JP7666727B2 - Synthesis condition generation method, synthesis condition generation device, and program - Google Patents

Description

The present invention relates to a synthesis condition generation method, a synthesis condition generation device, and a program.

Conventionally, synthesis conditions that give good evaluation values are searched for by repeating trials of measuring the evaluation values of substances generated according to given synthesis conditions (recipe). For example, as shown in Fig. 1, synthesis conditions that give good evaluation values are searched for by repeating trials in which _n is the number of trials, namely, (1) synthesis conditions _xn are generated, (2) a sample (substance) is generated according to the synthesis conditions xn, and (3) the sample is evaluated to measure an evaluation value _yn .

For example, molecular beam epitaxy (Non-Patent Document 1) is a method for producing a thin film (material, sample) according to given synthesis conditions. In addition, thin film synthesis and bulk synthesis methods such as sputtering, pulsed laser ablation, physical vapor deposition, chemical vapor deposition, spin coating, atomic layer deposition, floating zone method, flux method, Czochralski method, etc. are also included. In addition, Bayesian optimization is a method for generating synthesis conditions to be tried next under a problem setting in which evaluation values for synthesis conditions are always obtained (Patent Document 1, Non-Patent Documents 2 and 3). Note that since the process of producing a material according to synthesis conditions and measuring the evaluation value of the material using an evaluation index designed in advance according to the use of the material is complicated, there may be cases where the relationship between the synthesis conditions and the evaluation value cannot be explicitly described, but Bayesian optimization is known as a method that can search for synthesis conditions even in such situations.

JP 2018-147075 A

Y. Krockenberger et al. Emerging superconductivity hidden beneath chargetransfer insulators, Scientific Reports 3:2235, 2013. J. Snoek, H. Larochelle, and R. P. Adams: Practical Bayesian Optimization of Machine Learning Algorithms, Advances in Neural Information Processing Systems 25, pp. 2951-2959, 2012. Y. K. Wakabayashi et al. Machine-learning-assisted thin-film growth: Bayesian optimization in molecular beam epitaxy of SrRuO3 thin films, APL Materials 7, 101114, 2019.

However, the conventional method of searching for synthesis conditions that give good evaluation values has the problem that there may be synthesis conditions for which no evaluation value can be obtained. This is because stable substances are not necessarily produced under all synthesis conditions within the search range of synthesis conditions. In addition, it is possible that a substance with a different composition or crystal structure from the desired substance may be produced under certain synthesis conditions.

One embodiment of the present invention has been made in consideration of the above points, and aims to generate synthesis conditions that will yield an optimal substance under given evaluation indexes.

In order to achieve the above object, a synthesis condition generation method according to one embodiment is a synthesis condition generation method for generating synthesis conditions in a trial in which the synthesis of a substance according to synthesis conditions, the measurement of an evaluation value for evaluating the substance, and the generation of the synthesis conditions are sequentially performed, and when there is a trial n' in which the evaluation value y _n' (n'∈{1, ..., N}) of the substance could not be measured among the N trials so far, a computer executes an evaluation value conversion procedure for replacing the evaluation value y _n' in trial n' with the worst evaluation value, a prediction procedure for predicting the evaluation value _y of an untried synthesis condition x using the synthesis condition x _n and evaluation value y n in trial n (n=1, ..., N), and a generation procedure for generating synthesis conditions x N+1 in trial N+1 that have an evaluation value better than the best value of the evaluation value y _n (n=1, ..., N ₎ using the result of predicting the evaluation value y of the untried synthesis condition x.

It is possible to generate synthesis conditions that result in the optimal material under given evaluation criteria.

FIG. 13 is a diagram showing an example of a trial for obtaining a synthesis condition with a good evaluation value. 1 is a diagram illustrating an example of an overall configuration of a synthesis condition generation system according to an embodiment of the present invention. FIG. 2 is a diagram illustrating an example of a hardware configuration of a synthesis condition generating device according to the present embodiment. FIG. 2 is a diagram illustrating an example of a functional configuration of a synthesis condition generating device according to the present embodiment. 11 is a flowchart illustrating an example of a synthesis condition generation process according to the embodiment. FIG. 13 is a diagram showing evaluation values in a simulation experiment. FIG. 13 is a diagram showing the results of a simulation experiment. 1 shows the results of _SrRuO3 experiments.

