Phase change property prediction method and device based on complex parameters

Abstract

The invention discloses a phase change property prediction method and device based on complex parameters, and the method comprises the steps: firstly selecting a set coarse graining degree for a target substance system, carrying out the modeling, selecting a force field, and determining a phase change parameter range; setting parameters are adjusted, equilibrium state molecular dynamics simulation is carried out under one or more simulation conditions, a simulation result is obtained, and energy of the setting parameters and total energy of the system are recorded; based on a simulation result, setting the energy of parameters and the total energy of the system, and calculating a partition function by summing the sampled system structure; then on the basis of set parameters, the partition function is extended to a complex plane from a real number field through a reweighting strategy; finally, a partition function is calculated in a complex plane set parameter area, zero points of the partition function are obtained and connected into a curve, and the intersection point of the curve and the real axis is the phase change point of the target substance system. According to the method, the problems of high cost, dependence on existing data, large calculation amount, poor interpretability and the like in the prior art are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of phase transition property prediction of materials, and particularly relates to a phase transition property prediction method and device based on complex parameters. BACKGROUND

[0002] Phase transition is a process of discontinuous change in properties of a substance when external conditions such as temperature and pressure change. The corresponding phase transition point directly determines the application temperature range of the material, the operation interval of biological molecules, and other key characteristics, and has important application value in the fields of material research and development, biological engineering, electronic devices, etc. In the research and development stage of a substance, early prediction of phase transition properties through theoretical means can greatly reduce the blindness of experimental synthesis, reduce research and development costs and shorten the research and development cycle. Therefore, phase transition property prediction has become a research focus in related fields. At present, the mainstream phase transition property research methods in the industry include experimental measurement method, data-driven method, simulation method based on computational chemistry, and statistical mechanics theory method: the experimental measurement method directly measures the phase transition behavior by preparing samples, which is the most direct verification method; the data-driven method relies on existing experimental data to achieve prediction through neural network, decision tree and other model fitting interpolation; the simulation method based on computational chemistry adjusts the phase transition related parameters to capture the phase transition characteristics through the construction of a molecular model and the dynamic simulation of the phase transition; the statistical mechanics theory method explains the phase transition mechanism through phenomenological models such as mean field theory and Landau phase transition theory. These methods have certain applications in different scenarios and provide diversified technical paths for phase transition research.

[0003] However, the existing technology still has many defects that are difficult to overcome: the experimental measurement method is accurate in results, but the sample preparation and testing process is costly and time-consuming, which cannot meet the needs of efficient research and development; the data-driven method relies heavily on a large amount of existing data, has poor interpretability of the fitting model, and unknown extrapolation performance, which can only perform well in limited interpolation scenarios, making it difficult to cope with phase transition prediction of new materials or data-deficient systems; the simulation method based on computational chemistry is prone to hysteresis effect due to continuous parameter scanning simulation, or large amount of calculation caused by bisection positioning of the phase transition point, and repeated submission of calculation tasks limits the prediction efficiency; the statistical mechanics theory method has a large number of parameters that are not meaningful, which cannot be directly derived from the molecular system, making it more suitable for explaining the phase transition mechanism rather than directly predicting the phase transition point. In addition, the phase transition theorem proposed by Li Zhengdao and Yang Zhenning relates the phase transition to the zero point of the complex plane of the partition function, but this theory has only been used to verify its correctness in toy models, and has not been effectively calculated in actual molecular simulation systems, failing to be transformed into a practical prediction technology.

[0004] Therefore, there is an urgent need for a phase transition property prediction method based on complex parameters to solve the problems of high cost, dependence on existing data, large amount of calculation, and poor interpretability of the existing technology. SUMMARY

[0005] To address this, the present invention provides a method and apparatus for predicting phase transition properties based on complex parameters, which solves the problems of high cost, reliance on existing data, large computational load, and poor interpretability of existing phase transition property prediction methods. Through complex parameter extension, reweighting, and optional MBAR data integration, it achieves efficient, accurate, and multi-system-applicable phase transition point prediction.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting phase transition properties based on complex parameters, characterized in that it includes:

[0007] The target material system is modeled with a set coarsening degree and a set force field is selected; the parameter range for the phase transition of the target material system is determined; based on the parameter range, equilibrium molecular dynamics simulation is performed under one or more simulation conditions by adjusting the set parameters, the simulation results are obtained, and the energy of the set parameters and the total energy of the target material system are recorded.

[0008] Based on the simulation results, the energy of the set parameters, and the total energy of the target material system, the partition function of the target material system is calculated by summing the system structure sampled from the molecular dynamics simulation.

[0009] Based on the set parameters, the partition function is extended from the real number domain to the complex plane through a reweighting strategy;

[0010] The partition function is calculated within a set parameter region on the complex plane to obtain the zero point of the partition function on the complex plane; the zero points are connected to form a curve; the intersection of the curve and the real axis is the phase transition point of the target material system.

[0011] As a preferred option for the phase transition property prediction method based on complex parameters, if the simulation results under various simulation conditions are obtained through equilibrium molecular dynamics simulation during the process of extending the partition function from the real number domain to the complex plane, then before executing the reweighting strategy, the simulation data of multiple ensembles are integrated into the target ensemble through the MBAR strategy.

[0012] During the simulation data integration process, the weights of each simulation sample under the target ensemble are obtained by iteratively solving the weight equation.

