Analysis method, program, and analysis device

Abstract

The present invention provides an analytical method, program, and apparatus that enable efficient analysis of chemical reactions and yield highly interpretable results. [Solution] The analysis method of the present disclosure is performed by a computer and comprises the following steps: an acquisition step of acquiring measured data relating to a chemical reaction in which a final product is produced from a starting material and a list of components that may be present in the reaction system of the chemical reaction; a reaction equation group generation step of generating a group of reaction equations including reaction equations of reactions that may occur in the reaction system; an optimization step of optimizing the rate constant estimated for each of the components present in the reaction system based on the corresponding reaction equation using the measured data; and an extraction step of extracting from the group of reaction equations the reaction equations in which the optimized rate constant does not satisfy a predetermined criterion.

Description

Technical Field

[0001] The present disclosure relates to an analysis method, a program, and an analysis apparatus for analyzing a chemical reaction to be analyzed.

Background Art

[0002] In order to efficiently produce a desired substance by a chemical reaction, the chemical reaction is analyzed. Conventionally, the analysis of a chemical reaction has been performed, for example, by a researcher repeating experiments while changing reaction conditions to find efficient reaction conditions.

[0003] Since the number of combinations of reaction conditions can be extremely large, the researcher needs to narrow down the reaction conditions that seem to be efficient to some extent based on past findings and then conduct experiments. With such an analysis method, the researcher may expend a great deal of labor or spend a lot of time. For this reason, for example, as in Patent Documents 1 and 2, technologies for analyzing chemical reactions with low load and in a short time have been developed by using artificial intelligence algorithms.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] In a technique for analyzing a chemical reaction using an artificial intelligence algorithm, a machine learning model for predicting a reaction path included in the chemical reaction is learned using a large amount of learning data. When only a small amount of learning data can be prepared, overfitting is likely to occur, and the prediction accuracy of the machine learning model decreases.

[0006] Furthermore, machine learning models using neural networks and other technologies often lack clear rationale for their predictions, leading to a perception of low interpretability. Low interpretability can sometimes discourage the use of response pathways predicted by machine learning models.

[0007] This disclosure is made in view of these circumstances and aims to provide an analytical method, program, and analytical apparatus that can efficiently analyze chemical reactions and obtain highly interpretable results. [Means for solving the problem]

[0008] An analysis method according to one aspect of this disclosure is performed by a computer, comprising: an acquisition step of acquiring measured data relating to a chemical reaction in which a final product is produced from a starting material and a list of components that may be present in the reaction system of the chemical reaction; a reaction equation group generation step of generating a group of reaction equations including reaction equations of reactions that may occur in the reaction system; an optimization step of optimizing the rate constant estimated based on the corresponding reaction equation for each of the components present in the reaction system using the measured data; and an extraction step of extracting from the group of reaction equations the reaction equations in which the optimized rate constant does not satisfy a predetermined criterion.

[0009] A program according to one aspect of this disclosure causes a computer to perform the following steps: obtain measured data relating to a chemical reaction in which a final product is produced from a starting material and a list of components that may be present in the reaction system of the chemical reaction; generate a group of reaction equations including all reaction equations of reactions that may occur in the reaction system; optimize the rate constant estimated for each of the components present in the reaction system based on the corresponding reaction equation using the measured data; and extract from the group of reaction equations the reaction equations in which the optimized rate constant does not satisfy a predetermined criterion.

[0010] An analysis apparatus according to one aspect of the present disclosure includes: an acquisition unit that acquires measured data relating to a chemical reaction in which a final product is produced from a starting material and a list of components that may be present in the reaction system of the chemical reaction; a reaction equation group generation unit that generates a group of reaction equations including all reaction equations of reactions that may occur in the reaction system; an optimization unit that optimizes the rate constant estimated for each of the components present in the reaction system based on the corresponding reaction equation using the measured data; and an extraction unit that extracts from the group of reaction equations the reaction equations in which the optimized rate constant does not satisfy a predetermined criterion. [Effects of the Invention]

[0011] According to this disclosure, chemical reactions can be analyzed efficiently, and since the coefficients in the reaction equations are integers, highly interpretable results can be obtained. Furthermore, by considering higher-order reactions in the initial reaction network generation, it becomes possible to represent complex concentration changes. [Brief explanation of the drawing]

[0012] [Figure 1] Block diagram showing an example of the functional configuration of the analysis device according to the embodiment of this disclosure. [Figure 2] This diagram illustrates the stoichiometric matrix Sn×m, molecular matrix Mm×l, and atomic balance matrix Bn×l when four types of molecules are assumed to be present in the reaction system: CH3OH, CH2O, CO, and H2. [Figure 3] A diagram showing an example of a reaction network diagram. [Figure 4] A flowchart illustrating an example of how the analysis device works. [Figure 5] In this embodiment, the graph shows the results of fitting the analysis results from the analysis device with actual measurement data obtained from simulation. [Figure 6] A diagram illustrating the hardware configuration of a computer that will be used to implement the analysis system. [Modes for carrying out the invention]

[0013] Each embodiment of this disclosure will be described in detail below with reference to the drawings. However, unnecessarily detailed explanations, such as detailed explanations of already well-known matters or redundant explanations of substantially identical configurations, may be omitted.

