Time series based weighted probability density processing method and related devices

Abstract

The application discloses a time series-based weighted probability density processing method and related equipment, and the method comprises the following steps: obtaining an approximate function of a first time series and a second time series respectively based on a linear interpolation method; obtaining a time point at each interval boundary based on the approximate function of the first time series; dividing the approximate function of the first time series and the approximate function of the second time series into time series segments based on the time point; obtaining the time series segments, and assigning a weight of the time series segment to a corresponding interval to obtain a weighted probability density. The application obtains a time point of an approximate function of a variable at each interval boundary, divides the approximate function of the variable into time series segments according to the obtained time point, and assigns a weight to the interval, so that the calculation of the weighted probability density of the variable is closer to the true value than the result calculated by a weighted histogram without interpolation, and the result along the change range of the variable is very small.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer, in particular to a time series based weighted probability density processing method and related equipment. BACKGROUND

[0002] Time series are ubiquitous in the research of chemistry, physics, biology and materials. In experimental research, the observations recorded at different time for some variables are time series of the variables. In theoretical research, computer simulation, especially molecular dynamics simulation, is widely used in the basic and applied research of natural science. The results of these simulations are also time series of some variables. In the analysis of these time series, estimating the probability density function of a variable and the conditional expectation of a variable are common operations.

[0003] In the prior art, when the width of the interval is large, if the time series values in the time interval are distributed in multiple intervals, assigning all the weights in the time interval to the same interval will result in inaccurate weighted probability density function and large numerical oscillation.

[0004] Therefore, the prior art still needs to be improved and developed. SUMMARY

[0005] The main purpose of the present application is to provide a time series based weighted probability density processing method and related equipment, which aims to solve the problem that in the prior art, when the time interval is large, if the time series values in the time interval are distributed in multiple intervals, assigning all the weights in the time interval to the same interval will result in inaccurate calculation and large numerical oscillation.

[0006] To achieve the above purpose, the present application provides a time series based weighted probability density processing method, which comprises the following steps:

[0007] obtaining an approximate function of the first time series and the second time series based on linear interpolation method respectively;

[0008] obtaining the time at the boundary of each interval based on the approximate function of the first time series;

[0009] Based on the stated time, both the approximation function of the first time series and the approximation function of the second time series are divided into time series segments;

[0010] The time series segments are obtained, and the weights of the time series segments are assigned to the corresponding intervals to obtain the weighted probability density.

[0011] Optionally, in the time series-based weighted probability density processing method, the approximate functions of the first and second time series are both piecewise continuous functions with iΔt as the segmentation point.

[0012] Optionally, the weighted probability density processing method based on time series, wherein obtaining the time at each interval boundary based on the approximation function of the first time series further includes:

[0013] The range of values ​​of variable g in the first time series g(t) is divided into multiple intervals.

[0014] Optionally, in the time-series-based weighted probability density processing method, the step of segmenting both the approximation function of the first time series and the approximation function of the second time series into time series segments based on the time point specifically involves:

[0015] Based on the stated time, the time interval [iΔt, (i+1)Δt] is divided into time series segments by approximating the first time series g(t) and the second time series f(t).

[0016] Optionally, in the aforementioned time-series-based weighted probability density processing method, the formula for calculating the weighted probability density is:

[0017]

[0018] in, Let f(t) represent the weighted probability density function, g represent the variable, Δg represent the interval width, N represent the number of values ​​in the discretized expression of the time series f(t), Δt represent the time interval between two adjacent points in the time series, i represent a natural number between 0 and N, and g represents the index of the i-th value in the time series. i Let g(t) be the value of the first time series at time iΔt. i+1 Let f be the value of the first time series g(t) at time (i+1)Δt. i Let f(t) represent the value of the second time series f(t) at time iΔt. i+1 Let f(t) represent the value of the second time series f(t) at time (i+1)Δt, and P(g) represent the value of the second time series f(t) at time (i+1)Δt. i g i+1 , g, Δg) represent piecewise functions.