[0013] As a preferred embodiment of the phase transition property prediction method based on complex parameters, in the process of performing equilibrium molecular dynamics simulations under one or more simulation conditions by adjusting the set parameters, the set parameters include one or more of the following: temperature, pressure, electric field, and cosolvent concentration.

[0014] As a preferred embodiment of the phase transition property prediction method based on complex parameters, the expression for the partition function is: ; ; In the formula, Z is an exponential function; Z is a partition function. It is the reciprocal of temperature; Boltzmann's constant; For temperature; The energy of the state.

[0015] As a preferred embodiment of the phase transition property prediction method based on complex parameters, in the process of extending the partition function from the real number domain to the complex plane, the set parameter can be a complex number; when the set parameter is temperature, the reweighted partition function expression is:

[0016]

[0017]

[0018]

[0019] In the formula, The desired system in Partition function at temperature; For the sample in The weights below; Boltzmann's constant; and These are the temperatures before and after reweighting, respectively. for The reciprocal of; for The reciprocal of;

[0020] When the set parameter is pressure, the reweighted partition function expression is:

[0021]

[0022] In the formula, and These represent the pressure before and after reweighting, respectively. This represents the volume of the simulated system in the sample.

[0023] When the set parameter is an electric field, the reweighted partition function expression is:

[0024]

[0025] In the formula, and These represent the pressure before and after reweighting, respectively. Let be the dipole moment of the simulated system in this sample.

[0026] As a preferred embodiment of the phase transition property prediction method based on complex parameters, when the set parameters are used in equilibrium molecular dynamics simulations under several simulation conditions, simulation data are obtained under several ensembles; when the difference between the several ensembles is temperature, the weighting equation expression of MBAR is:

[0027]

[0028]

[0029]

[0030] In the formula, It is an exponential function; subscript Numbering of simulated trajectories under various conditions; For state Samples in For state Samples in Potential energy; Boltzmann's constant; For state Temperature; For state Free energy; The desired state Samples in In state Weights in; For state The number of samples collected; It is the reciprocal of the temperature at each state; For state The number of samples collected;

[0031] The corresponding reweighted partition function expression is:

[0032]

[0033] In the formula, It is the reciprocal of the target temperature;

[0034] When the differences among several ensembles are parameters other than temperature, the weighting equation for MBAR is expressed as follows:

[0035]

[0036]

[0037] In the formula, For state State in the potential energy function Samples in Potential energy; It is the reciprocal of temperature; For state Free energy;

[0038] The corresponding reweighted partition function expression is:

[0039]

[0040] In the formula, The potential energy function of the target state is the state. Samples in Potential energy.

[0041] This invention also provides a complex parameter-based phase transition property prediction device, which, based on the above complex parameter-based phase transition property prediction method, includes:

[0042] The equilibrium molecular dynamics simulation module is used to model the target material system with a selected coarsening degree and select a set force field; determine the parameter range for the phase transition of the target material system; and, based on the parameter range, perform equilibrium molecular dynamics simulations under one or more simulation conditions by adjusting the set parameters to obtain simulation results, and record the energy of the set parameters and the total energy of the target material system.

[0043] The partition function calculation module is used to calculate the partition function of the target material system by summing the system structure sampled from the molecular dynamics simulation based on the simulation results, the energy of the set parameters and the total energy of the target material system.

[0044] The partition function extension module is used to extend the partition function from the real number domain to the complex plane based on the set parameters and through a reweighting strategy;

[0045] The phase transition point determination module is used to calculate the partition function within a set parameter region on the complex plane to obtain the zero point of the partition function on the complex plane; connect the zero points to form a curve; the intersection of the curve and the real axis is the phase transition point of the target material system.

[0046] As a preferred embodiment of the phase transition property prediction device based on complex parameters, in the partition function extension module, if the simulation results under various simulation conditions are obtained through equilibrium molecular dynamics simulation during the process of extending the partition function from the real number domain to the complex plane, then before executing the reweighting strategy, the simulation data of multiple ensembles are integrated into the target ensemble through the MBAR strategy.

[0047] During the simulation data integration process, the weights of each simulation sample under the target ensemble are obtained by iteratively solving the weight equation.

[0048] As a preferred embodiment of a phase transition property prediction device based on complex parameters, in the equilibrium molecular dynamics simulation module, during the process of performing equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting the set parameters, the set parameters include one or more of the following: temperature, pressure, electric field, and cosolvent concentration.

[0049] As a preferred embodiment of the phase transition property prediction device based on complex parameters, the expression of the partition function in the partition function calculation module is as follows:

[0050]

[0051]

[0052] In the formula, Z is an exponential function; Z is a partition function. It is the reciprocal of temperature; Boltzmann's constant; For temperature; The energy of the state.

[0053] As a preferred embodiment of a phase transition property prediction device based on complex parameters, in the partition function extension module, the set parameter can be a complex number during the process of extending the partition function from the real number domain to the complex plane; when the set parameter is temperature, the reweighted partition function expression is:

[0054]

[0055]

[0056]

[0057] In the formula, The desired system in Partition function at temperature; For the sample in The weights below; Boltzmann's constant; and These are the temperatures before and after reweighting, respectively. for The reciprocal of; for The reciprocal of;

[0058] When the set parameter is pressure, the reweighted partition function expression is:

[0059]

[0060] In the formula, and These represent the pressure before and after reweighting, respectively. This represents the volume of the simulated system in the sample.

[0061] When the set parameter is an electric field, the reweighted partition function expression is:

[0062]

[0063] In the formula, and These represent the pressure before and after reweighting, respectively. Let be the dipole moment of the simulated system in this sample.