[0014] (Configuration of the analysis device) Figure 1 is a block diagram showing an example of the functional configuration of an analysis device 10 according to an embodiment of the present disclosure. In the example shown in Figure 1, the analysis device 10 comprises an acquisition unit 11, a reaction equation group generation unit 12, an optimization unit 13, an extraction unit 14, and an output unit 15. The analysis device 10 is a computer, such as a stationary or portable PC (Personal Computer) or a tablet terminal. The functional configuration exemplified in Figure 1 is realized by executing a pre-prepared program in the analysis device 10, which is a computer.

[0015] Of the functional configurations of the analysis device 10, the functions of the reaction equation group generation unit 12, the optimization unit 13, and the extraction unit 14 constitute an analytical model for analyzing the chemical reaction to be analyzed. This analytical model takes as input the components (atoms and molecules) that may exist in the reaction system of the chemical reaction to be analyzed and the time-series data of the concentrations of observable components measured in an actual experiment of the chemical reaction to be analyzed, and outputs a reaction equation that is highly likely to actually occur in the chemical reaction to be analyzed. The configuration of the analysis device 10 will be described in detail below.

[0016] The acquisition unit 11 acquires data from an external source necessary for the analysis device 10 to perform the analysis of the chemical reaction to be analyzed. The data necessary for performing the analysis of the chemical reaction to be analyzed includes, at a minimum, a list of components that may be present in the reaction system of the chemical reaction, and measured data related to the chemical reaction.

[0017] The list of components that can be present in the reaction system of the chemical reaction being analyzed includes all atoms and molecules corresponding to the starting materials, final products, and intermediate substances. This ensures that the coefficients in the reaction equation are integers, resulting in highly interpretable results. The experimental data for the chemical reaction being analyzed includes various data measured during experiments conducted by researchers on the chemical reaction in which the final product is produced from the starting materials. Specifically, the experimental data for the chemical reaction being analyzed includes at least time-series data of the concentrations of observable components present in the reaction system. This allows for time-series prediction of unmeasurable components.

[0018] The reaction equation group generation unit 12 generates a group of reaction equations that include reaction equations of reactions that may occur in the reaction system of the chemical reaction to be analyzed. Using the components (atoms and molecules) included in the list acquired by the acquisition unit 11, the reaction equation group generation unit 12 comprehensively generates reaction equations in which the stoichiometric coefficients are integers, based on the law of mass action.

[0019] The reaction equation group generation unit 12 automatically generates a group of reaction equations by performing the following matrix calculations. First, the stoichiometric coefficient matrix S n×m , molecular matrix M m×l , atomic balance matrix B n×l This defines the number of reactions, where n is the number of reactions, m is the number of different types of molecules in the reaction system, and l is the number of different types of atoms in the reaction system. If the maximum value of the stoichiometric coefficients is d, then the number of reactions produced, n, is (2d+1). m It is represented as follows.

[0020] Increasing the maximum value d of the stoichiometric coefficient allows for the representation of more complex reaction equations. However, increasing d exponentially increases the number of reactions n, which can lead to an explosion in the computational load in the optimization unit 13 (described later), making the calculation difficult or requiring an enormous amount of time. To prevent this, the maximum value d of the stoichiometric coefficient is appropriately set by the user of the analysis device 10, taking into account computational resources and the complexity of the assumed reaction system.

[0021] Stoichiometric coefficient matrix S n×m is defined as a matrix that writes out all the stoichiometric coefficients that can occur in the reaction system. The molecular matrix M m×l is defined as a matrix that represents the types and numbers of atoms that the molecules present in the reaction system possess. The atomic balance matrix B n×l is defined as a matrix that indicates whether the reaction has atomic balance on the left and right sides of the reaction equation.

[0022] Figure 2 shows the stoichiometric coefficient matrix S n×m , the molecular matrix M m×l , and the atomic balance matrix B n×l in the case where it is assumed that four types of molecules, CH3OH, CH2O, CO, and H2, exist in the reaction system. In the example shown in Figure 2, d = 3, m = 4, n = 7 4 = 2401. The atomic balance matrix B n×l of the reaction is calculated by the inner product of the stoichiometric coefficient matrix S n×m and the molecular matrix M m×l .

[0023] In the atomic balance matrix, each row represents each reaction, and each column represents each atom, and the values become the ones that quantitatively indicate whether the atomic balance on the left and right sides is achieved. Here, when there is a reaction with atomic balance, in the atomic balance matrix, the L 1 norm of the row of the balanced reaction becomes 0. Therefore, by extracting the row with the L 1 norm of 0, the stoichiometric coefficients of the reaction with atomic balance can be obtained.

[0024] Furthermore, from the reactions with atomic balance, only the reactions with the reaction rate order of d or less are extracted. This is done to adjust the calculation amount in the optimization unit 13 described later. The extraction of the reactions with the reaction rate order of d or less is achieved by defining a matrix V n×m in which the positive and negative values of the stoichiometric coefficient matrix S n×m are inverted and the negative values are set to 0, and extracting only the rows where the sum in the row direction of the matrix V n×m is d or less.

[0025] In this way, the reaction equation group generator 12 defines a stoichiometric coefficient matrix and a molecular matrix based on the components included in the list, calculates the atomic balance matrix by calculating their inner product, and extracts the stoichiometric coefficients of reactions with atomic balance by calculating the norm of the atomic balance matrix. Furthermore, the reaction equation group generator 12 extracts from the extracted reactions those with a reaction rate of order d or lower. This makes it possible to extract reactions that are expected to occur in the chemical reaction under analysis and that have a reasonably high probability of actually occurring.

