A method for predicting the state of a light source.

Abstract

A method for predicting the state of a light source, including a laser system, includes: acquiring features of the light source that represent the operating mode of the light source; clustering the features into clusters using a machine learning algorithm that utilizes unsupervised learning, wherein the clusters represent the states of the light source; generating an inter-cluster transition matrix that represents the transition probability of the light source transitioning between clusters after a time interval, wherein the clusters include one or more terminal clusters for which the probability of transitioning to another cluster is zero; and generating a non-binary prediction of the future clusters and states of a given light source having features corresponding to a given cluster and state by applying the transition matrix one or more times.

Description

Technical Field

[0001] Cross - reference to Related Applications

[0001] This application claims priority to U.S. Application No. 63 / 510,915, filed on June 29, 2023, and titled METHODS FOR PREDICTING STATES OF LIGHT SOURCES, and U.S. Application No. 63 / 567,039, filed on March 19, 2024, and titled METHODS FOR PREDICTING STATES OF LIGHT SOURCES, the entireties of which are incorporated herein by reference.

Background Art

[0002]

[0002] The present disclosure relates to methods for predicting the state of a light source, such as a laser system, and more particularly to methods for predicting the state of a light source used when providing light to a lithographic apparatus.

[0003]

[0003] The light (which may be laser radiation) used for semiconductor photolithography is typically supplied by a light source or, in some cases, a system called a laser system. These light sources generate ultraviolet radiation as a series of pulses at a specified repetition rate within a range, for example, from about 500 Hz to about 6 kHz. In view of the high economic value generated during the semiconductor manufacturing process, performance and uptime are important for users of the light sources of such photolithographic exposure equipment.

Summary of the Invention

[0004]

[0004] In some general embodiments, methods are provided for predicting the state of a light source, including a laser system, the method comprising: acquiring features of the light source, the features representing the operating modes of the light source; clustering the features into clusters, the clusters representing the states of the light source, using a machine learning algorithm that utilizes unsupervised learning; generating a transition matrix between clusters, the transition matrix representing the transition probabilities that the light source will transition between clusters after a time interval, and the clusters include one or more terminal clusters that have a probability of zero of transitioning to another cluster; and generating a non-binary prediction of future clusters and states of a given light source having features corresponding to a given cluster and state by applying the transition matrix one or more times.

[0005]

[0005] The implementation may include one or more of the following features: The light source may be a member of a group of similar light sources having similar components, operating methods, and features. The method may further include calculating the probability of transitions between a first cluster and a second cluster within a given time using a Markov chain by iteratively applying a transition matrix. The first cluster may represent the current state of a given light source, and the second cluster may be a terminal cluster. The time interval may be in the range of 1 hour to 1 week. The time interval may be 1 day.

[0006]

[0006] The characteristics of the light source may include historical data from a set of similar light sources. The characteristics of the light source may include characteristics of two or more modules of the light source. The characteristics of the light source may include characteristics of the main oscillator (MO) module and characteristics of the power amplifier (PA) or power ring amplifier (PRA) module.

[0007]

[0007] Generating a transition matrix between clusters may involve using historical data to generate the probability that a light source will transition between clusters after a time interval. The method may further involve using a Markov chain to determine the probability of a transition between a first cluster and a second cluster within a given time limit by iteratively applying the transition matrix up to a time limit.

[0008]

[0008] The method may further include: acquiring updated features of a light source, the updated features representing updated operating modes of the light source; clustering the features and updated features into updated clusters using a machine learning algorithm that utilizes unsupervised learning, the updated clusters representing states of the light source; generating an updated transition matrix between the updated clusters, the updated transition matrix representing transition probabilities of the light source transitioning between updated clusters after a time interval, and the updated clusters including one or more terminal clusters with a probability of zero transitioning to another updated cluster; and generating non-binary predictions of future updated clusters and states of a given light source having features corresponding to a given updated cluster by applying the updated transition matrix one or more times. The updated terminal clusters may be different from the previous terminal cluster.

[0009]

[0009] The features may include one or more time-dependent features or history-dependent features. One or more time-dependent features or history-dependent features may include one or more rates of change of one or more aspects of the light source. One or more time-dependent features or history-dependent features may include one or more measures of the variability of one or more aspects of the light source. One or more time-dependent features or history-dependent features may include one or more measures of the central tendency of one or more aspects of the light source.

[0010]

[0010] In an additional general embodiment, a method is provided for predicting the state of a light source, such as a laser system, which includes acquiring features of the light source, the features representing the operating mode of the light source, and the features including one or more time-dependent or history-dependent features; clustering the features into respective clusters representing each state of the light source using a machine learning algorithm utilizing unsupervised learning; generating a transition matrix representing each probability that the light source will transition between each cluster after a time interval; and generating a probability matrix representing the probability that a given light source will be in each respective cluster after N time intervals by raising the transition matrix to the power of N.