[0064] As a preferred embodiment of a phase transition property prediction device based on complex parameters, in the partition function extension module, when the set parameters are used for equilibrium molecular dynamics simulation under several simulation conditions, simulation data under several ensembles are obtained; when the difference between the several ensembles is temperature, the weighting equation expression of MBAR is:

[0065]

[0066]

[0067]

[0068] In the formula, It is an exponential function; subscript Numbering of simulated trajectories under various conditions; For state Samples in For state Samples in Potential energy; Boltzmann's constant; For state Temperature; For state Free energy; The desired state Samples in In state Weights in; For state The number of samples collected; It is the reciprocal of the temperature at each state; For state The number of samples collected;

[0069] The corresponding reweighted partition function expression is:

[0070]

[0071] In the formula, It is the reciprocal of the target temperature;

[0072] When the differences among several ensembles are parameters other than temperature, the weighting equation for MBAR is expressed as follows:

[0073]

[0074]

[0075] In the formula, For state State in the potential energy function Samples in Potential energy; It is the reciprocal of temperature; For state Free energy;

[0076] The corresponding reweighted partition function expression is:

[0077]

[0078] In the formula, The potential energy function of the target state is the state. Samples in Potential energy.

[0079] The present invention has the following advantages:

[0080] First, it has low data dependence and lower R&D costs: It does not require a large amount of experimental data or existing databases. Prediction can be completed with only a small amount of equilibrium molecular dynamics simulation data, which greatly reduces the resource investment in experimental synthesis and simulation calculation and shortens the R&D cycle.

[0081] Second, it has high computational efficiency and more thorough sampling: the complex plane extension of the partition function is achieved through the reweighting strategy, and the multi-ensemble data is integrated by the optional MBAR strategy, which effectively overcomes the problem of insufficient sampling in molecular simulation, avoids the high computational cost caused by a large number of parameter scans, and improves prediction efficiency.

[0082] Third, it has a wide range of applications and strong versatility: it supports phase transition prediction with multiple set parameters such as temperature, pressure, and electric field, and can be adapted to different systems such as condensed matter, polymer materials, and biomolecules, covering a variety of phase transition types such as melting and protein folding, with flexible application scenarios.

[0083] Fourth, the results are highly interpretable and accurate in prediction: Based on the core logic of the phase transition theorem, the phase transition point is solved directly through the zero point of the partition function, without the need for a complex fitting model. The physical meaning is clear, and interference such as hysteresis effect can be avoided, thus improving the reliability and accuracy of the prediction results. Attached Figure Description

[0084] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0085] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0086] Figure 1 This is a flowchart illustrating the phase transition property prediction method based on complex parameters provided in Embodiment 1 of the present invention.

[0087] Figure 2 This is a schematic diagram of the partition function on the complex plane in Example 1 of a possible embodiment provided in Embodiment 1 of the present invention;

[0088] Figure 3 This is a schematic diagram of the protein folding structure in Example 2 of a possible embodiment provided in Embodiment 1 of the present invention;

[0089] Figure 4 This is a schematic diagram of the partition function on the complex plane in Example 2 of a possible embodiment provided in Embodiment 1 of the present invention;

[0090] Figure 5 This is a schematic diagram of the intersection point of the curve formed by the zero point and the real axis in Example 2 of a possible embodiment provided in Embodiment 1 of the present invention;

[0091] Figure 6 This is a schematic diagram of the architecture of the phase transition property prediction device based on complex parameters provided in Embodiment 2 of the present invention. Detailed Implementation

[0092] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0093] Example 1

[0094] See Figure 1 Embodiment 1 of the present invention provides a method for predicting phase transition properties based on complex parameters, comprising the following steps:

[0095] S1. Model the target material system by selecting and setting the degree of coarsening and selecting the set force field; determine the parameter range of the target material system undergoing phase transition; based on the parameter range, perform equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting the set parameters, obtain the simulation results, and record the energy of the set parameters and the total energy of the target material system.

[0096] S2. Based on the simulation results, the energy of the set parameters, and the total energy of the target material system, the partition function of the target material system is calculated by summing the system structure sampled from the molecular dynamics simulation.

[0097] S3. Based on the set parameters, the partition function is extended from the real number domain to the complex plane through a reweighting strategy;

[0098] S4. Calculate the partition function within the set parameter region on the complex plane to obtain the zero point of the partition function on the complex plane; connect the zero points to form a curve; the intersection of the curve and the real axis is the phase transition point of the target material system.

[0099] In this embodiment, in step S1, the target material system is modeled with a set coarsening degree and a set force field is selected; the parameter range for the phase transition of the target material system is determined; based on the parameter range, equilibrium molecular dynamics simulation is performed under one or more simulation conditions by adjusting the set parameters to obtain simulation results, and the energy of the set parameters and the total energy of the target material system are recorded.

[0100] Specifically, the initial step involves selecting an appropriate level of coarsening for modeling based on the type of the target material system and the required research precision. This simplifies the complex molecular system into a computationally friendly model structure. Simultaneously, a force field matching the system's characteristics is chosen to ensure simulation accuracy. Subsequently, through literature review, preliminary exploratory experiments, or theoretical analysis, the approximate parameter range for phase transitions in the target system is determined, providing a clear direction for subsequent simulations. Based on this parameter range, parameters such as temperature, pressure, electric field, and co-solvent concentration are adjusted, and equilibrium molecular dynamics simulations are conducted under one or more different simulation conditions. During the simulation, the system must be maintained in equilibrium to ensure the reliability of the sampled data. Finally, the energies directly related to the set parameters and the total energy of the target material system are recorded simultaneously during the simulation, providing core data support for subsequent partition function calculations.