[0026] In this embodiment, the reaction equation group generation unit 12 outputs a group of reaction equations that include multiple reaction equations representing the reactions generated and extracted as described above, based on the input list of atoms and molecules. Alternatively, the reaction equation group generation unit 12 may output a reaction network diagram showing the reaction pathway from the starting material through the intermediate material to the final product. In this case, each node in the reaction network diagram is either the starting material, intermediate material, or final product in the chemical reaction being analyzed, and the edges connecting the nodes correspond to the respective reaction equations.

[0027] Figure 3 shows an example of a reaction network diagram. Figure 3 shows an example of a reaction network diagram when the starting material, intermediate material, or final product is one of the following: H2, O2, CO, CH4, H2O, or CH3OH. In Figure 3, among the edges connecting the nodes corresponding to each substance, dashed lines represent reactions that do not actually occur, while solid lines represent reactions that can actually occur.

[0028] The optimization unit 13 optimizes the rate constants estimated based on the corresponding reaction equations for each component (atoms and molecules) present in the reaction system, using measured data. This allows the optimization unit 13 to fit the rate constants in each reaction equation included in the reaction equation group generated by the reaction equation group generation unit 12 to rate constants that match the measured data.

[0029] The optimization unit 13 sets a constrained nonlinear optimization problem that satisfies predetermined constraints and minimizes the difference between the time-series data of the concentration of a component in the measured data and the time-series data of the concentration calculated based on the estimated rate constant for each component. By solving the optimization problem set in this way, the optimization unit 13 fits the estimated rate constant to the measured data for each reaction equation. In the following description, the rate constant estimated by the optimization unit 13 for each reaction equation may be referred to as estimated data.

[0030] The optimization unit 13 performs optimization as follows. First, it performs the following. First, the dataset B = {1, 2, 3, ..., N B Define}. The number of datasets is N. B The result is |B|. Dataset B consists of measured data from experiments conducted under different conditions. Experiments conducted under different conditions include, for example, chemical reactions in which one raw material is added to another, but the amount of the other raw material added is different from one another. In this case, the data included in Dataset B is assigned in ascending order, for example, from the data obtained in experiments with small amounts of added material.

[0031] Next, we define all components present in the reaction system as C. The total number of components is N. C =|C|. Furthermore, in experiments, not all components present in the reaction system are necessarily observable; therefore, we define the observable components as M. Note that in experiments, component observation can be performed, for example, by gas chromatography. The number of observable components is N. M =|M|

[0032] Next, the reactions included in the group of reaction equations generated by the reaction equation group generation unit 12 are R={1,2,3,···,N}. R This is defined as follows. In reaction R, the numbers indicate the order in which they were generated by the reaction equation group generation unit 12.

[0033] Finally, regarding the time axis T b,j ={t:t is the sampling time for each dataset and each component}b∈B,j∈M, and so on.T,B,J =|T b,j The | symbol indicates the number of points on the time axis for each component of each dataset. The number of sampling points is defined differently for each dataset and each component.

[0034] Here, if the number of datasets B is significantly less than the number of responses R, overfitting occurs, making it difficult to obtain a reasonable convergence result. The optimization unit 13 considers the case where the number of datasets B is significantly less than the number of responses R and sets up a constrained optimization problem as described above. By adding various constraints during optimization, the search range for solutions is narrowed, thereby stabilizing convergence. As a result, even with a small amount of data, the method becomes highly generalizable and robust to noise.

[0035] The constrained optimization problem in the optimization unit 13 is formulated as shown in equations (1) through (7) below. Equation (1) is the objective function of the optimization, and equations (2) through (7) are equations relating to the constraints.

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[0036] The first term of equation (1) represents the mean squared error (MSE) between the measured data and the estimated data, scaled by the maximum concentration (mole fraction) of each component. b,j,tThis represents the mole fraction of experimental data with the dimensions of dataset, component, and time. b,j,t This represents the mole fraction of the estimated data. max,j This represents the maximum mole fraction including all data sets for each component.

[0037] The second term in equation (1) is a normalization term. In this embodiment, it is assumed that the number of reaction R, which represents the degrees of freedom for optimization, exceeds the number of measured data. In this case, the search space for the optimization problem becomes enormous, making convergence difficult. By introducing a normalization term into equation (1), equation (1) becomes a convex function, and as a result, convergence can be stabilized. λ1 is a hyperparameter and is appropriately set according to the problem by, for example, the user of the analysis device 10.

[0038] The third term of equation (1) is a term that restricts the relative magnitudes of the concentrations (mole fractions) of multiple datasets so as not to change over time, and also restricts the mole fractions of the last points in the datasets on the time axis to be as equally spaced as possible between the datasets. This makes the obtained results relatively close to general chemical data, and consequently, the results can be made closer to human intuition. In this embodiment, the third term of equation (1) is a constraint that the concentrations of the last points in the datasets on the time axis are equally spaced, but in this disclosure, they do not have to be equally spaced, and can be set to intervals specified by the user of the analysis device 10.

[0039] Specifically, in equations (5) and (6), in order to prevent the left-hand side from becoming 0, the slack variable s is used. b,j By setting the denominator, the slack variable s b,j We are making sure that it does not become 0.