[0011]

[0011] The implementation may include one or more of the following features: One or more time-dependent features or history-dependent features may include one or more rates of change of one or more aspects of the light source. One or more time-dependent features or history-dependent features may include one or more measures of the variability of one or more aspects of the light source. One or more time-dependent features or history-dependent features may include one or more measures of the central tendency of one or more aspects of the light source. A cluster may include one or more clusters with a probability of transitioning to another cluster of zero.

[0012]

[0012] In an additional general embodiment, a method is provided for examining a significant change in the distribution of light source data or features in order to detect a significant change in the distribution of the data or features used by a model for prediction, detection, simulation, etc., in particular, the method comprising: determining the cumulative distribution function of the model training data; determining the cumulative distribution function of the data to be used by the model for prediction, detection, simulation, etc. ("modeling data"); and determining whether, at any given time, the cumulative distribution function of the modeling data has deviated by a value exceeding an acceptable limit from the cumulative distribution function of the training data.

[0013]

[0013] The implementation form may include one or more of the following:

[0014]

[0014] If the cumulative distribution function of the modeling data does not deviate from the cumulative distribution function of the training data by an amount exceeding the tolerance at any given time, (a) repeatedly decrease the tolerance, and (b) determine whether the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by an amount exceeding the tolerance at any given time, until the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by an amount exceeding the tolerance at a given time, and report the last tolerance and / or the second to last tolerance.

[0015]

[0015] The permissible value may be in the range of greater than zero to 0.1.

[0016]

[0016] Details of one or more implementations are described in the accompanying drawings and the following description. Other features will also become apparent from the description and drawings, as well as from the claims. [Brief explanation of the drawing]

[0017] [Figure 1A]

[0017] This is a flowchart of one implementation form of a procedure for predicting the state of a light source. [Figure 1B]

[0018] This is a flowchart of another implementation of a procedure for predicting the state of a light source. [Figure 2A]

[0019] This diagram shows an example of multiple clusters or states of a light source, illustrating the probability of transitioning between clusters or states after a specified time interval. [Figure 2B]

[0020] This figure illustrates another example of multiple clusters or states of a light source, showing the transition probabilities of transitioning between clusters or states after a time interval. [Figure 3]

[0021] This is an example of a transition matrix corresponding to the figure in Figure 2B, with the corresponding clusters from Figure 2B displayed in the rows and columns. [Figure 4]

[0022] An example of the calculated probabilities of transitions from and to the illustrated clusters after 14 time intervals, obtained by raising the transition matrix of FIG. 3 to the 14th power. [Figure 5]

[0023] A block diagram of an example of a light source or laser system (in this case a deep ultraviolet (DUV) light source) that can be used together with the processes described herein. [Figure 6]

[0024] A block diagram of an example of a lithographic apparatus that can be used together with the light source of FIG. 5. [Figures 7A-7D]

[0025] A graph showing a method of examining significant changes in the distribution of light source data or characteristics.

Embodiments for Carrying Out the Invention

[0018]

[0026] FIG. 1A is a flowchart of one implementation of a procedure for predicting the state of a light source. As used herein, the “state” of a light source refers to the physical state and / or operating state of the light source, characterized by the light source having characteristics corresponding to one of a plurality of clusters previously determined and / or defined by the use of unsupervised machine learning using historical data including characteristics. The “characteristics” used in this sense include direct measurements from the light source or light source module or equipment or devices associated with or connected to the light source, as well as values calculated based on such measurements (such as calculated performance metrics measured and calculated over time). Such characteristics at least partially characterize the operation, performance or state of the light source, or are related thereto if not.

[0019]

[0027] As shown in FIG. 1A, the procedure and method P100A for predicting the state of a light source includes obtaining the characteristics of the light source (S10A). As will be referred to and discussed in more detail below, including the description regarding FIG. 5, the characteristics represent or are related to the operating mode of the light source. The procedure P100A further includes clustering the characteristics into clusters that represent or correspond to states via unsupervised machine learning (S12A), generating a transition matrix for transitions between clusters including terminal clusters (defined and discussed in more detail below) (S14A), and generating a non-binary prediction of the future clusters and states of a given light source by applying the transition matrix one or more times (S16A).

[0020]

[0028] FIG. 1B is a flowchart of another implementation of the procedure for predicting the state of a light source. As shown in FIG. 1B, the procedure and method P100B for predicting the state of a light source includes obtaining the characteristics of the light source, where the characteristics include one or more time-dependent characteristics or history-dependent characteristics (S10B). The procedure P100B further includes clustering the characteristics via unsupervised learning (S12B), generating a transition matrix for transitions between clusters (S14B), and generating a non-binary prediction of the future clusters and states of a given light source by applying the transition matrix one or more times (S16B). Aspects and details regarding the use and application of the procedure or methods P100A and P100B are discussed below.