One embodiment of the present invention will be described below. In the following embodiment, a synthesis condition generation system 1 that can generate synthesis conditions for obtaining an optimal substance under a given evaluation index will be described.

<Overall configuration of synthesis condition generation system 1>
An example of the overall configuration of the synthesis condition generating system 1 according to this embodiment is shown in Fig. 2. As shown in Fig. 2, the synthesis condition generating system 1 according to this embodiment includes a synthesis condition generating device 10, a material generating device 20, and a material evaluating device 30.

The synthesis condition generating device 10 generates synthesis conditions to be used in the current trial using the synthesis conditions (recipe) obtained up to the previous trial and its evaluation value, with n as an index representing the number of trials. Synthesis conditions are conditions for obtaining a certain substance by proceeding with the reaction of one or more raw materials by a certain method (for example, the amount of composition elements, reaction temperature, timing of inputting raw materials, etc.), and are generally expressed as vectors. As an example, in a task for generating a _SrRuO3 thin film, the synthesis conditions are expressed as a vector having three elements: (a) the supply amount of Ru, (b) the temperature of the substrate to which the thin film is attached, and (c) the distance between the ozone nozzle that supplies oxygen atoms O and the substrate. Hereinafter, the nth trial is also referred to as "trial n", and the synthesis conditions used to generate a substance in trial n are "x _n ".

The material generating device 20 generates a material (sample) by promoting the reaction of the raw material according to the synthesis conditions generated by the synthesis condition generating device 10. The material generating device 20 is, for example, a device that generates a material by thin film synthesis/bulk synthesis methods such as molecular beam epitaxy, sputtering, pulsed laser ablation, physical vapor deposition, chemical vapor deposition, spin coating, atomic layer deposition, floating zone method, flux method, Czochralski method, etc. As an example, in the task of generating a _SrRuO3 thin film, a thin film generating device using a molecular beam epitaxy method can be used as the material generating device 20.

The material evaluation device 30 measures an evaluation value obtained by evaluating the material (sample) generated by the material generation device 20 using a predetermined evaluation index. As the evaluation index, an existing evaluation index according to the desired material and its shape (thin film, bulk, etc.) may be used. As an example, in a task of generating a _SrRuO3 thin film, the residual resistivity ratio (RRR) may be used as an evaluation index for measuring the quality of the arrangement of elements in the thin film.

Hereinafter, the evaluation value will be defined as consisting of binary information indicating whether or not a substance (sample) is a stable substance or a desired substance, and a scalar value indicating the quality of that substance, and will take a scalar value if the substance is stable or the desired substance, and NaN if the substance is neither stable nor the desired substance. For example, if one wishes to obtain an insulator with high electrical resistance, the evaluation value will be the electrical resistance value if the desired sample is obtained, and NaN if not. Note that NaN stands for Not a Number.

In the following description, the evaluation value for the material generated by the material generating device 20 according to the synthesis condition _xn is defined as "y _n ", and the larger the evaluation value, the better the evaluation. Note that in cases where the smaller the evaluation value, the better the evaluation, it is possible to similarly apply this embodiment by, for example, inverting the sign of the evaluation value.

Here, in the synthesis condition generation system 1 according to the present embodiment, the synthesis condition generation device 10 generates synthesis conditions x _N+1 using synthesis conditions obtained in past trials and their evaluation values {(x _n , _yn )|n=1,...,N} (where N is the number of trials so far), the material generation device 20 generates a substance (sample) according to the synthesis conditions x _N+1 , and the material evaluation device 30 evaluates the sample and measures the evaluation value y _N+1 . By repeating such trials, synthesis conditions that give a good evaluation value are searched for. In the following, the material generation device 20 and the material evaluation device 30 are treated as black boxes, and the synthesis condition generation device 10 generates synthesis conditions x _N + ₁ that give a better evaluation value in the N+1th trial using the synthesis conditions obtained in past trials and their evaluation values {(x _{n ,} yn )|n=1,...,N} will be described. As a result, by repeating these trials, it is possible to generate synthesis conditions that can obtain an optimal substance.

However, the overall configuration of the synthesis condition generation system 1 shown in Figure 2 is an example and is not limited to this. For example, the synthesis condition generation device 10 and two or more devices among the material generation device 20 and the material evaluation device 30 may be realized by the same device.