[0040] The numerator of the third term in equation (1) is y^ Nb,j,1 -y^ 1,j,1 is the scaling term. ε is a term to prevent the denominator from becoming infinite. In this implementation, 10 -9Although it was set to this value, this value may be freely set by, for example, the user of the analysis device 10. λ2 is a hyperparameter and is appropriately set by, for example, the user of the analysis device 10, depending on the problem.

[0041] Equation (2) shows the constraints on the differential equation of mole fractions for the reaction equation generated in the reaction network. b,j (t) represents the mole fraction of each component, including all components, including those that are not observable. The left-hand side of equation (2) is a general expression of the differential equation for the reaction rate.

[0042] In the right-hand side of equation (2), s ij The stoichiometric coefficients of the reaction generated by the reaction equation group generation unit 12 are shown. In the right-hand side of equation (2), v ij The stoichiometric coefficient is s ij This is obtained by reversing the sign of the positive and negative values, and further setting negative values ​​to 0. ij This corresponds to the order of the mole fraction of the numerator on the left-hand side of the reaction equation.

[0043] Equation (2) is obtained by substituting equation (9), which is a differential equation for reaction rate, into the following equation (8), which is a general expression for reaction rate, and then rearranging the equation.

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[0044] As a result, the reaction rate r in equation (2) b,i (t) is eliminated, and as a result the number of constraints in the optimization problem is reduced, which can lower the computational load of the Hessian, as described later.

[0045] Equation (3) is the initial value x for optimization in the differential equation of equation (2). b,j (0) is the initial mole fraction of the measured value x b,j init This indicates that it will be set to [this value].

[0046] Equation (4) shows the mole fraction x of all components, including unobservable components. b,j This shows that (t) is scaled by j∈M, which is the set of observable components. This allows the mole fractions of all components to be calculated, and the sum of the mole fractions of only the observable components can be set to 1, enabling the same scaling as the experimental data.

[0047] Equations (2) through (4) are equations relating to the constraints of the nonlinear optimization problem.

[0048] Equations (5) and (6) are constraints on incorporating data features in order to achieve small data fitting. As described above, in this embodiment, multiple experiments are conducted under different conditions when measuring the experimental data. By making the conditions in the multiple experiments different from each other, characteristic regularities may emerge in the experimentally measured experimental data for each component in the reaction system.

[0049] A concrete example is as follows: Suppose we have time-series data of the mole fractions of each component present in a reaction system, obtained from multiple experiments in which the amounts of other raw materials added to a given raw material are varied. Specifically, regarding the relative magnitudes of the last points on the time axis of each observable component in the measured data, there may be two types of components: (i) components arranged in descending order of mole fraction, and (ii) components arranged in descending order of mole fraction, based on the amount of other raw materials added. In equation (5), the components corresponding to (i) are defined by the set j∈C￣, and in equation (6), the components corresponding to (ii) are defined by the set j∈C_.

[0050] The constraint exists between two adjacent datasets when multiple datasets are sorted in descending order of the amount of other added ingredients added. In equations (5) and (6), when multiple datasets are sorted in descending order of the amount of other added ingredients added, the elements of the new set obtained by removing the last element of the set are b∈B\N bThis is how it is expressed. Due to these constraints, in optimization based on measured data, it is possible to prevent situations where the relative molar concentrations of components in the measured data are swapped, and to calculate estimated data (rate constants) that more closely match the measured data.

[0051] Equation (7) is given by the mole fraction, rate constant, and the slack variable s in equations (5) and (6). b,j This indicates that it is a non-negative value.

[0052] By solving the above equation, the optimization unit 13 can calculate a rate constant that fits the measured data.

[0053] First, the optimization unit 13 estimates the initial value of the velocity constant by solving a linear equation based on the first term of equation (1) such that the first derivative value obtained from the measured data matches the first derivative value estimated by calculation. The linear equation for estimating the initial value of the velocity constant is expressed by the following equation (10).

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[0054] Equation (10) is obtained by differentiating the mole fractions of the measured data and the estimated data with respect to time in the first term of equation (1), which is the objective function for optimization. According to equation (10), the solution is uniquely determined because it is linearized, making it suitable for calculating initial values.

[0055] Next, the optimization unit 13 calculates the initial values ​​of the mole fractions for each component based on the initial values ​​of the rate constants. This corresponds to calculating equations (3) and (4) above.

[0056] Finally, the optimization unit 13 solves the optimization problem of equation (1) using the estimated initial values ​​of the rate constant and the mole fraction, and fits the measured data and the estimated data (estimated rate constant). This allows for the calculation of a rate constant that matches the measured data.

[0057] The optimization problems in the optimization unit 13, expressed in equations (1) to (7), can be solved using Newton's method with the KKT (Karush-Kuhn-Tucker) condition. In Newton's method with the KKT condition, a Hessian matrix is ​​calculated for all variables when solving the optimization problem. Therefore, by applying a projection matrix to the Hessian, a reduced Hessian matrix (H) is obtained, which is used in the extraction unit 14 and represents the quadratic sensitivity of the objective function to parameter changes. red It can be easily calculated.