[0021]

[0029] By detecting or detecting and storing the operating patterns of a light source over time, features representing the operating patterns of the light source can be acquired over time. To successfully predict future states, the light sources may be a group of similar light sources having similar components, operating methods, and similar detected and stored features. Features may include performance measurements or other metrics, and may include one or more time-dependent or history-dependent features or metrics. Features may include, for example, bandwidth and center wavelength, pulse energy, average power, peak intensity, power per pulse, and energy efficiency. Trends, measured values ​​of central trends, and / or rates of change relating to any of these may also be features. In this way, several time- and / or history-dependent behaviors can be represented in the prediction methods disclosed herein.

[0022]

[0030] Once features representing the operating behavior of a light source are obtained, these features are then clustered using "unsupervised" machine learning. Unsupervised learning is a type of machine learning that uses algorithms to analyze and cluster unlabeled datasets, allowing the algorithms to discover relationships that might otherwise go undiscovered. However, the term "unsupervised" does not mean the complete absence of human interaction or supervision. Features (understood as data corresponding to or representing features) can be prepared in advance by normalizing the distribution of individual features and excluding extreme outliers. Some clustering algorithms also require a pre-specified number of clusters so that the clusters can be optimized by trying different numbers of clusters and comparing the results. Once a finite set of useful clusters is obtained, clusters represent the state space of a light source or laser system, so "cluster" and "state" (of a light source or laser system having features that make up a cluster) can be considered synonymous. Experts in this subject can interpret or characterize clusters, or at least parts of clusters, in such a way that cluster (state) information can be appropriately understood or used by others, as clusters that have a high probability of transitioning to themselves (clusters that have high stability and a high probability of being in the same cluster / state after a given time interval).

[0023]

[0031] A variety of algorithms can be used for clustering, including but not limited to affinity propagation, agglomerative clustering, BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies), DBSCAN (Density-Based Spatial Clustering of Applications with Noise), k-means or minibatch k-means, mean shift, OPTICS (Ordering Points To Identify the Clustering Structure), spectral clustering, and Gaussian mixture models. The tunable parameters within these algorithms may generally require multiple runs, followed by comparative evaluation of results to find optimized parameter settings that produce a useful finite set of clusters.

[0024]

[0032] Once useful clusters are defined, a probability matrix can be generated using the collected and stored features or "historical data." Based on the historical percentage of transitions from each given cluster to each other cluster (out of all transitions from a given cluster), the expected probability of transitioning from each cluster to each other cluster after a given or pre-selected specified time interval is determined. The specified time interval can be chosen based on available historical data, for example, by selecting a time frequency that is equal to or greater than or equal to most or all of the sampling frequencies of the historical data. The specified time interval can be as short as, for example, just 10 minutes or less, or as long as a week or more, but is usually in the range of 1 hour to 1 week, with 1 day being a potentially useful interval.

[0025]

[0033] Figure 2A is an example diagram of multiple clusters (clusters C1, C2, and C3) representing the states of a light source, showing the percentage probability of transitions between clusters or states (indicated by arrows) after a specified time interval, such as one day. For example, the probability that the light source state C3 will transition to state C1 after a specified time interval is 10%. As shown in Figure 2A, some clusters (in this example, clusters TC1, TC2, and TC3) are terminal clusters, defined as clusters that do not have a probability of transitioning to another state and result in (i.e., require) the removal of the light source module in a light source such as light source 564, which will be discussed below with respect to Figure 5. Therefore, such terminal clusters represent states that require a major maintenance operation with significant downtime to return the light source to a state suitable for use in photolithography. Identification and / or classification of such terminal clusters may be performed by experts in this subject when defining the clusters or after defining them. Figure 2B is a diagram of another example of multiple clusters representing the state of a light source, and is essentially identical to Figure 2A, except that only one terminal cluster TC (which may take the form of a congruence of two or more terminal clusters) is defined to facilitate discussion of Figures 3 and 4 below.

[0026]

[0034] Referring to Figures 2A and 2B, and assuming that the specified time interval for this example is 1 day (24 hours), clusters C1, C2, and C3 are all clusters or states in which the light source can generate light useful for photolithography. However, as can be seen from the examination of the transition probabilities shown in the figures, clusters or states C1, C2, and C3 are not very similar to each other. Cluster or state C1 is the most stable cluster or state, and a light source in cluster or state C1 has a 94.99% probability of being in cluster or state C1 after 1 day, and only a 0.01% probability of being in the terminal cluster or state after 1 day. A light source in cluster or state C1 has a 4.9% probability of being in cluster or state C2 after 1 day, and only a 0.1% probability of being in cluster or state C3 after 1 day. From the illustrated clusters C2 and C3, and similar examinations of their respective transition probabilities, it can be seen that cluster or state C2 has an intermediate level of stability corresponding to a 40% probability of being in cluster or state C2 after one day, while C3 is very unstable and has a relatively high 60% probability of being in the terminal cluster or state (TC in Figure 2B or TC3 in Figure 2A) after one day.

