and virial particles of the initial data set to generate first principles structure data, which includes: energy, atomic force and virial force data of the first principles structure; perform machine learning training based on the first principles structure data to generate a deep potential energy model; perform molecular dynamics simulation exploration based on the deep potential energy model to generate error data of the deep potential energy model, and then mark the error data.

[0140] Among them, the model training module is also used to calculate the energy, force and virial particles of the initial data set using the Vienna ab initio simulation package and the Perdew-Burke-Ernzerhof generalized gradient approximation; four dynamic programming models are trained using the deep potential training software based on the energy, atomic force, and virial force data of the first principles structure; the stochastic gradient descent method is used to control the weights of the energy and force losses in the total loss function to generate four deep potential models with different initial random seeds; molecular dynamics simulation exploration is performed using the four deep potential models to obtain the energy error and force error of the four deep potential models; the energy error and force error that fall between the first preset trust level and the second preset trust level are marked to generate a machine learning potential function.

[0141] A polarization calculation module is used to perform molecular dynamics simulation based on a deep potential energy model evaluated by a preset test method to simulate the phase change process of the two-dimensional electrocaloric material;

[0142] Among them, the polarization calculation module is also used to calculate the energy error and the mean absolute error of the energy error between the deep potential energy model and the first-principles results, evaluate the fitting performance, use the R-square factor to measure the consistency between the two, and calculate the atomic force error and its mean absolute error, and evaluate the fitting performance; use the Vienna ab initio simulation method to perform first-principles calculations of energy and force, use the Perdew-Burke-Ernzerhof generalized gradient approximation method to describe the electron exchange correlation, and use the projected enhanced wave pseudopotential to simulate the ion-nuclear effect; calculate the energy and force of the potential function of the deep potential energy model, and then compare the calculated energy and atomic force with the first-principles results; compare the dynamic programming and first-principles calculations. The non-harmonic double-well potential of ferroelectric materials is used to evaluate the difference error between the two; the phonon spectra of the materials are calculated separately and compared to accurately calculate the phonon dispersion; the polarization is calculated using the first definition of Born's effective charge; the influence of the external electric field is obtained using the second definition of Born's effective charge; the temperature is simulated using force field parameters; after the temperature reaches thermodynamic equilibrium, the polarization intensity is calculated according to the polarization calculation method based on the first definition of Born's effective charge, and a curve of polarization intensity changing with temperature is generated; a preset external electric field is set, and molecular dynamics simulations are repeated at different temperatures to generate a curve of polarization intensity changing with the electric field under different electric fields; the temperature is kept constant at the preset temperature, and a cyclic change simulation of the electric field in the preset range is performed to generate a hysteresis loop at the preset temperature.

[0143] The performance calculation module is used to simulate the polarization dynamics of two-dimensional electrocaloric materials under an external electric field, and then calculate the refrigeration performance of two-dimensional electrocaloric materials.

[0144] Among them, the performance calculation module is also used to apply an external electric field in the initial adiabatic polarization stage while keeping the total entropy constant, so as to experience a transition from initial non-polarized / disordered to polarized / ordered, resulting in heating of the electrocaloric material; keep the electric field unchanged, exchange heat with the surrounding environment under the electric field, and use an isobaric isothermal ensemble to reduce the temperature to the initial temperature, so as to experience a transition from polarized / ordered to polarized / ordered phase; remove the electric field while maintaining a constant system entropy, use an isobaric isenthalpic ensemble, so as to experience a transition from polarized / ordered phase to non-polarized / disordered phase, so that the temperature of the material decreases; keep the electric field at zero, so that the system exchanges heat with the outside world, and use an isobaric isothermal ensemble to experience a return from non-polarized / disordered phase to non-polarized / disordered; thereby obtaining the adiabatic temperature change and isothermal entropy change under the required temperature and electrocaloric conditions, and then obtain the refrigeration performance of the two-dimensional electrocaloric material based on the adiabatic temperature change and isothermal entropy change.

[0145] In some embodiments, the present application also relates to a computer medium having a computer program stored thereon, and the computer program is executed by a processor to implement the method for calculating the refrigeration performance of a two-dimensional electrocaloric material based on machine learning potential.

[0146] In some embodiments, the present application also relates to a computer, comprising the computer medium described above.

[0147] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0148] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential, characterized in that: The following steps are involved: Step S1: Calculate the energy, force and virial particles of the initial data set to generate first principle structure data, wherein the first principle structure data includes: energy, atomic force and virial force data of the first principle structure; Step S2: Perform machine learning training based on first principle structural data to generate a deep potential energy model; Step S3: performing molecular dynamics simulation exploration according to the deep potential energy model, generating error data of the deep potential energy model, and then marking the error data; Step S4: performing molecular dynamics simulation according to the deep potential energy model evaluated by a preset test method to simulate the phase change process of the two-dimensional electrocaloric material; Step S5: simulating the polarization dynamics of the two-dimensional electrocaloric material under an external electric field, and then calculating the refrigeration performance of the two-dimensional electrocaloric material.

2. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 1, characterized in that: In step S1, calculations of energy, forces, and virial particles are performed on the initial data set using the Vienna ab initio simulation package and the Perdew-Burke-Ernzerhof generalized gradient approximation; Among them: the projected enhanced wave pseudopotential is used to represent the effect of ion nuclei, and in order to achieve the convergence of energy and atomic forces, an energy cutoff of 400 eV and a K-point spacing of 3×3×1 are used. -6 When the self-consistent field iteration stops, the energy, atomic force, and dimensional data of the first-principles structure are generated.

3. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 2, characterized in that: In step S2, the method comprises the following steps: Step S20: using deep potential training software to train four dynamic programming models based on the energy, atomic force, and dimensional force data of the first principle structure; Step S20: Using the stochastic gradient descent method to control the weights of energy and force losses in the total loss function, four deep potential energy models with different initial random seeds are generated.

4. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 3 is characterized in that: In step S3, the method comprises the following steps: Step S30: using four deep potential energy models to perform molecular dynamics simulation exploration to obtain energy errors and force errors of the four deep potential energy models; Step S31: marking the energy error and force error that fall between the first preset trust level and the second preset trust level, and then generating a machine learning potential function.

5. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 4, characterized in that: In step S30, during exploration, isothermal and isobaric deep potential molecular dynamics simulations are used to sample relevant configurations of a set of thermodynamic states spanning the phase diagram region, the initial configuration used in the simulation including Pnma and Cmcm phases with a supercell of 5×5×1, a temperature range of 100K-700K, a pressure range of 1atm-1GPa, and a time range of 2ps-20ps.

6. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 1, characterized in that: In step S4, the method comprises the following steps: Step S400: Calculate the energy error between the deep potential model and the first principles and the mean absolute error of the energy error, evaluate the fitting performance, use the R square factor to measure the consistency between the two, calculate the atomic force error and its mean absolute error, and evaluate the fitting performance; Step S401: using the Vienna ab initio simulation method to perform first-principles calculations of energy and force, using the Perdew-Burke-Ernzerhof generalized gradient approximation method to describe the electron exchange correlation, and using the projected enhanced wave pseudopotential to simulate the ion-nuclear effect; Step S402: Calculate energy and force for the potential function of the deep potential energy model, and then compare the calculated energy and atomic force with the first principle calculation results; Step S403: comparing the non-harmonic double-well potential of the ferroelectric material obtained by dynamic programming and first-principles calculation, and evaluating the difference error between the two; Step S404: Calculate the phonon spectra of the materials respectively and compare them, and then accurately calculate the phonon dispersion.

7. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 6, characterized in that: In step S4, the method further comprises the following steps: Step S405: Calculate the polarization using the first definition of Born's effective charge: Where P is the polarization intensity, Z * is the Born effective charge tensor, V is the volume of the unit cell, e is the electron charge, and δd is the displacement of the polarized phase atoms relative to the non-polarized phase; Step S406: Use the second definition of Born's effective charge: The influence of the external electric field is obtained: Where E is the external electric field and F is the additional force exerted on the atom by the external electric field.

8. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 7, characterized in that: In step S4, the method further comprises the following steps: Step S407: using force field parameters to perform temperature rise simulation; Step S408: after the temperature reaches thermodynamic equilibrium, the polarization intensity is calculated according to the polarization method of the first definition of Born's effective charge, and a curve of polarization intensity versus temperature is generated; Step S409: setting a preset external electric field, repeating the molecular dynamics simulation at different temperatures, and generating a curve of polarization intensity changing with the electric field under different electric fields; Step S410: keeping the temperature constant at a preset temperature, performing a simulation of the cyclic variation of the electric field within a preset interval, and generating a hysteresis loop at the preset temperature.

9. The method for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential according to claim 1, characterized in that: In step S5, the method comprises the following steps: Step S50: During the initial adiabatic polarization stage, an external electric field is applied while keeping the total entropy constant, thereby undergoing a transition from initial non-polarized / disordered to polarized / ordered, resulting in heating of the electrocaloric material; Step S51: Keep the electric field unchanged, exchange heat with the surrounding environment under the electric field, and use the isobaric and isothermal ensemble to reduce the temperature to the initial temperature, thereby experiencing a transition from polarization / order to polarization / order phase; Step S52: removing the electric field while maintaining a constant system entropy, using an isobaric and isoenthalpic ensemble, thereby experiencing a transition from a polarized / ordered phase to a non-polarized / disordered phase, causing the temperature of the material to drop; Step S53: Keep the electric field at zero, make the system exchange heat with the outside, and use an isobaric and isothermal ensemble to experience the process from the non-polarized / disordered phase back to the non-polarized / disordered phase; Step S54: Repeat steps S50 to S53 to obtain the adiabatic temperature change and isothermal entropy change under the required temperature and electric card, and then obtain the refrigeration performance of the two-dimensional electric card material based on the adiabatic temperature change and isothermal entropy change.

10. A system for calculating the refrigeration performance of two-dimensional electrocaloric materials based on machine learning potential, characterized in that: A method for calculating the refrigeration performance of a two-dimensional electrocaloric material based on machine learning potential according to any one of claims 1 to 9, comprising: A model training module is used to calculate the energy, force and virial particles of the initial data set to generate first principle structure data, which includes: energy, atomic force and virial force data of the first principle structure; perform machine learning training based on the first principle structure data to generate a deep potential energy model; perform molecular dynamics simulation exploration based on the deep potential energy model to generate error data of the deep potential energy model, and then mark the error data; A polarization calculation module is used to perform molecular dynamics simulation based on a deep potential energy model evaluated by a preset test method to simulate the phase change process of the two-dimensional electrocaloric material; The performance calculation module is used to simulate the polarization dynamics of two-dimensional electrocaloric materials under an external electric field, and then calculate the refrigeration performance of two-dimensional electrocaloric materials.

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