Method for configuring technical system to be configured

Abstract

A method for configuring a technical system to be configured. According to various embodiments, a method for configuring a technical system to be configured is described, comprising: acquiring a reference observation; performing condition processing on the reference system model according to reference observation acquired for the reference system; for the technical system to be configured, acquiring observations of the results of the technical system to be configured for the various values of the configuration parameters; adapting a priori model for the relationship between the value of the configuration parameter and the result provided by the technical system to be configured to the observations acquired for the technical system to be configured, wherein the priori model consists of a weighted combination of conditionally processed reference system models; determining a posterior model for a relationship between a value of the configuration parameter and a result provided by the technical system to be configured by conditionally processing the adapted priori model according to observations acquired for the technical system to be configured; and configuring the technical system to be configured using the determined posterior model.

Description

Technical Field

[0001] The present disclosure relates to a method for configuring a technical system to be configured. Background Art

[0002] In the case of production processes and machining processes (e.g., drilling, milling, heat treatment, etc.), process parameters such as process temperature, process time, vacuum or gas atmosphere, etc. are set to achieve the desired characteristics of the workpiece, such as hardness, strength, thermal conductivity, electrical conductivity, density, microstructure, macrostructure, chemical composition, etc. The process parameters can be determined by a model-based optimization method, such as a Bayesian optimization method. In this case, a model for the production or machining process can be determined based on the measurement data. However, this may require a large amount of measurement data and therefore require high costs (e.g., time consumption and / or cost consumption). The cost can be reduced by determining the model (also referred to as transfer learning) based on a learned model that describes a process related to the production or machining process in combination with the measurement data. For example, both models can describe drilling or milling for different machines (and using comparable process parameters). In this case, the learned model can be used as the basis for the model to be learned, and thereby reduce the required amount of measurement data. For this reason, an efficient approach is desirable. Summary of the invention

[0003] According to various embodiments, a method for configuring a technical system to be configured is provided, comprising:

[0004] for each one or more technical reference systems, collecting reference observations of the results of the reference system for different values ​​of configuration parameters (i.e. relations of which results the reference system provides when the reference system is configured with the corresponding one or more values ​​of the one or more configuration parameters);

[0005] for each reference system, conditioning a corresponding reference system model for the relationship between values ​​of configuration parameters and results provided by the reference system according to reference observations collected for the reference system;

[0006] For the technical system to be configured, collecting observations of the results of the technical system to be configured for various values ​​of the configuration parameters;

[0007] adapting an a priori model of the relationship between values ​​of configuration parameters and results provided by the technical system to be configured to the observations collected for the technical system to be configured (for example using a likelihood approach), wherein the a priori model consists of a weighted combination of conditioned reference system models;

[0008] determining an a posteriori model for the relationship between values ​​of configuration parameters and results provided by the technical system to be configured by conditioning the adapted a priori model on observations collected for the technical system to be configured; and

[0009] Using the determined a posteriori model, the technical system to be configured is configured (ie, for example, such that a desired result is achieved with the values ​​of the configuration parameters according to the a posteriori model).

[0010] The technical reference system can be very similar to the system to be configured, to the extent that it differs with respect to variations that are achieved in that the system to be configured and the reference system are physically the same system, but are operated at different times (from which differences already arise solely, for example due to temperature, air pressure, available bandwidth or computing power, etc.).

[0011] The acquisition of observations for the technical system to be configured does not necessarily need to take place after conditioning the reference system model, but can also have occurred at least partially previously. The conditioning of the a priori model can also include step-by-step conditioning based on step-by-step observations, for example according to evaluations of acquisition functions.

[0012] The above method can be used in particular for optimizing black-box functions. A black-box function is a function in which the gradient of the function is unavailable. Therefore, optimization algorithms based on gradient descent are not directly applicable. In addition, the function evaluation may be distorted due to noise (e.g., measurement noise). However, usually, data from the black-box function in question is available to support optimization, such as data from previous optimizations for the task in question. The above method enables the efficient use of such so-called metadata (scalability in terms of data efficiency, computational complexity, and the number of meta-tasks) in the optimization process. In particular, it enables a "hot start" of the Bayesian optimization of the function based on metadata.