[0027]

[0035] Once clusters are defined and transition probabilities are known, a transition matrix can be formed, like the transition matrix M in Figure 3, which represents the probability of a light source transitioning between each cluster after a specified time interval (in this example, one day). The transition matrix is ​​generated by forming a rectangular matrix with a number of rows and columns equal to the number of clusters. The rows of the transition matrix represent the current cluster (state) of a given light source, and the columns represent the cluster (state) of that light source after one time interval (in this example, one day). The transition matrix M shown in Figure 3 corresponds to the diagram in Figure 2B, with the corresponding clusters displayed in the rows and columns. Reading row C1 from left to right, as indicated by the column headings, it shows the probability that light source C1 is in C1 after one time interval or one day, the probability that it is in C2 after one day, and so on. Each row contains the probability of transitioning from that row's cluster (state) to all other possible clusters (states), so the sum of each row is equal to 1. While the relative order of rows and columns does not necessarily have no effect on the function of a transition matrix, the convention of using the same order for rows and columns makes it easier to recognize and locate cells in a matrix.

[0028]

[0036] Using a transition matrix like the transition matrix M in Figure 3, a probability matrix can be generated that represents the probability that a given light source or laser system is in each respective cluster (starting from within a given cluster) after N time intervals by raising the transition matrix to the power of N, or in other words, by squaring the matrix M N-1 times. Figure 4 is an example of the calculated probability of transitions from any cluster to any cluster after 14 time intervals have elapsed (for example, 14 days in this example), obtained by raising the transition matrix of Figure 3 to the power of 14. In other words, Figure 4 shows the matrix operation on the matrix M in Figure 3 [M] 14The resulting matrix M14 (with row and column labels) is shown. Therefore, the resulting matrix M14 in Figure 4 represents the predicted probability that a given light source, starting from a given cluster shown in the rows (left), will be in the cluster shown in the columns (top) after 14 days. For example, as shown in Figure 4, a light source in cluster C1 has a predicted probability of being in cluster C1 after 14 days of 67.16%, and a probability of being in the terminal cluster TC of 24.73%. Note that the time interval used is not limited to one day, but can be selected to have any desired duration up to the period or cycle of the historical data used. Also note that the probability matrix can be generated over any desired number of time intervals, not just 14 in this example. 14 days is used only as an example of a general or convenient time for predicting future states. Generally speaking, the probabilities in the probability matrix generated by raising the transition matrix M to the power of N provide a non-binary (more than two states) prediction of the future clusters (future states) of a light source or laser system at any point in time over N future time intervals, by applying the transition matrix M N times (in other words, by raising the transition matrix M to the power of N).

[0029]

[0037] As a possible additional advantage of the processes and methods disclosed herein, defined clusters and their associated states can be statistically learned based on available historical data, so that additional features of light sources in a particular state—that is, features that might otherwise remain undetected—can be recognized. The transition matrix itself can also be analyzed to discover high-probability paths leading to undesirable states (whether terminal clusters (terminal states) or other undesirable states, such as states that may be undesirable in application for light source identification). Identifying high-probability paths to such undesirable states may be used to discover ways to reduce the probability of such paths and thus reduce the probability of reaching or passing through such undesirable states.

[0030]

[0038] The Markov chain analysis and prediction techniques disclosed herein do not represent a complete fit of Markov mathematics or Markov statistics to the behavior of light sources. Markov statistics generally require time independence and path (or history) independence of state change probabilities, conditions that are not met in the actual light sources or laser systems in question. However, in the processes and methods described herein, time-dependent features and / or history-dependent features may and / or be used in the features selected for clustering. Thus, a "geography" of time-related effects and / or history-related effects is incorporated to some extent into the clustering and transition probability determination.

[0031]

[0039] In an additional embodiment, the features used to perform clustering, determine transition probabilities, generate a transition matrix, and estimate those probabilities can be periodically updated by adding updated features to previously used features. Alternatively, older features can be selectively removed from previously used features. The resulting updated features can generate updated clusters that differ from the previous clusters, and may even include terminal clusters that differ from the previous terminal clusters. Different updated transition probabilities are also generated. Different updated transition matrices are also generated and subsequently used to estimate possible light source states until the next subsequent update of features. In an implementation, predicting terminal states within a given time, either at or beyond a given probability, can immediately generate recommendations for preventative or proactive maintenance scheduled for that time, which can optionally be sent to one or more maintenance personnel or one or more organizations. Alternatively, preventative or proactive maintenance may be initiated immediately and automatically, or at an automatically selected future time.