<Hardware configuration of the synthesis condition generation device 10>
An example of the hardware configuration of the synthesis condition generating device 10 according to this embodiment is shown in Fig. 3. As shown in Fig. 3, the synthesis condition generating device 10 according to this embodiment has an input device 101, a display device 102, an external I/F 103, a communication I/F 104, a RAM (Random Access Memory) 105, a ROM (Read Only Memory) 106, an auxiliary storage device 107, and a processor 108. Each of these pieces of hardware is connected to each other so as to be able to communicate with each other via a bus 109.

The input device 101 is, for example, a keyboard, a mouse, a touch panel, etc. The display device 102 is, for example, a display, a display panel, etc. Note that the synthesis condition generation device 10 may not have at least one of the input device 101 and the display device 102, for example.

The external I/F 103 is an interface with an external device such as a recording medium 103a. The synthesis condition generation device 10 can read and write data from and to the recording medium 103a via the external I/F 103. Examples of the recording medium 103a include a flexible disk, a CD (Compact Disc), a DVD (Digital Versatile Disk), a SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

The communication I/F 104 is an interface for connecting the synthesis condition generation device 10 to a communication network. The RAM 105 is a volatile semiconductor memory (storage device) that temporarily stores programs and data. The ROM 106 is a non-volatile semiconductor memory (storage device) that can store programs and data even when the power is turned off. The auxiliary storage device 107 is a storage device (storage device) such as a hard disk drive (HDD) or a solid state drive (SSD). The processor 108 is an arithmetic device such as a central processing unit (CPU) or a graphics processing unit (GPU).

The synthesis condition generation device 10 according to this embodiment has the hardware configuration shown in FIG. 3, and is therefore capable of realizing the synthesis condition generation process described below. Note that the hardware configuration shown in FIG. 3 is merely an example, and the hardware configuration of the synthesis condition generation device 10 is not limited thereto. For example, the synthesis condition generation device 10 may have multiple auxiliary storage devices 107 and multiple processors 108, or may have various other hardware besides the hardware shown in the figure.

<Functional configuration of the synthesis condition generating device 10>
FIG. 4 shows a functional configuration example of the synthesis condition generating device 10 according to this embodiment. As shown in FIG. 4, the synthesis condition generating device 10 according to this embodiment has an evaluation value input unit 201, an evaluation value prediction unit 202, a synthesis condition search unit 203, and a synthesis condition output unit 204. Each of these units is realized, for example, by a process in which one or more programs installed in the synthesis condition generating device 10 are executed by the processor 108 or the like. In addition, the synthesis condition generating device 10 according to this embodiment has a storage unit 205. The storage unit 205 is realized, for example, by the auxiliary storage device 107 or the like. Note that the storage unit 205 may be realized, for example, by a storage device such as a database server connected to the synthesis condition generating device 10 via a communication network.

The evaluation value input unit 201 inputs an evaluation value _yN evaluated by the material evaluation device 30 in trial N (previous trial). The evaluation value _yN is stored in the storage unit 205.

Here, since each evaluation value _yn (n=1,...,N) can take NaN, a conversion process is required when _yn =NaN. In addition, the prediction accuracy when the evaluation value prediction unit 202 predicts the evaluation value may deteriorate due to differences in scale of each element constituting the synthesis condition _xn and the scale of the evaluation value _yn itself. Therefore, in order to ensure the prediction accuracy and efficiently search for synthesis conditions, normalization processing of the synthesis condition _xn and its evaluation value _yn is required. Therefore, when the evaluation value input unit 201 inputs the evaluation value _yn , it converts the evaluation value _yn to _yn ' for each n=1,...,N by the following conversion process, and normalizes the synthesis conditions _xn and _yn ' by the following normalization process.

Conversion Process The evaluation value input unit 201 converts each evaluation value y _n (n=1, . . . , N) according to the following formula (1).

ここで、

Where:

である。すなわち、ｙ_ｎ＝ＮａＮである場合は、これまでの試行における最悪の評価値とする。ただし、これまでのすべての試行でｙ_ｎ＝ＮａＮである場合は、

That is, if y _n =NaN, the worst evaluation value in the trials so far is used. However, if y _n =NaN in all trials so far,

とする。このように、評価値が得られなかった合成条件に対しては、これまで得られた評価値の最悪の値で代用する。これにより、従来手法の問題点である「評価値が得られない合成条件があり得る」という点が解決される。

In this way, for a synthesis condition for which no evaluation value has been obtained, the worst evaluation value obtained so far is substituted. This solves the problem of the conventional method that "there may be synthesis conditions for which no evaluation value can be obtained."