[0058] However, the optimization algorithm used to solve the optimization problem in the optimization unit 13 in this disclosure is not limited to Newton's method using the KKT condition. In this disclosure, other optimization algorithms such as genetic algorithms, Bayesian optimization, gradient descent, Gauss-Newton method, EM algorithm, ant colony optimization, and reinforcement learning may also be used. However, if a method other than Newton's method is used, the reduced Hessian matrix described above must be calculated separately. The reduced Hessian matrix can be calculated using methods such as the difference method or automatic differentiation.

[0059] The extraction unit 14 extracts reaction equations from the reaction equation group generation unit 12 whose rate constants, optimized by the optimization unit 13, do not meet a predetermined standard. In other words, the extraction unit 14 removes reaction equations from the reaction equation group whose rate constants meet a predetermined standard.

[0060] The reaction equation group generation unit 12 generates a group of reaction equations that comprehensively include all possible reaction equations that may occur in the reaction system. Therefore, the reaction equations included in the group include reaction equations that have little effect on the formation of the final product. Furthermore, the fewer the number of reactions (the number of reaction equations included in the reaction equation group), the higher the interpretability of the analysis results output by the analysis device 10. In light of these circumstances, the extraction unit 14 performs pruning (removal of branches) of the reaction equations included in the reaction equation group.

[0061] Specifically, the extraction unit 14 performs pruning in the following two steps. The first step is to remove from the group of reaction equations reaction equations that have a rate constant of 0 as estimated by the optimization unit 13. The second step is to remove from the group of reaction equations reaction equations that have the least importance of the rate constant.

[0062] As described above, the optimization unit 13 estimates the rate constant for each reaction equation included in the reaction equation group and fits the estimated rate constant to the measured data. Therefore, a reaction equation in which the rate constant estimated by the optimization unit 13 is 0 can be interpreted as an equation that represents a reaction that does not actually occur in the reaction system of the chemical reaction. The first step is to remove reaction equations that do not actually occur from the reaction equation group in this manner.

[0063] The second step involves determining the importance (saliency) L, which is defined by a method called OBS (Optimal Brain Surgeon). q The importance of the rate constant L is calculated for the rate constant of the reaction equation, and the most important rate constant among the group of reaction equations is determined. q This is a process to remove small reaction equations.

[0064] OBS takes into account all elements of the Hessian matrix of the objective function and assigns importance L to each element. q This is a method for estimating the velocity constant k. According to OBS, the velocity constant k i Importance L q It is calculated by the following formula (11).

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[0065] L q The subscript q indicates the parameter number. H is a two-dimensional matrix called the Hessian matrix. The Hessian represents the quadratic sensitivity of the objective function with respect to the parameters in an optimization problem. The diagonal terms of the Hessian are [H] qq This represents the second-order sensitivity with respect to parameter q, and also [H -1 ] qqThis is the diagonal term of the inverse of the Hessian matrix.

[0066] The extraction unit 14 is [H -1 ] qq and k i Using L q Calculate k i The value obtained by the rate constant optimization unit 13 is used here. -1 ] qq This includes the reduced Hessian matrix H mentioned above. red H is the inverse matrix of red -1 You can use it.

[0067] H red From H red -1 Regarding the calculation of the inverse matrix of , depending on the state of the matrix, it is not always possible to calculate the inverse matrix. In such cases, first H red Calculate the obtained H red Apply eigenvalue decomposition to the expression, and if an eigenvalue of 0 exists, add a small infinitesimal term to the diagonal. This gives the importance L q While minimizing the impact on the inverse matrix H red -1 This can be made computable.

[0068] The inverse matrix H calculated in this way red -1 Using equation (11), the extraction unit 14 has a rate constant k i Corresponding importance level L q It is possible to calculate this.

[0069] In the second step, the extraction unit 14 removes from the group of reaction equations the reaction equation whose rate constant is not zero and which has the lowest importance. Since reaction equations with low importance in rate constants correspond to reactions that are unlikely to actually occur in the reaction system of the chemical reaction being analyzed, this step makes it possible to remove reaction equations of reactions that are unlikely to actually occur from the group of reaction equations.

[0070] In this way, the extraction unit 14 removes reaction equations from the group of reaction equations that satisfy predetermined criteria, specifically those with an estimated rate constant of 0 and those with the lowest calculated importance. As a result, the extraction unit 14 can extract reaction equations from the group of reaction equations that have a rate constant other than 0 and are of relatively high importance.

[0071] Here, the optimization unit 13 and the extraction unit 14 repeatedly perform the steps described above until the number of reaction equations included in the reaction equation group reaches a predetermined number. The predetermined number can be freely set by the user of the analysis device 10, but it may also be determined using statistical methods. For example, statistical methods include the Akaike information criterion and the Bayesian information criterion. By using the Akaike information criterion, it is possible to construct a simple model that fits well and avoids overfitting. Alternatively, by using the Bayesian information criterion, it is possible to construct a simple model that fits well and avoids overfitting, even with large-scale data. The predetermined number is an integer greater than or equal to 1.