[0032]

[0040] Figure 5 is a block diagram of an example of a light source 564 or laser system (in this example, a deep ultraviolet (DUV) source) in which the processes and methods described herein may be used together. Figure 6 is a block diagram of an example of a lithography apparatus 610 in which the DUV source of Figure 5 may be used together. Referring to Figures 5 and 6, the light source or laser system 564 is a dual-stage pulsed laser system that generates a pulsed light beam 505, which is directed to the photolithography exposure apparatus 610 of Figure 6. The laser system 564 includes a solid-state or gas discharge main oscillator (MO) system 560, a power amplification (PA) system such as a power ring amplifier (PRA) system 565, a relay optical system 570, and an optical output subsystem 575. This laser system 564 is a deep UV (DUV) laser system 564, and the pulsed light beam 505 has wavelengths within the DUV wavelength range, which includes, for example, wavelengths from about 100 nanometers (nm) to about 400 nm.

[0033]

[0041] The MO system 560 may also include, for example, an MO chamber module 561 in which a discharge between electrodes (not shown) causes a lathing gas discharge in a lathing gas, creating a population inversion of high-energy molecules such as argon, krypton, or xenon, generating relatively broadband radiation, which is line-narrowed to a relatively very narrow bandwidth and center wavelength selected in a line-narrowing module ("LNM") 562. The MO system 560 may also include an MO output coupler (MO OC) 563, which may include a partial reflection mirror that, together with a reflection grating (not shown) in the LNM 562, forms an oscillator cavity in which the MO system 560 oscillates to form a seed output pulse. The MO system 560 may also include a line-center analysis module (LAM) 564, which may include, for example, an etalon spectrometer for fine wavelength measurements and a grating spectrometer for coarser resolution.

[0034]

[0042] The relay optical system 570 shown in Figure 5 may include an MO wavefront engineering box (WEB) 571, which serves to redirect the output of the MO system 560 toward the PA system 565 and may also include, for example, beam expansion using a multiprism beam expander (not shown) and coherence breakdown in the form of, for example, an optical delay path (not shown).

[0035]

[0043] The PA system 565 includes a PRA chamber module 566, which is also an oscillator formed by, for example, an output optical beam injection and output coupling optical system (not shown) from the MO system 560, which can be incorporated into a PRA web 567 and can be re-directed by a beam reverser 568 to return through a gain medium in the chamber 561. The PRA web 567 can incorporate a partially reflective input / output coupler (not shown), a maximum reflection mirror for the nominal operating wavelength (which may be approximately 193 nm in the case of an ArF system), and one or more prisms. The PA system 565 optically amplifies the output optical beam from the MO system 560.

[0036]

[0044] The optical output subsystem 575 may include a bandwidth analysis module (BAM) 576 at the output of the PA system 565. The bandwidth analysis module 576 receives pulses of the output light beam from the PA system 565 and extracts a portion of the light beam for measurement purposes, for example, to measure the output bandwidth and pulse energy. The pulses of the output light beam then pass through an optical pulse stretcher module (OPuS) 577 and an output coupled automatic shutter measurement module (CASMM) 578. The CASMM 578 may also be the location of a pulse energy meter, which may also be the source of features in the form of stored signals and resulting data. One purpose of the OPuS 577 may be to convert a single output pulse into a pulse train. Secondary pulses generated from the original single output pulse may be delayed relative to each other. By distributing the energy of the original laser pulse into a secondary pulse train, the effective pulse length of the light beam can be extended, while simultaneously reducing the peak pulse intensity.

[0037]

[0045] One or more (and possibly all) of the components of the laser system 564 (MO chamber 561, LNM 562, MO web 571, PRA chamber 566, PRA web 567, OPuS 577, BAM 576) can provide one or more features that represent an operating mode of the laser system 564, such as one or more operating modes of the components MO chamber 561, LNM 562, MO web 571, PRA chamber 566, PRA web 567, OPuS 577, BAM 576 and other components not shown. Features that represent an operating mode of the laser system 564 may relate to the performance of the laser system 564, such as power output, power output variability, center wavelength, spectral width (FWHM, etc.), and / or energy efficiency. Features that represent an operating mode of the laser system 564 may relate to the performance of a particular component (or "module") of the laser system 564, including two or more or three or more modules. Illustrative features include power output, power output variability, center wavelength, spectral width (such as FWHM), and / or energy efficiency of the MO chamber 561 considered alone, or the PRA chamber 566 considered alone, or the PRA chamber 566 considered together with the MO chamber 561. Features describing the operating mode of the laser system 564 may relate to one or more inspection durations, such as inspection duration (or "duration of use" since the last replacement or inspection), whether measured, for example, in units of time, laser pulses, or both. Features describing the operating mode of the laser system 564 may relate to one or more measures of trend, such as a measure of central trend, rate of change, variability, or stability, including those applied to a moving window. In other words, features describing the operating mode of the laser system 564 may include one or more time-dependent or history-dependent features, such as those described above or others. Such features, collected over time and stored for many light sources, are then clustered as discussed above.