[0101] In this embodiment, in step S2, based on the simulation results, the energy of the set parameters, and the total energy of the target material system, the partition function of the target material system is calculated by summing the system structure sampled from the molecular dynamics simulation.

[0102] Specifically, the partition function obtained using molecular simulation is:

[0103]

[0104]

[0105] In the formula, Z is an exponential function; Z is a partition function. It is the reciprocal of temperature; Boltzmann's constant; For temperature; Let be the energy of the state; the summation of the first equality traverses all states of the system, and the summation of the second equality traverses the system architecture sampled by the molecular simulation. The first equality is the definition of the partition function under the canonical ensemble.

[0106] Regarding the result of the second equality, assuming the molecular simulation trajectory is sufficiently long and has sampled all states of the molecular system, then... The summation already includes all states of the system. Since the simulation sampling results conform to a Boltzmann distribution, the energy is... The frequency of occurrence of a state is proportional to At this point, the second equality in the above equation holds true when the difference is a constant factor. Since we only care about the zeros of the partition function, the constant factor (or normalization constant) is not important and is omitted here. Also, note that... This is the number of structural samples in the molecular simulation, which in a typical molecular simulation process is the normalization factor used when averaging the trajectories, consistent with the intuitive meaning of the partition function. This partition function forms the basis for subsequent reweighting.

[0107] In this embodiment, in step S3, based on the set parameters, the partition function is extended from the real number domain to the complex plane through a reweighting strategy.

[0108] Specifically, using the partition function calculated in step S2 and the set parameters determined in step S1 as the core, a reweighting strategy is employed to extend the domain of the partition function. The core logic of the reweighting strategy is to map the partition function data under existing simulation conditions to partition functions under other parameter conditions by introducing weighting factors. Unlike traditional reweighting, this step allows the target set parameters to be complex numbers. By extending the parameters from the real domain to the complex domain, the partition function is extended from the real domain to the complex plane.

[0109] In this embodiment, the reweighting method is a commonly used method for processing molecular simulation data. It can obtain properties under another simulation condition by reweighting simulation data under a certain condition. In this invention, the reweighting method is used to extend the parameters from the real number domain to the complex number domain.

[0110] If the quantity that needs to be reweighted in the simulation is temperature, assume the simulation is in The process is carried out at a specific temperature, requiring the system to be in a state of equilibrium. Properties at temperature. The energy collected by molecular simulation is... The sample needs to be weighted. Then calculate the sample average. The following formula can be used to calculate... The partition function simulated at temperature is mapped as follows The partition function at temperature (for the right side of the definition of the partition function) Reweighting, that is, reweighting Become ):

[0111]

[0112]

[0113]

[0114] In the formula, The desired system in Partition function at temperature; For the sample in The weights below; Boltzmann's constant; and These are the temperatures before and after reweighting, respectively. for The reciprocal of; for The reciprocal of.

[0115] Molecular simulation in The following will proceed, so It must be a real number. In typical reweighted methods, the target temperature... It is also a real number. In this embodiment, it is considered that... It can be a complex number, thus extending the partition function to the complex plane. Simultaneously, energy... Only the potential energy of the simulated system is taken because various heating methods are used to control the temperature during molecular simulation sampling. The kinetic energy of the simulated system is the same for all samples and can be ignored. Forcibly introducing kinetic energy would only introduce additional noise.

[0116] In this embodiment, similarly, the reweighted partition function can be derived when other parameters of the system need to be reweighted.

[0117] For example, in studying pressure-related phase transitions, reweighted pressure is used. The energy related to pressure is... ,in For pressure, Let represent the volume of the simulated system. The corresponding reweighted form of the partition function is:

[0118]

[0119] In the formula, and These represent the pressure before and after reweighting, respectively. This represents the volume of the simulated system in the sample.

[0120] When studying phase transitions related to electric fields, a reweighted electric field is used. The energy related to the electric field is... ,in For electric field, It is a dipole moment. It's a vector dot product. Note that, typically, the energy of a charged particle in an electric field is... ,in For electric field, For charge, The position parameter is rewritten here in a form related to the system's dipole moment to facilitate energy calculation in molecular simulations. The corresponding reweighted form of the partition function is:

[0121]

[0122] In the formula, and These represent the pressure before and after reweighting, respectively. Let be the dipole moment of the simulated system in this sample.

[0123] When studying phase transitions controlled by other parameters, the reweighted form of the corresponding partition function can also be written based on the energy term corresponding to that parameter.

[0124] The reweighting methods described above only reweight trajectories under one simulation condition. However, due to time constraints in molecular simulations, using simulation data from only one condition often leads to insufficient sampling. To mitigate this limitation, simulation data from multiple conditions can be combined when calculating the partition function, thus expanding the sample range obtained from the simulation. The MBAR method can integrate simulation data from multiple ensembles into a single simulation ensemble, extending the reweighting method from reweighting simulation data under a single condition to reweighting simulation data under multiple conditions. Assuming that... Simulations were conducted under different external parameters, and the results were obtained. A ensemble (also known as Simulated data under (each state).