[0072] Specifically, the optimization unit 13 estimates a rate constant that fits the measured data for each reaction equation included in the reaction equation group generated by the reaction equation group generation unit 12, and the extraction unit 14 removes reaction equations with a rate constant of 0 and the reaction equations with the least importance from the reaction equation group based on the estimation results. By repeatedly executing these steps, the optimization unit 13 and the extraction unit 14 first remove reaction equations with a rate constant of 0 from the reaction equation group, and then remove reaction equations in order of increasing importance. As a result, when the number of reaction equations included in the reaction equation group reaches a predetermined number, the iteration stops. This makes it possible to extract a predetermined number of reaction equations that are relatively likely to actually occur in the reaction system of the chemical reaction being analyzed, resulting in a reaction pathway that can explain the analysis results. Consequently, the analysis device 10 can output a reaction pathway with high interpretability as the analysis result.

[0073] Furthermore, an upper limit may be set on the number of repetitions. This is because if OBS is repeated more times than necessary, excessive pruning may occur, potentially leading to larger errors. The number of repetitions may be set in advance to a predetermined number (for example, 5 times), or it may be set to an appropriate number based on, for example, the number of reaction equations extracted by the extraction unit 14 (a predetermined number).

[0074] The output unit 15 outputs the analysis results, including the reaction equations extracted by the processes performed by the optimization unit 13 and the extraction unit 14. The output unit 15 can output and display the analysis results on, for example, a display device on the analysis device 10 or a display device installed outside the analysis device 10.

[0075] In this disclosure, there are no particular limitations on the display method when the output unit 15 displays the analysis results on a display device. The output unit 15 may, for example, display the reaction equations finally extracted by the extraction unit 14 in list format, or it may display them in the form of a reaction network diagram. The reaction network diagram output by the output unit 15 as an analysis result is constructed by connecting nodes corresponding to the starting materials, intermediate materials, and final products with edges corresponding to the reaction equations extracted by the extraction unit 14. This makes it possible to understand at a glance what pathway the reaction is actually following in the chemical reaction being analyzed.

[0076] The output unit 15 may output only the predetermined number of extracted reaction equations as the analysis result, or it may output an analysis result that includes all of the generated reaction equations and the predetermined number of extracted reaction equations.

[0077] (Example of operation) Next, we will describe an example of the operation of the analysis device 10. Figure 4 is a flowchart illustrating an example of the operation of the analysis device 10.

[0078] In step S1, the analysis device 10 acquires measured data (time-series data of the concentration of each component) related to the chemical reaction to be analyzed, and a list of components including atoms and molecules that may be present in the reaction system of the chemical reaction. The analysis device 10 may acquire the measured data and the list of components based on input operations by the user of the analysis device 10, for example, via an operating device, or it may receive the measured data and the list of components from another computer that is communicatively connected to the analysis device 10.

[0079] In step S2, the analysis device 10 generates a group of reaction equations based on the component list.

[0080] In step S3, the analysis device 10 estimates the rate constant for each reaction equation included in the group of reaction equations, and calculates the optimized rate constant by optimizing the estimated rate constant so that it fits the measured data. As described above, step S3 is performed by setting an optimization objective function for the rate constant and the molar concentration of each component for each reaction equation, and performing optimization calculations to minimize the objective function, including various constraints.

[0081] In step S4, the analysis device 10 extracts from the group of reaction equations reaction equations in which the rate constant optimized in step S3 does not meet a predetermined criterion. The predetermined criterion is either that the rate constant is 0, or that the importance of the rate constant is the lowest.

[0082] In step S5, the analysis device 10 determines whether the number of extracted reaction equations is less than or equal to a predetermined number. If it is determined in step S5 that the number of extracted reaction equations is less than or equal to a predetermined number (step S5:Y), the analysis device 10 proceeds to step S6. If it is not determined in step S5 that the number of extracted reaction equations is less than or equal to a predetermined number (step S5:N), the analysis device 10 returns to step S3.

[0083] In step S6, the analysis device 10 outputs analysis results based on the extracted reaction equation. This allows the user of the analysis device 10 to understand what kind of reaction actually occurs in the reaction system of the chemical reaction being analyzed, and how the final product is produced from the starting materials.

[0084] In this way, the analysis device 10 comprehensively generates a set of reaction equations based on all atoms and molecules that may be present in the reaction system of the chemical reaction being analyzed, estimates a rate constant optimized to fit the measured data for each reaction equation, and extracts those that do not meet predetermined criteria based on the estimated rate constant. As a result, it can be expected that the analysis results from the analysis device 10 will extract reaction equations of reactions that are highly likely to actually occur in the reaction system. Furthermore, the process of optimizing the rate constant in step S3 and the process of removing reaction equations whose optimized rate constants meet the criteria in step S4 are repeated until the number of remaining reaction equations reaches a predetermined number, so that reaction equations that are more likely to actually occur can be extracted. For this reason, the analysis device 10 makes it possible to accurately extract important reactions in the chemical reaction being analyzed in a relatively short time, without placing a heavy burden on the user.

[0085] (Examples) The following describes an example of analysis using the analysis device 10. In the following example, the chemical reaction to be analyzed is set to a chemical reaction in which chlorine is reacted with ethylene (C2H4) to produce chloride. The list of components that may be present in the reaction system of this chemical reaction includes C2H4, C2H3Cl, C2H4Cl2, C2H3Cl3, HCl, and Cl2 as molecules, and C, H, and Cl as atoms.

[0086] In this case, by setting the maximum value of the stoichiometric coefficient d=3, the following 46 reaction equations R1 to R46 were obtained as a group of reaction equations.