[0019] Optionally, in the time series-based weighted probability density processing method, the formula for the piecewise function is:

[0020]

[0021] Among them, sgn(g i+1 -g i H(g) is the sign function. i -g, Δg) represents the defined function H(x, Δg) where x = g i The value of H(g) when -g is given. i+1 -g, Δg) represents the defined function H(x, Δg) where x = g i+1 The value when -g.

[0022] Optionally, in the aforementioned time-series-based weighted probability density processing method, the formula for the function H(x, Δg) is:

[0023]

[0024] Furthermore, to achieve the above objectives, the present invention also provides a system for calculating weighted probability density values ​​in a time series, wherein the system for calculating weighted probability density values ​​in a time series includes:

[0025] The function acquisition module is used to obtain approximate functions for the first time series and the second time series based on the linear interpolation method, respectively.

[0026] The time acquisition module is used to acquire the time at each interval boundary based on an approximation function of the first time series;

[0027] The function segmentation module is used to segment both the approximate function of the first time series and the approximate function of the second time series into time series segments based on the time point.

[0028] The assignment module is used to obtain the time series segment and assign the weight of the time series segment to the corresponding interval to obtain the weighted probability density.

[0029] Furthermore, to achieve the above objectives, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a time-series-based weighted probability density processing program stored in the memory and executable on the processor, wherein when the time-series-based weighted probability density processing program is executed by the processor, it implements the steps of the time-series-based weighted probability density processing method as described above.

[0030] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a time-series-based weighted probability density processing program, which, when executed by a processor, implements the steps of the time-series-based weighted probability density processing method as described above.

[0031] In this invention, approximate functions for a first time series and a second time series are obtained based on linear interpolation. The time at each interval boundary is obtained based on the approximate function of the first time series. Based on these times, both the approximate functions of the first and second time series are divided into time series segments. The weights of these time series segments are then assigned to the corresponding intervals to obtain a weighted probability density. This invention obtains the times of the approximate functions of variables at each interval boundary, divides the approximate functions of variables into time series segments according to the obtained times, and assigns weights to the intervals. This results in a weighted probability density calculation that is closer to the true value than the result calculated by a weighted histogram without interpolation, and the result exhibits a smaller variation along the variable, meaning the error and error rate are significantly lower. Attached Figure Description

[0032] Figure 1 The flux along Φ calculated using the weighted histogram expression in existing technologies is... Result diagram;

[0033] Figure 2 This is a schematic diagram of the average force calculated using the weighted histogram expression in the prior art;

[0034] Figure 3 This is a flowchart of a preferred embodiment of the weighted probability density processing method based on time series data of the present invention;

[0035] Figure 4 This is a schematic diagram of the corresponding segmentation of the time series obtained by linear interpolation in this invention within each interval;

[0036] Figure 5 This is a schematic diagram showing the relationship between the time interval [iΔt, (i+1)Δt] and the position of the small box in this invention;

[0037] Figure 6 This is the flux along Φ calculated using the weighted probability density expression in this invention. Result diagram;

[0038] Figure 7 This is a schematic diagram of the average force calculated using the weighted probability density expression in this invention;

[0039] Figure 8 This is a schematic diagram of a preferred embodiment of the weighted probability density processing system based on time series data of the present invention.

[0040] Figure 9 This is a schematic diagram of the operating environment of a preferred embodiment of the device of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0042] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0043] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0044] In the prior art, assuming g(t) is the first time series of variable g, then the expression for the probability density function ρ(g) of variable g is: Where δ(x) is the Dirac delta function; define f(t) as the second time series of any variable, where the derivative of the second time series f(t) with respect to time t (df(t) / dt) is also a variable. Consider the weighted probability density function of g(t) with weights of df(t) / dt, which is a function of the variable g. To represent, its expression is The weighted probability density function can be viewed as a generalization of the probability density function; that is, the probability density function is a special case of the weighted probability density function (when df(t) / dt = 1 or when f(t) = t). The conditional mean of a variable and the weighted probability density function are closely related; the expression for the conditional mean of the variable df(t) / dt with respect to the variable g(t) at g(t) = g is: It is easy to see that E(g;f) = F(g;f) / ρ(g) or F(g;f) = E(g;f)*ρ(g), so F(g;f) is also called the probability density weighted conditional expectation. In physical chemistry, flux is a kind of weighted probability density. Flux along a certain generalized coordinate can be regarded as the weighted probability density of the coordinate itself with the weight of the generalized velocity corresponding to that generalized coordinate, that is, the case when both variables g and f are generalized coordinates. There is a very close relationship between flux and reaction rate, which can be used for the identification of reaction coordinates and the calculation of kinetic parameters. In molecular dynamics simulations, when the variable f is the potential energy of the simulated system and the variable g is a generalized coordinate, the weighted probability density along the generalized coordinate, with the change of potential energy over time as the weight, and the entropy of the flux, constitute the mean force of that generalized coordinate. The mean force can provide information about the various important states of the system (including reaction states, transition states, and product states). At the same time, the mean potential can be calculated from the mean force. Therefore, the mean force along the reaction coordinate is very important for calculating the thermodynamic parameters and reaction mechanisms of the system.