[0125] in, When the difference between the states is temperature, the weighting equation for MBAR is as follows:

[0126]

[0127]

[0128]

[0129] In the formula, It is an exponential function; subscript Numbering of simulated trajectories under various conditions; For state Samples in For state Samples in Potential energy; Boltzmann's constant; For state Temperature; For state Free energy; The desired state Samples in In state Weights in; For state The number of samples collected; It is the reciprocal of the temperature at each state; For state The number of samples collected;

[0130] The corresponding reweighted partition function expression is:

[0131]

[0132] In the formula, It is the reciprocal of the target temperature;

[0133] when When the difference between the states is a parameter other than temperature, the weighting equation for MBAR is as follows:

[0134]

[0135]

[0136] In the formula, For state State in the potential energy function Samples in Potential energy; It is the reciprocal of temperature; For state Free energy;

[0137] The corresponding reweighted partition function expression is:

[0138]

[0139] In the formula, The potential energy function of the target state is the state. Samples in Potential energy.

[0140] In this embodiment, in the above formula, the energy term related to external parameters... The expression depends on the specific external parameters. For example, when the pressure changes, the energy is... ,in, For pressure, To simulate the volume of the system. When the parameter is changed to the electric field, the energy is... ,in For external electric field, Let be the dipole moment of the system. This is a vector dot product. When the concentration of the co-solvent in the solution changes, the energy is... , The concentration of the co-solvent The solvent-accessible surface area of ​​the solute. It is a coefficient related to the properties of the co-solvent. Similar energy terms may exist for other externally induced phase transitions.

[0141] In this embodiment, in step S4, the partition function is calculated within a set parameter region on the complex plane to obtain the zero point of the partition function on the complex plane; the zero points are connected to form a curve; the intersection of the curve and the real axis is the phase transition point of the target material system.

[0142] Specifically, a sufficiently large region of parameters is selected on the complex plane, and the partition function of the complex plane extended in step S3 is fully calculated. Multiple parameter points within this region are traversed to obtain the corresponding partition function values ​​for each point. Then, based on the condition that the partition function value is zero, all zero points of the partition function on the complex plane are selected. These zero points are directly related to the phase transition characteristics of the system. Since the simulated system differs somewhat from the thermodynamic limit, the zero points may not perfectly approximate the real axis; therefore, all zero points need to be connected to form a continuous curve. Finally, according to the Li-Yang phase transition theorem, the intersection of this curve and the real axis is the phase transition point of the target material system. The parameter values ​​corresponding to this intersection point, such as temperature and pressure, are the key parameters for the phase transition of the system.

[0143] In one possible implementation, two verification examples are provided as follows:

[0144] Example 1: Finding the phase transition point of a two-dimensional Ising model

[0145] The Ising model is a simplified model for describing ferromagnetic materials and can be used to describe the transition between ferromagnetism and paramagnetism in materials.

[0146] T1. Construct the simulation system and perform simulation:

[0147] structure A two-dimensional mesh is constructed, with a spin pointer placed at each mesh point, which can spin upwards or downwards. Two-dimensional periodic boundary conditions are used, meaning the left, right, top, and bottom boundaries of the mesh are interconnected, to simulate an infinitely large mesh. It is assumed that... The two spins connected by the edges of the grid are nearest neighbors. The total energy of the system is:

[0148]

[0149] In the formula, The total energy of the system; for The spin; for The spin (two spin directions are) or ), To obtain a simplified dimensionless interaction energy, summate all nearest neighbors in the grid. To correct the neighbor and The energy coefficient is calculated repeatedly.

[0150] In this model, a ferromagnetic phase transition may occur. When the temperature is above the transition temperature, all spins are randomly aligned; when the temperature is below the transition temperature, all spins are aligned in one direction.

[0151] In the initial state, all spins are pointing towards Orientation. In each step of the simulation, attempt to flip a random spin; the energy change before and after the flip is... .like Then accept this spin flip. If Then The probability of accepting this spin flip is [percentage missing]. In the formula, [formula missing]. It is an exponential function. It is the reciprocal of temperature. It is Boltzmann's constant. This is a simulated temperature. Here we take... (Use simplified units) It refers to the energy change before and after the spin flip.

[0152] A simulated trajectory was run at temperatures of 2, 2.4, 2.8, and 3.2 degrees Celsius. Each simulated trajectory ran for 320,000 steps, with the data from the last 160,000 steps used for analysis. Data was recorded every 500 steps.

[0153] T2. Calculate the partition function under complex parameters:

[0154] The four simulated trajectories under conditions 2, 2.4, 2.8, and 3.2 were merged into the same ensemble using the MBAR method, and the partition function at complex temperatures was calculated. The partition function was calculated at the following complex temperatures:

[0155]

[0156]

[0157] In the formula, The real part representing temperature; The imaginary part representing temperature. and Take integers from 0 to 999. That is, calculate the partition function at 1,000,000 complex temperatures, where the real part of the temperature is... to Between, the imaginary part is to Between. The calculation results are as follows: Figure 2 As shown, where, Figure 2 B and Figure 2A is exactly the same, except that the color bar has changed in order to show the point-like minimum value.

[0158] T3. Locating the phase transition point:

[0159] from Figure 2 As can be seen, the partition function exhibits clear point-like minima. Since current scanning calculation methods cannot calculate the precise zeros, these point-like minima are considered to be the zeros of the partition function. These zeros connect to form a clear curve, and the intersection of the curve and the real axis is 2.73, which is the phase transition point.