[0087] R1: 3C2H4Cl2 ⇒ 3C2H4 + 3Cl2 R2:3C2H4Cl2⇒2C2H4+C2H3Cl+HCl+2Cl2 R3: 2C2H4Cl2 + C2H3Cl3 ⇒ 2C2H4 + C2H3Cl + 3Cl2 R4:3C2H4Cl2⇒2C2H4+C2H3Cl3+HCl+Cl2 R5:C2H3Cl+C2H4Cl2+HCl⇒2C2H4+2Cl2 R6:2C2H4Cl2⇒2C2H4+2Cl2 R7: C2H3Cl + 2C2H4Cl2 ⇒ 2C2H4 + C2H3Cl3 + Cl2 R8:C2H4Cl2+C2H3Cl3+HCl⇒2C2H4+3Cl2 R9:2C2H4Cl2+C2H3Cl3⇒C2H4+2C2H3Cl+HCl+2Cl2 R10: C2H3Cl + HCl ⇒ C2H4 + Cl2 R11: 2C2H3Cl3+HCl⇒C2H4+C2H3Cl+3Cl2 R12:C2H4Cl2+C2H3Cl3⇒C2H4+C2H3Cl+2Cl2 R13: C2H4Cl2⇒ C2H4+Cl2 R14: C2H3Cl3 + HCl ⇒ C2H4 + 2Cl2 R15:3C2H4Cl2⇒C2H4+C2H3Cl+C2H3Cl3+2HCl R16:3C2H4Cl2⇒C2H4+2C2H3Cl+2HCl+Cl2 R17: 2C2H3Cl+HCl⇒C2H4+C2H3Cl3 R18:2C2H4Cl2⇒C2H4+C2H3Cl3+HCl R19:2C2H4Cl2⇒C2H4+C2H3Cl+HCl+Cl2 R20:C2H4Cl2+2C2H3Cl3⇒C2H4+2C2H3Cl+3Cl2 R21:C2H3Cl+C2H4Cl2⇒C2H4+C2H3Cl3 R22: C2H4Cl2 ⇒ C2H3Cl + HCl R23: C2H3Cl + HCl ⇒ C2H4Cl2 R24:2C2H4Cl2+Cl2⇒C2H3Cl+C2H3Cl3+2HCl R25: C2H4Cl2 + Cl2 ⇒ C2H3Cl3 + HCl R26:C2H3Cl+Cl2⇒C2H3Cl3 R27:2C2H4Cl2⇒2C2H3Cl+2HCl R28:C2H3Cl3⇒C2H3Cl+Cl2 R29:3C2H4Cl2⇒3C2H3Cl+3HCl R30:C2H4Cl2+C2H3Cl3⇒2C2H3Cl+HCl+Cl2 R31:3C2H3Cl3⇒3C2H3Cl+3Cl2 R32:C2H4Cl2+2C2H3Cl3⇒3C2H3Cl+HCl+2Cl2 R33:2C2H3Cl3⇒2C2H3Cl+2Cl2 R34:2C2H4Cl2+C2H3Cl3⇒3C2H3Cl+2HCl+Cl2 R35:2C2H3Cl3+HCl⇒C2H3Cl+C2H4Cl2+2Cl2 R36:C2H3Cl3+HCl⇒C2H4Cl2+Cl2 R37:C2H4+C2H3Cl3⇒C2H3Cl+C2H4Cl2 R38:C2H4+2C2H3Cl3⇒3C2H3Cl+HCl+Cl2 R39:C2H4+C2H4Cl2+C2H3Cl3⇒3C2H3Cl+2HCl R40:C2H4+C2H3Cl3+HCl⇒2C2H4Cl2 R41:C2H4+C2H3Cl3⇒2C2H3Cl+HCl R42:C2H4+C2H4Cl2+Cl2⇒2C2H3Cl+2HCl R43:C2H4+2C2H3Cl3⇒2C2H3Cl+C2H4Cl2+Cl2 R44:C2H4+Cl2⇒C2H3Cl+HCl R45:C2H4+Cl2⇒C2H4Cl2 R46:C2H4+2Cl2⇒C2H3Cl3+HCl

[0088] Instead of experiments, simulations were used to create two sets of measured data: time-series concentration data for when 1 equivalent amount of chlorine was added to 1 equivalent amount of ethylene (hereinafter referred to as measured data 1), and time-series concentration data for when 2 equivalent amounts of chlorine were added to 1 equivalent amount of ethylene (hereinafter referred to as measured data 2). In other words, the analysis device 10 acquired two types of measured data with different amounts of added chlorine.

[0089] Furthermore, simulations have shown that the following four reactions occur in the reaction system when ethylene is reacted with chlorine. R44: C2H4 + Cl2 ⇒ C2H3Cl + HCl R45: C2H4 + Cl2 ⇒ C2H4Cl2 R22: C2H4Cl2 ⇒ C2H3Cl + HCl R26: C2H3Cl + Cl2 ⇒ C2H3Cl3

[0090] Figure 5 is a graph showing the results of fitting the analysis results from the analysis device 10 with measured data obtained from simulation in this embodiment. In Figure 5, the measured data is shown as points, and the data obtained from the analysis results is shown as lines.

[0091] As shown in Figure 5, the points representing the measured data and the lines representing the analysis results almost coincide. This clearly indicates that the analysis device 10 is functioning correctly.