Normalization Processing Hereinafter, the synthesis condition _xn is assumed to be a vector composed of D elements, where _xn = [xn _,1 ,...,xn _,D ] ^T , where T represents the transpose of a vector or matrix.

D elements xn _,d (d=1,...,D) represent conditions for obtaining a certain material by a certain method. As an example, in a task of producing a _SrRuO3 thin film, xn _,1 represents the supply amount of Ru, xn _,2 represents the temperature of the substrate on which the thin film is deposited, and xn _,3 represents the distance between the ozone nozzle that supplies oxygen atoms O and the substrate.

The lower and upper limits of the search range for the d-th element x _{n, d} are

とする。ただし、

However,

である。

It is.

At this time, the evaluation value input unit 201 normalizes the synthesis condition x _n =[x _n,1 , . . . , x _n,D ] ^T to obtain a normalized synthesis condition

の各要素を以下の式（２）により求める。

Each element of is calculated using the following formula (2).

同様に、評価値に関してもおおよその値の範囲

Similarly, the approximate range of evaluation values

が与えられるのであれば、評価値入力部２０１は、その範囲を用いて、以下の式（３）によりｙ_ｎ'を正規化した正規化評価値を求める。

is given, the evaluation value input unit 201 uses that range to obtain a normalized evaluation value by normalizing y _n ' using the following formula (3).

一方で、評価値に関するおおよその値の範囲が与えられない場合、評価値入力部２０１は、

On the other hand, if an approximate value range for the evaluation value is not given, the evaluation value input unit 201

として式（３）によりｙ_ｎ'を正規化した正規化評価値を求める。

Then, a normalized evaluation value is calculated by normalizing y _n ' using equation (3).

In the text of the specification below, the normalized composition condition obtained by normalizing the composition condition _xn is expressed as ^" _xn " and the normalized evaluation value obtained by normalizing the evaluation value _yn ' after the conversion process is expressed as " ^yn _' ". Furthermore, when there is no risk of misunderstanding, the normalized composition condition is also simply referred to as the "composition condition" and the normalized evaluation value is also simply referred to as the "evaluation value". Furthermore, the variable representing the normalized composition condition is expressed ^as "x", and the variable representing the normalized evaluation value is expressed as ^" y".

The evaluation value prediction unit 202 predicts the evaluation value ~y taken by the synthesis condition ~x that has not been tried so far, using the normalized synthesis condition ^and the normalized evaluation value D _N :={( ^~ _xn , ^~ _yn ')|n=1,...,N} obtained by the evaluation value input unit 201. Here, ^~ y is hereinafter defined as a random variable following a normal distribution with mean μ( ^~ x) and variance ^σ2 ( ^~ x) ^.

として、Ｄ_Ｎを用いて、合成条件^～ｘに依存するμ（^～ｘ）、σ^２（^～ｘ）をガウス過程により算出する。

Then, using D _N , μ( ^∼ x) and σ ² ( ^∼ x), which depend on the synthesis condition ^∼ x, are calculated by the Gaussian process.

In a Gaussian process, the joint distribution of ^.about.y ₁ ', . . . , ^.about.y _N ' is modeled as a normal distribution with covariance matrix K _N :

ここで、Ｋ_ｍｎは共分散行列Ｋ_Ｎのｍ行ｎ列の要素である。共分散行列Ｋ_Ｎの各要素を構成するｋ（^～ｘ_ｍ，^～ｘ_ｎ）はカーネル関数と呼ばれ、^～ｘ_ｍと^～ｘ_ｎの類似度を表している。すなわち、^～ｘ_ｍと^～ｘ_ｎが似通った値である場合、Ｋ_ｍｎは大きな値を取り、その結果、^～ｙ_ｍ'と^～ｙ_ｎ'の相関が高まる（似通った値を取りやすい）というモデルである。本実施形態では、一例として、カーネル関数ｋにはＲＢＦ（radial basis function）カーネルを採用した。

Here, K _mn is an element of the mth row and nth column of the covariance matrix K _N. k ( ^∼ x _m , ^∼ x _n ) constituting each element of the covariance matrix K _N is called a kernel function, and represents the similarity between ^∼ x _m and ^∼ x _n . That is, when ^∼ x _m and ^∼ x _n are similar values, K _mn takes a large value, and as a result, the correlation between ^∼ y _m ' and ^∼ y _n ' increases (they tend to take similar values). In this embodiment, as an example, a radial basis function (RBF) kernel is adopted for the kernel function k.