[0160] Example 2: Calculate the folding temperature of a protein

[0161] M1. Determine the substance to be calculated and its phase transition:

[0162] The substance to be calculated in this example is a G protein (PDB encoding: 2IGD). Its native structure is as follows: Figure 3 As shown in Figure A. In molecular simulations, coarse-grained simulations are used, transforming an amino acid residue into a particle, such as... Figure 3 As shown in Figure B, the simulation was performed using the structure-based AICG2+ force field developed by Li Wenfei et al. This is a structure-based force field that has been widely used to study structural changes in proteins, such as folding and allosteric transformation. No additional adjustments were made to the force field parameters.

[0163] M2, Perform molecular dynamics simulations:

[0164] Molecular dynamics simulations were performed on this protein. The simulations were conducted at 200K, 300K, 400K, and 450K. The simulation system consisted of isolated protein molecules with aperiodic boundary conditions. Cafemol 3.2.1 software was used for the simulations. The simulations started from the native state of the protein, with a single trajectory length of 50,000,000 steps and a time step of [missing information]. ,in This is the internal time unit of the simulation software. One simulation trajectory is run for each temperature. The simulation uses an NVT ensemble and a Langevin thermostat for temperature control. Energy data is stored every 10,000 steps, and the first fifth of the trajectory data is discarded during analysis.

[0165] A brief observation of the simulated trajectories revealed that at 200K, the protein primarily adopted its native state structure. At 450K, the protein primarily adopted its unfolded, folded structure, such as... Figure 3 As shown in Figure C, this indicates that between 200K and 450K, proteins undergo a phase transition from their native state to their unfolded state.

[0166] M3. Using the MBAR method, the four simulated trajectories at 200K, 300K, 400K, and 450K are merged into the same ensemble, and the partition function at complex temperatures is calculated:

[0167] The partition function is calculated at the following complex temperatures:

[0168]

[0169]

[0170] In the formula, The real part representing temperature; The imaginary part representing temperature. and Take integers from 0 to 999. That is, calculate the partition function at 1,000,000 complex temperatures, where the real part of the temperature is... to Between, the imaginary part is to between.

[0171] As can be seen, at complex temperatures, the partition function exhibits a clear point-like minimum, which is considered to be zero here, such as... Figure 4 As shown. Among them, Figure 4 B and Figure 4 A is exactly the same, except that the color bar has changed in order to show the point-like minimum value.

[0172] M4. Analyze the distribution of zeros, connect the curves formed by the zeros, and obtain the intersection points of the curves and the real axis:

[0173] The results are as follows Figure 5 As shown, Figure 5 In the diagram, the red horizontal line represents the real axis, and the red vertical line connects the two zeros closest to the real axis. After identifying the two zeros closest to the real axis, the point where they intersect the real axis is found. It can be concluded that the phase transition temperature (i.e., folding temperature) of this G protein under the given simulation conditions is 389 K. Figure 5 The position marked by the red pentagram on the central horizontal axis.

[0174] The application scenarios of this invention are as follows:

[0175] In the context of polymer material research and development, this invention can quickly predict the glass transition temperature and melting temperature of materials, providing accurate basis for optimizing the heat resistance, flexibility and other properties of materials, and shortening the research and development cycle.

[0176] In the context of biomolecular research, this invention can efficiently predict the folding temperature of proteins, helping to understand the mechanisms of biomolecular structural stability and providing technical support for fields such as drug design and enzyme engineering.

[0177] In the development of liquid crystal materials, this invention can accurately predict the phase transition conditions of liquid crystals from random phase to nematic phase, guide the design of liquid crystal molecular structures, and optimize their optical performance and application adaptability.

[0178] In the research and development of ferromagnetic materials, this invention can accurately locate the transition temperature between the ferromagnetic and paramagnetic states, providing key data support for the design of the temperature range of magnetic devices and the improvement of their performance.

[0179] In the exploration of novel functional materials, this invention does not rely on a large amount of experimental data and can quickly predict the phase transition characteristics of unknown materials, thereby reducing the cost of innovative research and development in fields such as new energy materials and environmental protection materials.

[0180] In the research scenario of materials under extreme conditions, this invention can predict the phase transition behavior of materials under special conditions such as electric fields and high pressures, providing a theoretical reference for the study of the properties of materials in extreme environments in fields such as astrophysics and nuclear fusion.

[0181] In pharmaceutical research and development, this invention can predict phase transitions and structural changes of drug molecules under different environmental conditions, guide drug dosage form design and storage condition optimization, and improve drug stability and efficacy.

[0182] In industrial material selection scenarios, this invention can quickly compare the phase transformation characteristics of different materials, providing a scientific basis for material selection in industries such as aerospace and electronic equipment, and ensuring the reliability of products under specific working conditions.

[0183] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0184] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0185] Example 2

[0186] See Figure 6 Embodiment 2 of the present invention also provides a phase transition property prediction device based on complex parameters, comprising:

[0187] The equilibrium molecular dynamics simulation module 001 is used to model the target material system by selecting a set coarsening degree and selecting a set force field; determine the parameter range of the target material system undergoing phase transition; based on the parameter range, perform equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting the set parameters, obtain simulation results, and record the energy of the set parameters and the total energy of the target material system.

[0188] The partition function calculation module 002 is used to calculate the partition function of the target material system by summing the system structure sampled from the molecular dynamics simulation based on the simulation results, the energy of the set parameters and the total energy of the target material system.