[0038]

[0046] The photolithography exposure apparatus 610 in Figure 6 processes a wafer 611 received by a wafer holder or stage 612. The light beam 505 is a pulsed light beam containing pulses of light separated in time. The photolithography exposure apparatus 610 may be a liquid immersion system or a dry system. Microelectronic features are formed in part, for example, by exposing portions of a radiation-sensitive photoresist material layer on the wafer 611 with the light beam 505.

[0039]

[0047] The use of the prediction processes and methods disclosed herein enables more flexible prediction of the future state of light sources or laser systems, including states with significant maintenance or downtime requirements. It offers increased flexibility compared to two-state prediction techniques by enabling the generation of probabilistic estimates for multiple states, not just two. It offers increased flexibility compared to methods requiring predefined states by using unsupervised learning to identify significant clusters or states that might otherwise go unnoticed. It offers increased flexibility compared to prediction techniques with binary time intervals by enabling predictions at a resolution of N, which is a predefined or pre-selected time interval, and preferably at any multiple of N.

[0040]

[0048] Detecting significant changes in the distribution of data used by a model for modeling compared to the distribution of data used to train the model can be important, as a sufficiently different distribution of modeling data can degrade the model's performance. Figures 7A–7D are graphs illustrating a method for examining significant changes in the distribution of light source data or features used by a model for prediction, detection, simulation, etc., compared to the distribution of the corresponding data used to train the model. Referring to Figures 7A, 7B, and 7C, the method includes determining the cumulative distribution function TD of the model training data items, as shown in Figure 7A; determining the cumulative distribution function PD of the data for use by the model for prediction, detection, simulation, etc. ("modeling data"), as shown in Figure 7B or Figure 7C; and determining whether the cumulative distribution function of the modeling data fluctuates above or below the cumulative distribution function TD of the training data by a tolerance TV at any given time, or in other words, determining whether the cumulative distribution function PD of the data for modeling purposes lies within the upper and lower boundaries UB and LB, which are separated above or below the cumulative distribution function TD of the training data by a tolerance TV. The tolerance value TV can be within a range such as greater than zero to 0.1, or 0.01 to 0.2, or 0.5 to 0.1. In the example shown in Figure 7B, the cumulative distribution function PD of the modeling data differs from the cumulative distribution function TD of the training data by a value exceeding the tolerance value TV, or in other words, the cumulative distribution function PD of the data for modeling purposes lies (partially) outside the lower boundary LB, which is separated from the cumulative distribution function TD of the training data by a value exceeding the tolerance value TV. This supports the conclusion that the distribution of the modeling data differs significantly from the distribution of the training data. In contrast, in the example shown in Figure 7C, the cumulative distribution function PD of the data for modeling purposes lies inside the upper and lower boundaries UB and LB, which are separated from the cumulative distribution function TD of the training data by a value exceeding the tolerance value TV. This supports the conclusion that the distribution of the modeling data does not differ significantly from the distribution of the training data.

[0041]

[0049] Referring to Figure 7D, as an alternative or additional implementation of the method, if the cumulative distribution function PD of the modeling data does not deviate by a value exceeding the tolerance TV from the cumulative distribution function TD of the training data at any given time, as shown in Figure 7C, the tolerance TV may be continuously decreased until the cumulative distribution function PD of the modeling data deviates by a value exceeding the tolerance TV from the cumulative distribution function TD of the training data at least at some time P. The minimum tolerance TV that is not exceeded, or the maximum tolerance that is exceeded by the cumulative distribution function PD of the modeling data (or both), may then be returned to or reported by another process or method.

[0042]