If the RBF kernel is a kernel function k, then for ^{.about.xm and .about.xn} _, which are D-dimensional _vectors , the kernel function k is expressed as follows:

ここで、Ａ＞０はカーネル関数に与えられるパラメータである。

Here, A>0 is a parameter given to the kernel function.

It should be noted that a kernel function other than the RBF kernel may be adopted as the kernel function k. For example, in cases where the evaluation value changes sharply with respect to the synthesis conditions ^to x, the Matern kernel described in Non-Patent Document 2 may be adopted. In addition to this, various other kernel functions may be adopted as necessary.

At this time, the evaluation value prediction unit 202 uses the above kernel function k(.,.) and D _N to calculate μ( ^.about.x ) and σ ² ( ^.about.x ) in the following equation (4).

したがって、この正規分布のパラメータを用いて、式（４）により未試行の合成条件^～ｘに対する評価値を予測することができる。なお、これにより、合成条件と評価値の関係が陽に記述される。

Therefore, using the parameters of this normal distribution, it is possible to predict the evaluation value for untried synthesis conditions ^∼ x by equation (4). This explicitly describes the relationship between the synthesis conditions and the evaluation value.

The synthesis condition search unit 203 searches for synthesis conditions ^~ x that give a better evaluation value ^~ y using the distribution of evaluation values predicted by formula (4). When a certain synthesis condition ^~ x is given, the corresponding μ( ^~ x) and ^σ2 ( ^~ x) are found by formula (9). Therefore, the best evaluation value in the trials so far is used as a measure of the quality of a certain synthesis condition ^~ x.

からの改善の期待値

Expected improvement from

を用いる。ただし、ｐ（^～ｙ）は平均μ（^～ｘ）、分散σ^２（^～ｘ）の正規分布の確率密度関数である。また、Φ（・）及びφ（・）はそれぞれ、平均０、分散１の標準正規分布の累積密度関数及び確率密度関数である。

where p( ^~ y) is the probability density function of a normal distribution with mean μ( ^~ x) and variance ^σ2 ( ^~ x). Also, Φ(·) and φ(·) are the cumulative density function and probability density function of a standard normal distribution with mean 0 and variance 1, respectively.

In the example shown in equation (10), the expected value of improvement in the evaluation value (Reference 1) is used, but other criteria can also be used to improve the efficiency of the search (References 2 and 3).

As a result, the problem of searching for a good synthesis condition ^~ x can be reduced to the problem of searching for a synthesis condition ^~ x that makes the formula (10) larger.

へと帰着する。

It all comes down to...

Here, when the dimension of the search space of the synthesis condition ^∼x is large, the number of points for evaluating formula (10) increases as an exponential function of the dimension. Therefore, in order to reduce the number of evaluations of formula (10), formula (10) is first evaluated on a coarse grid, and then a region having the top few points with the highest expected value of improvement at its vertices is selected, and the grid resolution is increased within that region for evaluation, thereby approximately maximizing formula (11). In other words, first, the search space is searched and evaluated on a grid with a coarse resolution, and then the region having the top few points with the highest evaluation results is searched and evaluated on a grid with a finer resolution.
This gives the synthesis condition ^.about.xN ₊₁ that approximately maximizes the expectation value of equation (10).

The synthesis condition output unit 204 performs an inverse normalization process (a process of returning normalization to the original state) shown in the following formula (12) on each element of the synthesis conditions ^to x _N+1 searched for by the synthesis condition search unit 203, and outputs x _N+1 = [x _N+1 , 1, ..., x _{N+1, D} ] ^T.