[0045] In actual calculations using existing technologies, the weighted probability density function of the variables... The calculation uses a weighted histogram to estimate the value of df(t) / dt (weighted by the values ​​of the variable df(t) / dt). This weighted histogram estimation method can be seen as a voting method. In this method, the range of variable g is first divided into multiple bins (a series of intervals generated when segmenting the range of variables in the histogram construction). Each observation sample votes in its corresponding bin, and the number of votes is the value of variable df(t) / dt. Assuming the center position of a small box is variable g, the specific expression for calculating the total number of votes for that small box (also known as the expression for the weighted histogram) is:

[0046]

[0047] in,

[0048] in, Let f(t) represent the weighted probability density function, g represent the variable, Δg represent the interval width, N represent the number of values ​​in the discretized expression of the time series f(t), Δt represent the time interval between two adjacent points in the time series, i is a natural number between 0 and N, and g represents the index of the i-th value in the time series. i Let g(t) be the value of the first time series at time iΔt. i+1 Let f be the value of the first time series g(t) at time (i+1)Δt. i Let f(t) represent the value of the second time series f(t) at time iΔt. i+1 H((g) represents the value of the second time series f(t) at time (i+1)Δt. i+1 +g i () / 2-g, Δg) means assigning all weights df(t) / dt within the time interval [iΔt, (i+1)Δt] to (g). i+1 +g i The interval where ) / 2 is located; to more intuitively illustrate the shortcomings of weighted histogram estimation, we will take flux and average force along a certain generalized coordinate as an example for specific explanation; in molecular dynamics simulations, alanine dipeptide is a commonly used model system. This system has two stable conformations, and the conformational change process mainly takes place along the dihedral angle Φ on the dipeptide backbone, that is, the dihedral angle Φ is the reaction coordinate of the conformational change process of this system; first consider the flux along the dihedral angle Φ. That is, when The case where f(t) and g(t) are both Φ(t). The flux along Φ estimated using a weighted histogram when Δt = 20 femtoseconds. See Figure 1 The solid black line indicates that the accurate value of the flux is 526 near the transition state (i.e., Φ = 0°). However, near the transition state, the result obtained from the expression of the weighted histogram oscillates between 280 and 780, with an error of approximately 250 from the accurate value, representing an error rate of 48%. Let V represent the potential energy of the system, then the average force acting on Φ is... The average force along Φ estimated using a weighted histogram is shown below. Figure 2 The black solid line in the middle; near the transition state, the accurate value of the average force is 0, and the numerical value obtained by the expression of the weighted histogram oscillates greatly, fluctuating between -42 and 33, with an error of about 38 from the accurate value; obviously, the obtained results are all inaccurate, and there are large numerical oscillations along Φ.

[0049] The time-series-based weighted probability density processing method described in the preferred embodiment of the present invention, such as... Figure 3 As shown, the time-series-based weighted probability density processing method includes the following steps:

[0050] Step S10: Obtain approximate functions for the first time series and the second time series based on the linear interpolation method.