[0050] The implementation forms may be further described in the following numbered clauses. 1. A method for predicting the state of a light source, including a laser system, The process involves acquiring the characteristics of a light source, where these characteristics represent the operating mode of the light source. This involves clustering features into clusters using a machine learning algorithm that utilizes unsupervised learning, where each cluster represents the state of a light source. The process involves generating a transition matrix between clusters, where the transition matrix represents the transition probability of a light source transitioning between clusters after a time interval, and each cluster includes one or more terminal clusters with a zero probability of transitioning to another cluster. For a given light source having features corresponding to a given cluster and state, a non-binary prediction of the future cluster and state of the given light source is generated by applying a transition matrix one or more times. Methods that include... 2. The method according to Clause 1, wherein the light source is a member of a group of similar light sources having similar components, operating methods, and characteristics. 3. The method according to Clause 1, further comprising using a Markov chain to calculate the probability of a transition between a first cluster and a second cluster in a given time by iteratively applying a transition matrix. 4. The method according to clause 3, wherein the first cluster represents the current state of a given light source, and the second cluster is the terminal cluster. 5. The time interval is within the range of 1 hour to 1 week, as described in Clause 1. 6. The time interval is one day, as described in Clause 1. 7. The characteristics of the light source are as described in Clause 1, including historical data from a set of similar light sources. 8. The characteristics of the light source include the characteristics of two or more modules of the light source, as described in Clause 7. 9. The method according to Clause 7, wherein the characteristics of the light source include the characteristics of the main oscillator (MO) module and the characteristics of the power amplifier (PA) or power ring amplifier (PRA) module. 10. The method according to Clause 7, wherein generating a transition matrix between clusters includes using historical data to generate the probability that a light source will transition between clusters after a time interval. 11. The method according to Clause 1, further comprising using a Markov chain to determine the probability of a transition between a first cluster and a second cluster within a given time limit by iteratively applying a transition matrix until a time limit is reached. 12. To obtain updated characteristics of a light source, where the updated characteristics represent updated operating modes of the light source. This involves clustering features and updated features into updated clusters using a machine learning algorithm that utilizes unsupervised learning, where the updated clusters represent the state of the light source. The method involves generating an updated transition matrix between updated clusters, where the updated transition matrix represents the transition probabilities of a light source transitioning between updated clusters after a time interval, and each updated cluster contains one or more terminal clusters with a zero probability of transitioning to another updated cluster. For a given light source having features corresponding to a given updated cluster, the application of the updated transition matrix one or more times generates a non-binary prediction of the future updated cluster and state of the given light source. The method described in Clause 1, further including the following: 13. The updated termination cluster is different from the immediately preceding termination cluster, as described in Clause 12. 14. The feature is the method described in Clause 1, wherein the feature includes one or more time-dependent or history-dependent features. 15. The method according to Clause 14, wherein one or more time-related or history-dependent features include one or more rates of change of one or more aspects of the light source. 16. The method according to Clause 14, wherein one or more time-related or history-dependent features include one or more measures of variability in one or more aspects of the light source. 17. The method according to Clause 14, wherein one or more time-related or history-dependent features include one or more measures of the central tendency of one or more aspects of the light source. 18. A method for predicting the state of a light source such as a laser system, The acquisition of characteristics of a light source, wherein the characteristics represent the operating mode of the light source, and the characteristics include one or more time-dependent or history-dependent characteristics. Using a machine learning algorithm based on unsupervised learning, the features are clustered into clusters representing each state of the light source, This involves generating a transition matrix that represents the probability of the light source transitioning between each cluster after a time interval, By raising the transition matrix to the power of N, a probability matrix is ​​generated that represents the probability that a given light source is in each cluster after N time intervals. Methods that include... 19. The method according to Clause 18, wherein one or more time-dependent or history-dependent features include one or more rates of change of one or more aspects of the light source. 20. The method according to Clause 18, wherein one or more time-dependent or history-dependent features include one or more measures of the variability of one or more aspects of the light source. 21. The method according to Clause 18, wherein one or more time-dependent or history-dependent features include one or more measures of the central tendency of one or more aspects of the light source. 22. The method according to clause 18, wherein the cluster includes one or more clusters with a probability of transitioning to another cluster of zero. 23. A method for examining significant changes in the distribution of light source data for use by a model for prediction, detection, simulation, etc., compared to the distribution of corresponding data used to train the model, Determining the cumulative distribution function of the model training data, This involves determining the cumulative distribution function of data ("modeling data") used by models for prediction, detection, simulation, etc. The objective is to determine whether the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by an acceptable amount at any given time point. Methods that include... 24. If the cumulative distribution function of the modeling data does not deviate from the cumulative distribution function of the training data by an acceptable value at any given time, then repeatedly (a) decrease the acceptable value, and (b) determine whether the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by an acceptable value at any given time until the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by an acceptable value at a given time. Report the last tolerance and / or the second to last tolerance. The method described in Clause 23, further including the method described in Clause 23. 25. The method described in Clause 23, wherein the permissible value is greater than zero and within the range of 0.1.

[0043]

[0051] The above-described implementation forms and other implementation forms are within the scope of the following claims.

Claims

1. A method for predicting the state of a light source, including a laser system, The acquisition of the characteristics of the light source, wherein the characteristics represent the operating mode of the light source. The process involves clustering the aforementioned features into clusters using a machine learning algorithm that utilizes unsupervised learning, wherein each cluster represents the state of the light source. The process involves generating a transition matrix between the clusters, wherein the transition matrix represents the transition probability that the light source will transition between the clusters after a time interval, and each cluster includes one or more terminal clusters with a probability of zero transitioning to another cluster. For a given light source having features corresponding to a given cluster and state, a non-binary prediction of the future cluster and state of the given light source is generated by applying the transition matrix one or more times. Methods that include...