これにより、Ｎ＋１回目の試行では合成条件ｘ_Ｎ＋１により物質（試料）の生成とその評価とが行われる。なお、この合成条件ｘ_Ｎ＋１は記憶部２０５に記憶される。

As a result, in the (N+1)th trial, a substance (sample) is generated and evaluated under the synthesis condition x _N+1 . Note that this synthesis condition x _N+1 is stored in the storage unit 205.

The storage unit 205 stores the synthesis conditions obtained in the past trials and their evaluation values {( _xn , _yn )|n=1, ..., N}. The storage unit 205 also stores the normalized synthesis conditions and normalized evaluation values {( ^xn _, ^yn _' )|n=1, ..., N}.

<Synthetic condition generation process>
Next, the synthesis condition generation process according to the present embodiment will be described with reference to Fig. 5. In the following, a case will be described in which, after N trials have been performed, a synthesis condition xN+1 that gives a better evaluation value in the N ₊ 1th trial is generated.

First, the evaluation value input unit 201 inputs an evaluation value _yN of the previous trial N (step S101). This evaluation value _yN is stored in the storage unit 205 as ( _xN , _yN ) in association with the synthesis condition _xN in the previous trial N. Note that the synthesis condition _xN in the previous trial N has already been stored in the storage unit 205.

Next, the evaluation value input unit 201 converts each of the evaluation values y _n (n=1, . . . , N) thus far into y _n ' by the conversion process of equation (1) (step S102).

Next, the evaluation value input unit 201 normalizes the synthesis conditions x _n (n=1, . . . , N) so far and the evaluation values y _n ' (n=1, . . . , N) after the conversion process by normalization processing (step S103).

That is, the evaluation value input unit 201 normalizes the combining condition _xn using equation (2) to generate a normalized combining condition ^∼xn , and also generates a normalized evaluation value ^∼yn ' by normalizing the ^{evaluation value yn' after the conversion process using equation (3). These normalized combining conditions and normalized evaluation values (∼xn} _{, ∼yn '} ⁾ _are stored in _the storage unit 205.

The following steps S104 to S107 are repeatedly executed for untried synthesis conditions ^to x in the search space. As described above, it is preferable to first repeat the following steps S104 to S107 with coarse grids in the search space as untried synthesis conditions, and then select an area having top several points with high expected improvement values as vertices, increase the resolution of the grids in that area, and repeat the following steps S104 to S107 with those grids as untried synthesis conditions. Steps S104 to S107 in a certain repetition are described below.

The evaluation value prediction unit 202 selects untried synthesis conditions ^∼ x from within the search space (step S104).

Next, the evaluation value prediction unit 202 predicts the evaluation value of the synthesis condition ^to x selected in step S104 above (step S105). Specifically, the evaluation value prediction unit 202 calculates the mean μ( ^to x) and variance σ ² ( ^to x) that determine the distribution of the evaluation values of the synthesis condition ^to x using equation (9).

Next, the synthesis condition search unit 203 uses the distribution of evaluation values predicted by equation (4) to calculate the expected value of equation (10) (the expected improvement from the highest evaluation value obtained in the first N trials) (step S106).

Then, the synthesis condition search unit 203 evaluates the expected values obtained in step S106 above (for example, sorting the expected values obtained so far in ascending or descending order, identifying the maximum value, etc.) (step S107).

By repeating the above steps S104 to S107, the synthesis condition ^.about.x _N+1 shown in equation (11) is approximately obtained.

The synthesis condition output unit 204 performs the inverse normalization process of the formula (12) on the synthesis condition ^∼ x _N+1 finally obtained by repeating the above steps S104 to S107, to generate the synthesis condition x _N+1 (step S108). Note that this synthesis condition x _N+1 is stored in the storage unit 205.

Then, the synthesis condition output unit 204 outputs the synthesis condition x _N+1 obtained in the above step S108 to the material generating device 20 (step S109).

As a result, synthesis conditions _N+1 for the N+1th trial are obtained. Therefore, in the N+1th trial, a sample (substance) is generated by the material generation device 20 according to these synthesis conditions _N+1 , and this sample is evaluated by the material evaluation device 30 to measure an evaluation value yN ₊₁ . By repeating such trials a predetermined number of times, the synthesis conditions used to generate the sample for which the best evaluation value (e.g., the maximum evaluation value) was measured are obtained as synthesis conditions for obtaining an optimal substance.