[0051] Furthermore, in practice, the recording of variables is generally done at finite time intervals, resulting in a time series that is a set of finite measurements. We define g(t) = [g(0), g(Δt), ..., g(iΔt), ..., g(NΔt)] as the discrete expression of the univariate time series of variable g, where Δt is the time interval between two adjacent points in the time series (in this invention, it is assumed that the time intervals between all adjacent points are the same, but this also applies when the time intervals are different), and N is the number of variable values ​​recorded in the time series. Similarly, we define f(t) = [f(0), f(Δt), ..., f(iΔt), ..., f(NΔt)] as the discrete expression of variable f. To simplify mathematical notation, we use g... i and f i Let g(iΔt) and f(iΔt) represent these values.

[0052] Specifically, to divide the time interval [iΔt, (i+1)Δt], it is necessary to obtain the values ​​of the first time series g(t) and the second time series f(t) within the time interval [iΔt, (i+1)Δt]. However, due to the limited observation or recording time precision, the true values ​​of the variables within the time interval are unknown, and approximate values ​​of the variables within the time interval [iΔt, (i+1)Δt] can only be obtained by interpolation. In this invention, the interpolation method used is linear interpolation, which has a simple expression and low computational cost. Through linear interpolation, approximate functions of the first time series g(t) and the second time series f(t) can be obtained.

[0053] Step S20: Obtain the time at each interval boundary based on the approximation function of the first time series.

[0054] Specifically, after dividing the range of the variable g in the first time series g(t) into multiple intervals, the time at the boundary of each interval is obtained based on the approximate function of the first time series g(t).

[0055] Step S30: Based on the time point, both the approximation function of the first time series and the approximation function of the second time series are divided into time series segments.

[0056] Specifically, based on the time interval, the time interval [iΔt, (i+1)Δt] is divided into time series segments by approximating the first time series g(t) and the second time series f(t).

[0057] Step S40: Obtain the time series segment and assign the weight of the time series segment to the corresponding interval to obtain the weighted probability density.

[0058] Specifically, after obtaining the time series segments, the weight of each time segment is assigned to the corresponding interval, such as... Figure 4 As shown, k is the sequence number of a certain interval, k-1 represents the sequence number of the previous interval, k+1 represents the sequence number of the next interval, and so on.

[0059] Furthermore, according to Figure 4 The approach described in the text is to calculate the weighted probability density of the variables and derive an expression for the weighted probability density, as follows:

[0060]

[0061] in,

[0062] in, Let f(t) represent the weighted probability density function, g represent the variable, Δg represent the interval width, N represent the number of values ​​in the discretized expression of the time series f(t), Δt represent the time interval between two adjacent points in the time series, i represent a natural number between 0 and N, and g represents the index of the i-th value in the time series. i Let g(t) be the value of the first time series at time iΔt. i+1 Let f be the value of the first time series g(t) at time (i+1)Δt. i Let f(t) represent the value of the second time series f(t) at time iΔt. i+1 Let f(t) represent the value of the second time series f(t) at time (i+1)Δt, and P(g) represent the value of the second time series f(t) at time (i+1)Δt. i g i+1 , g, Δg) denote a piecewise function, sgn(g i+1 -g i H(g) is the sign function. i -g, Δg) represents the defined function H(x, Δg) where x = g i The value of H(g) when -g is given. i+1 -g, Δg) represents the defined function H(x, Δg) where x = gi+1 The value of -g; the piecewise function P(g) i g i+1 The conditional part of the piecewise function P(g, Δg) requires all conditions to be true simultaneously; i g i+1 The first four cases in (g, Δg) correspond to respectively Figure 5 Case AD is the proportion of the time length of the time interval [iΔt, (i+1)Δt] that falls within the interval.