2. The method according to claim 1, wherein the light source is a member of a group of similar light sources having similar components, operating methods, and features.

3. The method according to claim 1, further comprising calculating the probability of a transition between a first cluster and a second cluster within a given time using a Markov chain by iteratively applying the transition matrix.

4. The method according to claim 3, wherein the first cluster represents the current state of a given light source, and the second cluster is a terminal cluster.

5. The method according to claim 1, wherein the time interval is within the range of one hour to one week.

6. The method according to claim 1, wherein the time interval is one day.

7. The method according to claim 1, wherein the features of the light source include historical data from a set of similar light sources.

8. The method according to claim 7, wherein the features of the light source include features of two or more modules of the light source.

9. The method according to claim 7, wherein the features of the light source include the features of a main oscillator (MO) module and the features of a power amplifier (PA) or power ring amplifier (PRA) module.

10. The method according to claim 7, wherein generating the transition matrix between clusters includes using the historical data to generate the probability that a light source will transition between clusters after the time interval.

11. The method according to claim 1, further comprising using a Markov chain to determine the probability of a transition between a first cluster and a second cluster within a given time limit by repeatedly applying the transition matrix until a time limit is reached.

12. The acquisition of updated characteristics of the light source, wherein the updated characteristics represent the updated operating mode of the light source. Clustering the aforementioned features and the updated features into updated clusters using a machine learning algorithm that utilizes unsupervised learning, wherein the updated clusters represent the state of the light source, and To generate an updated transition matrix between the updated clusters, wherein the updated transition matrix represents the transition probability that the light source will transition between the updated clusters after a time interval, and each updated cluster includes one or more terminal clusters with a probability of zero transitioning to another updated cluster. For a given light source having features corresponding to a given updated cluster, a non-binary prediction of the future updated cluster and state of the given light source is generated by applying the updated transition matrix one or more times. The method according to claim 1, further comprising:

13. The method according to claim 12, wherein the updated terminal cluster is different from the immediately preceding terminal cluster.

14. The method according to claim 1, wherein the aforementioned features include one or more time-dependent features or history-dependent features.

15. The method according to claim 14, wherein the one or more time-related features or history-dependent features include one or more rates of change of one or more embodiments of the light source.

16. The method according to claim 14, wherein the one or more time-related features or history-dependent features include one or more measures of the variability of one or more embodiments of the light source.

17. The method according to claim 14, wherein the one or more time-related features or history-dependent features include one or more measures of the central tendency of one or more embodiments of the light source.

18. A method for predicting the state of a light source such as a laser system, The acquisition of the characteristics of the light source, wherein the characteristics represent the operating mode of the light source, and the characteristics include one or more time-dependent or history-dependent characteristics. Using a machine learning algorithm that employs unsupervised learning, the aforementioned features are clustered into clusters representing each state of the light source, The light source generates a transition matrix representing the respective probabilities of transitioning between each of the clusters after a time interval, By raising the transition matrix to the power of N, a probability matrix is ​​generated that represents the probability that a given light source is in each cluster after N time intervals. Methods that include...

19. The method according to claim 18, wherein the one or more time-dependent features or history-dependent features include one or more rates of change of one or more embodiments of the light source.

20. The method according to claim 18, wherein the one or more time-dependent features or history-dependent features include one or more measures of the variability of one or more embodiments of the light source.

21. The method according to claim 18, wherein the one or more time-dependent or history-dependent features include one or more measures of the central tendency of one or more embodiments of the light source.

22. The method according to claim 18, wherein the cluster includes one or more clusters with a probability of transitioning to another cluster of zero.

23. A method for examining significant changes in the distribution of light source data for use by a model for prediction, detection, simulation, etc., compared to the distribution of corresponding data used to train the model, Determining the cumulative distribution function of the model training data, Determining the cumulative distribution function of the data ("modeling data") to be used by the model for prediction, detection, simulation, etc., The determination of whether the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by an acceptable value at any given time point. Methods that include...

24. If the cumulative distribution function of the modeling data does not deviate from the cumulative distribution function of the training data by a value exceeding the tolerance at any given time, then (a) the tolerance is repeatedly reduced, and (b) it is determined whether the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by a value exceeding the tolerance at any given time, until the cumulative distribution function of the modeling data deviates from the cumulative distribution function of the training data by a value exceeding the tolerance at a given time. Report the last acceptable value and / or the second to last acceptable value. The method according to claim 23, further comprising:

25. The method according to claim 23, wherein the allowable value is in the range of greater than zero to 0.1.

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