<Experimental Results>
Below, two types of experimental results using the synthesis condition generation system 1 according to this embodiment will be described. The first is an experiment using simulation data (hereinafter referred to as a simulation experiment), in which a two-dimensional synthesis condition search space is given as simulation data. The second is an experiment to generate _SrRuO3 by molecular beam epitaxy (hereinafter referred to as a _SrRuO3 experiment).

Simulation Experiment In this experiment, an evaluation value expressed by the following formula (13) was used.

ただし、各定数の値はそれぞれ以下である。

However, the values of each constant are as follows:

また、||ｖ||_１＝Σ_ｄ｜ｖ_ｄ｜はベクトルｖのＬ_１ノルムを表す。

Furthermore, ||v|| ₁ =Σ _d |v _d | represents the L ₁ norm of the vector v.

The above evaluation value is maximum at y≈1.24 near x≈[0.48, 0.52] ^T .

The search range for the composite condition is x∈[-1,1]×[-1,1]. However,

の範囲内でのみ評価値は式（１３）に従い、それ以外の範囲ではｙ＝ＮａＮとなる。本実験で用いた評価値を図示すると図６のようになる。

The evaluation value follows formula (13) only within the range, and y = NaN outside the range. The evaluation values used in this experiment are shown in FIG.

The results of this experiment are shown in Figure 7. In Figure 7, Our method represents the synthesis condition generation system 1 according to this embodiment. pad is a conventional method that treats NaN as an evaluation value of 0. In Figure 7, the horizontal axis represents the number of trials to obtain an evaluation value, and the vertical axis represents the highest evaluation value excluding NaN obtained up to that trial (i.e., the further the graph is in the upper left (fewer trials and higher evaluation values) the better).

As shown in Figure 7, the Our method achieved an evaluation value of over 1.20 after about 15 trials, whereas the PAD method achieved an evaluation value of less than 1.20 even after more than 30 trials. This shows that the Our method achieved a better evaluation value with fewer trials than the conventional method.

_SrRuO3 Experiment Each element of the synthesis conditions and its search range are shown in Table 1 below.

評価値は残留抵抗比ｙ：＝ρ（３００Ｋ）／ρ（４Ｋ）を用いた。ただし、薄膜生成に用いられた合成条件ｘの値によってはｙ＝ＮａＮである。

The evaluation value used was the residual resistance ratio y:=ρ(300K)/ρ(4K), where y=NaN depending on the value of the synthesis condition x used in forming the thin film.

The results of this experiment are shown in Figure 8. In Figure 8, the horizontal axis shows the number of trials to obtain an evaluation value, and the vertical axis shows the highest evaluation value obtained up to that trial. As shown in Figure 8, a continuous improvement in the evaluation value can be confirmed as the number of trials increases.

<Summary>
As described above, the synthesis condition generation system 1 according to this embodiment can automatically search in a synthesis condition space where material generation may or may not be successful to discover synthesis conditions with good evaluation values, and can be utilized, for example, in the creation of new materials, etc. Furthermore, the synthesis condition generation system 1 according to this embodiment can optimize (maximize or minimize) evaluation values with fewer trials than conventional methods, and is expected to have the effect of reducing the development period and development time of new materials and reducing costs.

The present invention is not limited to the specifically disclosed embodiments above, and various modifications, variations, and combinations with known technologies are possible without departing from the scope of the claims.

[References]
Reference 1: J. Mockus, V. Tiesis, and A. Zilinskas: The application of Bayesian methods for seeking the extremum. Towards Global Optimization 2, 1978.
Reference 2: N. Srinivas, A. Krause, S. Kakade, and M. Seeger: Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design, International Conference on Machine Learning, 2010.
Reference 3: E. Contal, V. Perchet, and N. Vayatis: Gaussian Process Optimization with Mutual Information, International Conference on Machine Learning, 2014.