[0063] The formula for the function H(x, Δg) is as follows:

[0064]

[0065] In this embodiment of the invention, the expression is applied to the alanine dipeptide model system, and the calculated flux along Φ is obtained. like Figure 6 The black solid line in the graph (the gray solid line represents the result obtained from the expression used in the weighted histogram) shows the calculated average force as follows: Figure 7 The black solid line in the graph represents the result obtained from the expression used in the weighted histogram. For flux... The estimation yields an expression for the weighted probability density, but the result obtained from this expression has significantly less numerical oscillation than that obtained from the expression for the weighted histogram. Figure 7 (The black solid line in the graph is smoother than the gray solid line); Note that near the transition state (i.e., Φ = 0°), the accurate value of the flux is 526; near the transition state, the weighted probability density expression yields 526, the same as the accurate value, i.e., the error rate is 0. In the estimation of the average force along Φ, the obtained average force near the transition state fluctuates between -5 and 5, with an error of approximately 5% from the accurate value. Therefore, in the weighted probability density calculations using flux and average force as examples, the expression for the weighted probability density is more accurate than the expression for the weighted histogram, reducing the error rate of the flux from 48% to 0% and the error of the average force from 38% to 5%.

[0066] Furthermore, such as Figure 8 As shown, based on the above-described time-series-based weighted probability density processing method, the present invention also provides a system for time-series-based weighted probability density processing, wherein the system includes:

[0067] The function acquisition module 51 is used to obtain approximate functions of the first time series and the second time series based on the linear interpolation method.

[0068] The time acquisition module 52 is used to acquire the time at each interval boundary based on an approximation function of the first time series;

[0069] The function segmentation module 53 is used to segment both the approximate function of the first time series and the approximate function of the second time series into time series segments based on the time.

[0070] The assignment module 54 is used to obtain the time series segment and assign the weight of the time series segment to the corresponding interval to obtain the weighted probability density.

[0071] Furthermore, such as Figure 9 As shown, based on the above-mentioned time series-based weighted probability density processing method and system, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 9 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0072] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc. Further, the memory 20 may include both internal and external storage devices. The memory 20 is used to store application software and various types of data installed on the terminal, such as program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a time-series-based weighted probability density processing program 40, which can be executed by the processor 10 to implement the time-series-based weighted probability density processing method of this application.

[0073] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the time series-based weighted probability density processing method.

[0074] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The components 10-30 of the terminal communicate with each other via a system bus.

[0075] In one embodiment, when processor 10 executes time-series-based weighted probability density processing program 40 in memory 20, the following steps are performed:

[0076] Approximate functions for the first and second time series were obtained using linear interpolation.

[0077] The time at each interval boundary is obtained based on the approximation function of the first time series;

[0078] Based on the stated time, both the approximation function of the first time series and the approximation function of the second time series are divided into time series segments;

[0079] The time series segments are obtained, and the weights of the time series segments are assigned to the corresponding intervals to obtain the weighted probability density.

[0080] The approximate functions of the first and second time series are piecewise continuous functions with iΔt as the segmentation point.

[0081] The step of obtaining the time at each interval boundary based on the approximation function of the first time series includes, prior to:

[0082] The range of values ​​of variable g in the first time series g(t) is divided into multiple intervals.

[0083] Specifically, the step of dividing the approximation functions of the first and second time series into time series segments based on the stated time point involves:

[0084] Based on the stated time, the time interval [iΔt, (i+1)Δt] is divided into time series segments by approximating the first time series g(t) and the second time series f(t).

[0085] The formula for calculating the weighted probability density is:

[0086]

[0087] in, Let f(t) represent the weighted probability density function, g represent the variable, Δg represent the interval width, N represent the number of values ​​in the discretized expression of the time series f(t), Δt represent the time interval between two adjacent points in the time series, i represent a natural number between 0 and N, and g represents the index of the i-th value in the time series. i Let g(t) be the value of the first time series at time iΔt. i+1 Let f be the value of the first time series g(t) at time (i+1)Δt. i Let f(t) represent the value of the second time series f(t) at time iΔt. i+1 Let f(t) represent the value of the second time series f(t) at time (i+1)Δt, and P(g) represent the value of the second time series f(t) at time (i+1)Δt. i g i+1 , g, Δg) represent piecewise functions.

[0088] The formula for the piecewise function is as follows:

[0089]

[0090] Among them, sgn(g i+1 -g i H(g) is the sign function. i -g, Δg) represents the defined function H(x, Δg) where x = g i The value of H(g) when -g is given. i+1 -g, Δg) represents the defined function H(x, Δg) where x = g i+1 The value when -g.