[0092] The analysis device 10 repeatedly performed optimization and extraction from the group of reaction equations, including the 46 reaction equations mentioned above, until only four reaction equations remained. As a result, the following four equations were extracted in descending order of their rate coefficients. R44:C2H4+Cl2⇒C2H3Cl+HCl(k1=2.851) R45:C2H4+Cl2⇒C2H4Cl2(k2=2.818) R22:C2H4Cl2⇒C2H3Cl+HCl(k3=0.974) R26:C2H3Cl+Cl2⇒C2H3Cl3(k4=0.954) The value in parentheses is the velocity constant.

[0093] Thus, the analysis device 10 can accurately extract the reaction equation of the reaction that actually occurs in the reaction system of the chemical reaction being analyzed, based on the input component list and measured data, and can also obtain highly reliable results even in areas where there is no data (interpolation and extrapolation areas).

[0094] (Example of hardware configuration for analysis equipment) The analysis device 10 described in the above embodiments is a computer, and the functions of the analysis device 10 are realized by the computer executing a predetermined program. Below, we will describe an example of the hardware configuration of the computer that realizes each function of the analysis device 10.

[0095] Figure 6 illustrates the hardware configuration of the computer 2100 that realizes the analysis device 10. As shown in Figure 6, the computer 2100 includes input devices 2101 such as input buttons and a touchpad, output devices 2102 such as a display and speakers, a CPU (Central Processing Unit) 2103, ROM (Read Only Memory) 2104, and RAM (Random Access Memory) 2105. The computer 2100 also includes storage devices 2106 such as a hard disk drive and an SSD (Solid State Drive), a reader 2107 that reads information from recording media such as a DVD-ROM (Digital Versatile Disk Read Only Memory) and a USB (Universal Serial Bus) memory, and a transceiver 2108 that communicates via a network. The above-mentioned parts are connected by a bus 2109.

[0096] The reading device 2107 reads the program for realizing the functions of each of the above-mentioned parts from the recording medium on which the program is recorded and stores it in the storage device 2106. Alternatively, the transmitting / receiving device 2108 communicates with a server device connected to the network and stores the program for realizing the functions of each of the above-mentioned parts downloaded from the server device in the storage device 2106.

[0097] The CPU 2103 copies the program stored in the memory device 2106 to the RAM 2105, and then sequentially reads and executes the instructions contained in that program from the RAM 2105, thereby realizing the functions of each of the above-mentioned parts. Furthermore, when the program is executed, information obtained from the various processes described in each embodiment is stored in the RAM 2105 or the memory device 2106 and used as appropriate. [Industrial applicability]

[0098] It is useful for analytical devices used to analyze chemical reactions. [Explanation of Symbols]

[0099] 10 Analysis device 11 Acquisition Department 12 Reaction Equation Group Generation Section 13 Optimization Unit 14 Extraction part 15 Output section

Claims

1. A data acquisition step involves obtaining measured data on the chemical reaction that produces the final product from the starting material and a list of components that may be present in the reaction system of the said chemical reaction. A reaction equation group generation step, which generates a group of reaction equations including reaction equations for reactions that may occur in the aforementioned reaction system, An optimization step is performed in which the rate constant estimated based on the corresponding reaction equation for each of the components present in the reaction system is optimized using the measured data, An extraction step is performed to extract from the group of reaction equations the reaction equations in which the optimized rate constant does not satisfy a predetermined criterion. A method of analysis performed by a computer.

2. The measured data includes at least time-series data of the observable concentrations of the components present in the reaction system. The analysis method according to claim 1.

3. The optimization step includes a step of performing constrained nonlinear optimization that satisfies predetermined constraints and minimizes the difference between the time-series data of the concentration of the component in the measured data and the time-series data of the concentration calculated based on the estimated rate constant for each component. The analysis method according to claim 2.

4. The optimization step and the extraction step are repeatedly performed until the number of reaction equations extracted in the extraction step reaches a predetermined number. The analysis method according to claim 1.

5. The extraction step includes at least one of the following steps: removing reaction equations with a rate constant of 0 from the group of reaction equations, and removing reaction equations with the least important rate constant from the group of reaction equations. The analysis method according to claim 4.

6. The aforementioned importance is the reduced Hessian matrix of the objective function of the constrained nonlinear optimization. The analysis method according to claim 5.

7. A procedure for obtaining experimental data on a chemical reaction that produces a final product from a starting material, and a list of components that may be present in the reaction system of the said chemical reaction, A procedure for generating a group of reaction equations that includes all possible reaction equations for the reactions that can occur in the aforementioned reaction system, A procedure for optimizing the rate constant, which is estimated based on the corresponding reaction equation for each of the components present in the reaction system, using the measured data; A procedure for extracting from the group of reaction equations the reaction equation in which the optimized rate constant does not satisfy a predetermined criterion, A program that causes a computer to execute something.

8. An acquisition unit that acquires measured data relating to a chemical reaction in which a final product is produced from a starting material and a list of components that may be present in the reaction system of the said chemical reaction, A reaction equation group generation unit that generates a group of reaction equations that includes all possible reaction equations for the reactions that can occur in the reaction system, An optimization unit that optimizes the rate constants estimated for each of the components present in the reaction system based on the corresponding reaction equation, using the measured data, An extraction unit for extracting from the group of reaction equations the reaction equations in which the optimized rate constant does not satisfy a predetermined criterion, An analytical device equipped with the following features.

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