[0189] The partition function extension module 003 is used to extend the partition function from the real number domain to the complex plane based on the set parameters and through a reweighting strategy;

[0190] The phase transition point determination module 004 is used to calculate the partition function within a set parameter region on the complex plane to obtain the zero point of the partition function on the complex plane; connect the zero points to form a curve; the intersection of the curve and the real axis is the phase transition point of the target material system.

[0191] In this embodiment, in the partition function extension module 003, if the simulation results under various simulation conditions are obtained through equilibrium molecular dynamics simulation during the process of extending the partition function from the real number domain to the complex plane, the simulation data of multiple ensembles are integrated into the target ensemble through the MBAR strategy before executing the reweighting strategy.

[0192] During the simulation data integration process, the weights of each simulation sample under the target ensemble are obtained by iteratively solving the weight equation.

[0193] In this embodiment, in the equilibrium molecular dynamics simulation module 001, during the process of performing equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting the set parameters, the set parameters include one or more of temperature, pressure, electric field and cosolvent concentration.

[0194] In this embodiment, in the partition function calculation module 002, the expression of the partition function is:

[0195]

[0196]

[0197] In the formula, Z is an exponential function; Z is a partition function. It is the reciprocal of temperature; Boltzmann's constant; For temperature; The energy of the state.

[0198] In this embodiment, in the partition function extension module 003, during the process of extending the partition function from the real number domain to the complex plane, the set parameter can be a complex number; when the set parameter is temperature, the reweighted partition function expression is:

[0199]

[0200]

[0201]

[0202] In the formula, The desired system in Partition function at temperature; For the sample in The weights below; Boltzmann's constant; and These are the temperatures before and after reweighting, respectively. for The reciprocal of; for The reciprocal of;

[0203] When the set parameter is pressure, the reweighted partition function expression is:

[0204]

[0205] In the formula, and These represent the pressure before and after reweighting, respectively. This represents the volume of the simulated system in the sample.

[0206] When the set parameter is an electric field, the reweighted partition function expression is:

[0207]

[0208] In the formula, and These represent the pressure before and after reweighting, respectively. Let be the dipole moment of the simulated system in this sample.

[0209] In this embodiment, in the partition function extension module 003, when the set parameters are used for equilibrium molecular dynamics simulation under several simulation conditions, simulation data under several ensembles are obtained; when the difference between the several ensembles is temperature, the weighting equation expression of MBAR is:

[0210]

[0211]

[0212]

[0213] In the formula, It is an exponential function; subscript Numbering of simulated trajectories under various conditions; For state Samples in For state Samples in Potential energy; Boltzmann's constant; For state Temperature; For state Free energy; The desired state Samples in In state Weights in; For state The number of samples collected; It is the reciprocal of the temperature at each state; For state The number of samples collected;

[0214] The corresponding reweighted partition function expression is:

[0215]

[0216] In the formula, It is the reciprocal of the target temperature;

[0217] When the differences among several ensembles are parameters other than temperature, the weighting equation for MBAR is expressed as follows:

[0218]

[0219]

[0220] In the formula, For state State in the potential energy function Samples in Potential energy; It is the reciprocal of temperature; For state Free energy;

[0221] The corresponding reweighted partition function expression is:

[0222]

[0223] In the formula, The potential energy function of the target state is the state. Samples in Potential energy.

[0224] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0225] Example 3

[0226] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a phase transition property prediction method based on complex parameters. The program code includes instructions for executing the phase transition property prediction method based on complex parameters of Embodiment 1 or any possible implementation thereof.

[0227] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0228] Example 4

[0229] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0230] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute the complex parameter-based phase transition property prediction method of Embodiment 1 or any possible implementation thereof by calling the program instructions.

[0231] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0232] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0233] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0234] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting phase transition properties based on complex variables, characterized in that, The method comprises the following steps: modeling and setting a coarse-graining degree for a target substance system, and setting a force field for the target substance system; determining a parameter range in which a phase transition of the target substance system occurs; based on the parameter range, performing equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting a set parameter, obtaining simulation results, and recording energy of the set parameter and total energy of the target substance system; based on the simulation results, the energy of the set parameter and the total energy of the target substance system, calculating a partition function of the target substance system by summing up system structures sampled by molecular dynamics simulation; based on the set parameter, extending the partition function from a real number domain to a complex plane by a reweighting strategy; calculating the partition function in a region of the set parameter on the complex plane to obtain a zero point of the partition function on the complex plane; connecting the zero point to form a curve; and an intersection of the curve and a real axis is a phase transition point of the target substance system.

2. The complex variable-based phase change property prediction method of claim 1, wherein, In the process of extending the partition function from the real number domain to the complex plane, if the simulation results under multiple simulation conditions are obtained by equilibrium molecular dynamics simulation, the simulation data of multiple ensembles are integrated into a target ensemble by an MBAR strategy before the reweighting strategy is performed; in the simulation data integration process, the corresponding weight of each simulation sample in the target ensemble is obtained by iteratively solving a weight equation.

3. The complex variable-based phase change property prediction method of claim 2, wherein, In the process of performing equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting the set parameter, the set parameter comprises one or more of temperature, pressure, electric field and cosolvent concentration.

4. The complex variable-based phase change property prediction method of claim 3, wherein, The expression of the partition function is: ； ； wherein is an exponential function; Z is a partition function; is the inverse of the temperature; is the Boltzmann constant; is the temperature; is the energy of the state.