[0091] The formula for the function H(x, Δg) is as follows:

[0092]

[0093] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a time-series-based weighted probability density processing program, which, when executed by a processor, implements the steps of the time-series-based weighted probability density processing method as described above.

[0094] In summary, this invention provides a weighted probability density processing method based on time series. The method includes: obtaining approximate functions of a first time series and a second time series respectively using linear interpolation; obtaining the time at each interval boundary based on the approximate function of the first time series; dividing both the approximate functions of the first and second time series into time series segments based on the times; obtaining the time series segments and assigning weights to the corresponding intervals to obtain the weighted probability density. This invention obtains the times of the approximate functions of variables at each interval boundary, divides the approximate functions of variables into time series segments according to the obtained times, and then assigns weights to the intervals. This makes the calculated weighted probability density of the variables closer to the true value than the result calculated by the weighted histogram without interpolation, and the result shows a very small change along the variable.

[0095] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0096] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The computer-readable storage medium can be a memory, magnetic disk, optical disk, etc.

[0097] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A weighted probability density processing method based on time series, characterized in that, The time-series-based weighted probability density processing method includes: First and second time series are extracted from molecular dynamics simulations. Approximate functions of the first and second time series are obtained based on linear interpolation. The first time series corresponds to the generalized coordinates of the molecular dynamics simulation, and the second time series corresponds to the potential energy of the molecular dynamics simulation. The approximation functions for both the first and second time series are based on... Let be a piecewise continuous function at the breakpoint, where For the time series A time interval; The first time series Medium variables The value range is divided into multiple intervals, and the time at the boundary of each interval is obtained based on the approximate function of the first time series; Based on the stated time, both the approximation function of the first time series and the approximation function of the second time series are divided into time series segments; The step of dividing both the approximation functions of the first and second time series into time series segments based on the stated time point specifically involves: Based on the stated time, the first time series The approximate function and the second time series The approximate function will be used for the time interval Divide into time series segments; The time series segments are obtained, and the weights of the time series segments are assigned to the corresponding intervals to obtain the weighted probability density. The weighted probability density is then applied to molecular dynamics simulations to obtain the corresponding simulation results, thereby reducing numerical oscillations. The formula for calculating the weighted probability density is: ； in, This represents the weighted probability density function, used as a weighted average of the potential energy changes in the molecular dynamics simulation corresponding to the second time series and the generalized coordinates of the molecular dynamics simulation corresponding to the first time series. Represents variables, This indicates that the first time series Medium variables The value range is divided into multiple intervals with varying widths. Representing time series The number of numerical values ​​in the discretized expression. The time interval between two adjacent points in a time series. From 0 to The natural number between 1 and 2 represents the 1st natural number in the time series. The index of each value. Represented as the first time series exist The value at time, Represented as the first time series exist The value at time, Represents the second time series At any moment The value, Represents the second time series At any moment The value, This represents a piecewise function.

2. The weighted probability density processing method based on time series data according to claim 1, characterized in that, The formula for the piecewise function is: ； in, For symbolic functions, This indicates the defined function of The value of time, This indicates the defined function of The value at time.

3. The time-series-based weighted probability density processing method according to claim 2, characterized in that, The function The formula is: 。 4. A weighted probability density processing system based on time series, characterized in that, The time-series-based weighted probability density processing system is applied to the time-series-based weighted probability density processing method according to any one of claims 1-3, wherein the time-series-based weighted probability density processing system comprises: The function acquisition module is used to obtain approximate functions for the first time series and the second time series based on the linear interpolation method, respectively. The time acquisition module is used to acquire the time at each interval boundary based on an approximation function of the first time series; The function segmentation module is used to segment both the approximate function of the first time series and the approximate function of the second time series into time series segments based on the time point. The assignment module is used to obtain the time series segment and assign the weight of the time series segment to the corresponding interval to obtain the weighted probability density.

5. A terminal, characterized in that, The terminal includes a memory, a processor, and a time-series-based weighted probability density processing program stored in the memory and executable on the processor. When the time-series-based weighted probability density processing program is executed by the processor, it implements the steps of the time-series-based weighted probability density processing method as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the steps of the time-series-based weighted probability density processing method as described in any one of claims 1-3.

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