REFERENCE SIGNS LIST 1 synthesis condition generation system 10 synthesis condition generation device 20 material generation device 30 material evaluation device 101 input device 102 display device 103 external I/F
103a Recording medium 104 Communication I/F
105 RAM
106 ROM
107 Auxiliary storage device 108 Processor 109 Bus 201 Evaluation value input unit 202 Evaluation value prediction unit 203 Synthesis condition search unit 204 Synthesis condition output unit 205 Storage unit

Claims (7)

A synthesis condition generation method for generating synthesis conditions in a trial in which a substance is generated according to a synthesis condition, an evaluation value is measured for evaluating the substance, and the synthesis condition is generated, the synthesis condition generation method comprising the steps of:
an evaluation value conversion procedure for replacing the evaluation value y _n′ in trial n′ with the worst evaluation value when there is a trial n′ in which the evaluation value y _n′ (n′∈{1, . . . , N}) of the substance cannot be measured among the N trials so far;
A prediction procedure for predicting an evaluation value y of an untried synthesis condition _{x using a synthesis condition x n and} an evaluation value y n in a trial n (n=1, . . . , N);
a generation step of generating a synthesis condition xN+1 in trial N+1 that has an evaluation value better than the best evaluation value _yn (n=1, . . . , N) by using a result of predicting the evaluation value y of the untried synthesis condition x _;
The computer executes
The prediction step comprises:
Selecting an untried synthesis condition x from grid points of a predetermined first resolution within a search space of synthesis conditions, and predicting an evaluation value y of the selected untried synthesis condition;
After all of the untried synthesis conditions x have been selected from the grid points of the first resolution, a predetermined number of the untried synthesis conditions x are selected based on a predetermined condition, and within an area having the selected untried synthesis conditions x as vertices, untried synthesis conditions x are selected from grid points of a second resolution higher than the first resolution, and an evaluation value y of the selected untried synthesis conditions is predicted . The prediction step comprises:
Using a synthesis condition x _n and an evaluation value y _n in a trial n (n=1, . . . , N), a mean μ(x) and a variance σ ² (x) that depend on the untried synthesis condition x are calculated as a result of the prediction;
The generating procedure includes:
2. The synthesis condition generating method according to claim ¹ , further comprising the steps of: calculating an expected value for which the evaluation value y of the untried synthesis condition x takes an evaluation value better than the best value using the mean μ(x) and the variance σ 2 (x); and generating an untried synthesis condition with the maximum expected value as the synthesis condition x _N+1 . The prediction step comprises:
3. The synthesis condition generating method according to claim 2, further comprising the steps of: selecting a predetermined number of the untried synthesis conditions x in descending order of expected value after all the untried synthesis conditions x have been selected from the grid points of the first resolution. The synthesis condition generation method includes:
A normalization procedure is further included for normalizing the synthesis condition x _N and the evaluation value y _N in the trial N;
The prediction step comprises:
The synthesis condition generating method according to claim 1 , further comprising the step of predicting an evaluation value y of the untried synthesis condition x using the normalized synthesis condition _xn and evaluation value _yn . The evaluation value conversion step includes:
5. The synthesis condition generating method according to claim 1, wherein if all evaluation values _yn (n=1, . . . , N) in trial n (n=1, . . . , N) cannot be measured, _yN =0 is set. A synthesis condition generating device for generating synthesis conditions in a trial in which a substance is generated according to a synthesis condition, an evaluation value is measured for evaluating the substance, and the synthesis condition is generated, the synthesis condition generating device comprising:
an evaluation value conversion unit that, when there is a trial n' in which the evaluation value y _n' (n' ∈ {1, ..., N}) of a substance cannot be measured among the N trials so far, replaces the evaluation value y _n' in the trial n' with the worst evaluation value;
A prediction unit configured to predict an evaluation value y of an untried synthesis condition _x by using a synthesis condition x _n and an evaluation value y n in a trial n (n=1, . . . , N);
a generation unit configured to generate a synthesis condition xN+1 in trial N+1 that has an evaluation value better than the best evaluation value _yn (n=1, . . . , N) by using a result of predicting the evaluation value y of the untried synthesis condition _x ;
having
The prediction unit is
Selecting an untried synthesis condition x from grid points of a predetermined first resolution within a search space of synthesis conditions, and predicting an evaluation value y of the selected untried synthesis condition;
After all of the untried synthesis conditions x have been selected from the grid points of the first resolution, a predetermined number of the untried synthesis conditions x are selected based on a predetermined condition, and within an area having the selected untried synthesis conditions x as vertices, an untried synthesis condition x is selected from grid points of a second resolution higher than the first resolution, and an evaluation value y of the selected untried synthesis condition is predicted . A program for causing a computer to execute the synthesis condition generation method according to any one of claims 1 to 5.

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