5. The complex variable-based phase change property prediction method of claim 4, wherein, In the process of extending the partition function from the real number domain to the complex plane, the set parameter can be a complex number; when the set parameter is temperature, the expression of the reweighted partition function is: ； ； ； In the formula, The desired system in Partition function at temperature; For the sample in The weights below; Boltzmann's constant; and These are the temperatures before and after reweighting, respectively. for The reciprocal of; for The reciprocal of; when the set parameter is pressure, the expression of the reweighted partition function is: ； wherein and are the pressure before / after reweighting, respectively; is the volume of the simulated system in the sample; when the set parameter is an electric field, the expression of the reweighted partition function is: ； wherein and are the pressure before / after reweighting, respectively; is the dipole moment of the simulated system in the sample.

6. The complex variable-based phase change property prediction method of claim 5, wherein, When the set parameter is used to perform equilibrium molecular dynamics simulation under several simulation conditions, simulation data under several ensembles are obtained; when the difference between the several ensembles is temperature, the weight equation expression of MBAR is: ； ； ； In the formula, It is an exponential function; subscript Numbering of simulated trajectories under various conditions; For state Samples in For state Samples in Potential energy; Boltzmann's constant; For state Temperature; For state Free energy; The desired state Samples in In state Weights in; For state The number of samples collected; It is the reciprocal of the temperature at each state; For state The number of samples collected; The corresponding reweighted partition function expression is: ； In the formula, is the inverse of the target temperature; When the difference between the several ensembles is a parameter other than temperature, the weight equation expression of MBAR is: ； ； wherein is the potential energy function of state is the free energy of state is the potential energy of a sampled sample in state is the inverse of the temperature; is the free energy of state​​ The corresponding reweighted partition function expression is: ； wherein the potential energy function of the state in the state of the target state.

7. Apparatus for predicting phase change properties based on complex variables, using the method for predicting phase change properties based on complex variables according to any one of claims 1 to 6, characterized in that The method comprises the following steps: a equilibrium molecular dynamics simulation module is used to model and set a coarse-graining degree for a target substance system, and set a force field for the target substance system; determining a parameter range in which a phase transition of the target substance system occurs; based on the parameter range, performing equilibrium molecular dynamics simulation under one or more simulation conditions by adjusting a set parameter, obtaining simulation results, and recording energy of the set parameter and total energy of the target substance system; The partition function calculation module is configured to calculate the partition function of the target material system by summing up the system structures sampled by the molecular dynamics simulation based on the simulation result, the energy of the set parameter, and the total energy of the target material system. The partition function extension module is configured to extend the partition function from the real number field to the complex plane by a reweighting strategy based on the set parameter. The phase transition point determination module is configured to calculate the partition function in the set parameter region on the complex plane, obtain the zero point of the partition function on the complex plane, connect the zero points to form a curve, and determine the phase transition point of the target material system as the intersection of the curve and the real axis.

8. The complex variable based phase change property prediction apparatus of claim 7, wherein, In the process of extending the partition function from the real number field to the complex plane, if the simulation result under multiple simulation conditions is obtained by equilibrium molecular dynamics simulation, the simulation data of multiple ensembles is integrated into a target ensemble by an MBAR strategy before the reweighting strategy is performed. In the simulation data integration process, the corresponding weight of each simulation sample in the target ensemble is obtained by iteratively solving a weight equation. In the process of adjusting the set parameter to perform equilibrium molecular dynamics simulation under one or more simulation conditions, the set parameter includes one or more of temperature, pressure, electric field, and cosolvent concentration.

9. The complex variable based phase change property prediction apparatus of claim 8, wherein, In the partition function calculation module, the expression of the partition function is ； ； wherein is an exponential function; Z is a partition function; is the inverse of the temperature; is the Boltzmann constant; is the temperature; is the energy of the state.

10. The complex variable based phase change property prediction apparatus of claim 9, wherein, In the process of extending the partition function from the real number field to the complex plane, the set parameter can be a complex number. When the set parameter is temperature, the expression of the reweighted partition function is ； ； ； wherein is the partition function of the system sought at temperature; is the weight of the sample at temperature; is the Boltzmann constant; and are the temperatures before / after reweighting, respectively; is the inverse of ; is the inverse of ; is the inverse of ; When the set parameter is pressure, the expression of the reweighted partition function is ； wherein and are the pre / post weightings of pressure, respectively; is the volume of the simulated system in the sample; When the set parameter is an electric field, the expression of the reweighted partition function is ； wherein and are the pressure before / after reweighting, respectively; is the dipole moment of the simulated system in the sample. In the partition function extension module, when the set parameter is used to perform equilibrium molecular dynamics simulation under multiple simulation conditions, simulation data under multiple ensembles is obtained. When the difference between the multiple ensembles is temperature, the weight equation expression of MBAR is ； ； ； In the formula, It is an exponential function; subscript Numbering of simulated trajectories under various conditions; For state Samples in For state Samples in Potential energy; Boltzmann's constant; For state Temperature; For state Free energy; The desired state Samples in In state Weights in; For state The number of samples collected; It is the reciprocal of the temperature at each state; For state The number of samples collected; The corresponding reweighted partition function expression is ； wherein is the inverse of the target temperature; When the difference between the multiple ensembles is a parameter other than temperature, the weight equation expression of MBAR is ； ； In the formula, For state State in the potential energy function Samples in Potential energy; It is the reciprocal of temperature; For state Free energy; The corresponding reweighted partition function expression is ； wherein the potential energy function of the state in the sampled sample of the target state.

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