[0013] A possible application of the method is parameter optimization in an industrial environment, such as optimizing a physical (production) process. A typical example is a laser welding process, in which two workpieces should be connected to each other by melting the workpieces temporally and locally with a laser beam. Here, parameters such as laser power and laser spot diameter are exemplary process parameters that should be optimized. For this optimization, it is typically necessary to perform the process and analyze the results at different parameter settings in cost-intensive and time-intensive experiments. It is therefore desirable to select the parameters for implementing these experiments with an understanding of the actual situation, and to use the available information efficiently and effectively, with the goal of achieving good enough parameter settings with as few experiments as possible. Other applications include, for example, the optimization of hyperparameters in algorithms (such as the number of hidden layers in a neural network) or the efficient calibration (and thus configuration) of physical (especially technical) systems.

[0014] The method can also be used for active learning. In the case of active learning, a model of one or more target variables is typically sought over the entire subset of the parameter space. For example, such a model can then be used to operate the system. If, for example, the relationship between the input voltage and the speed of the motor is known, the voltage can be set by inverting the model so that the desired speed is achieved.

[0015] Various embodiments are given below.

[0016] Embodiment 1 is a method as described above for configuring a technical system to be configured.

[0017] Embodiment 2 is a method according to embodiment 1, wherein adapting the a priori model comprises adapting weights of a weighted combination of the conditioned reference system models.

[0018] In this way, it is possible to take into account how well the knowledge from one of the relevant configuration tasks, namely the configuration of the reference system, can be transferred to the configuration of the technical system to be configured.

[0019] Embodiment 3 is a method according to embodiment 1 or 2, wherein the conditioned reference system model and the prior model for the system to be configured are Gaussian processes.

[0020] This enables efficient modeling, conditioning and combination of reference system models into an a priori model for the system to be configured.

[0021] Embodiment 4 is a method according to embodiment 3, wherein the covariance function of the prior model (also represented here by the common English term "Kemel") is composed of a weighted sum of the covariances of the reference system model (i.e., the weighted combination includes the weighted sum of the covariances, i.e., the weight of the weighted combination determines the weight of the weighted sum of the covariances) and a residual covariance function, wherein the adaptation of the prior model includes the adaptation of the residual covariance function.

[0022] This makes it possible to model relationships for the technical system to be configured that are not contained in the reference system model.

[0023] The mean of the prior model is, for example, given by the weighted sum of the means of the reference system model (wherein the weight of the mean of the reference system model and the weight of the covariance of the reference system model may be related to each other, for example the weight of the covariance of the reference system model is the square of the weight of the mean of the reference system model).

[0024] Embodiment 5 is a method according to Embodiment 3 or 4, wherein the weight of the first reference system model of the reference system model is determined by projecting the observations collected for the technical system to be configured onto the mean of the first reference system model, and the weight of the second reference system model of the reference system model is determined by projecting the residual of the observations collected for the technical system to be configured (i.e., minus the part described by projecting the observations onto the mean of the first reference system model).

[0025] This makes it possible, in particular in the case of a large number of reference systems, to determine the weights with significantly less effort than likelihood estimation and thus with a faster training speed. For another reference system model, the remaining part of the observations (which has not yet been acquired by a previous projection) can then be projected onto the mean of the reference system model (see Algorithm 2 below).

[0026] Embodiment 6 is a method according to any one of embodiments 1 to 5, comprising, for each reference system, generating the reference system model by adapting the corresponding reference prior model to observations collected for the reference system (e.g., by means of a likelihood scheme).

[0027] This improves the quality of the reference system model. Conditioning the reference a priori model on the corresponding observations thus provides an a posteriori model for the reference system.

[0028] Embodiment 7 is a data processing device (in particular a control device), which is configured to implement the method according to any one of Embodiments 1 to 6.

[0029] Embodiment 8 is a computer program having instructions, which, when executed by a processor, cause the processor to implement the method according to any one of embodiments 1 to 6.

[0030] Embodiment 9 is a computer-readable medium storing instructions, which, when executed by a processor, causes the processor to implement the method according to any one of embodiments 1 to 6. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In the accompanying drawings, like reference numerals generally refer to the same parts in completely different views. The accompanying drawings are not necessarily drawn to scale, with emphasis instead generally being placed on depicting the principles of the invention. In the following description, various aspects are described with reference to the following drawings.

[0032] Figure 1 A system for carrying out a physical or chemical process is shown.

[0033] Figure 2 The working mode of the meta-learning model according to one embodiment is shown.

[0034] Figure 3 A flow chart is shown which illustrates a method for configuring a technical system to be configured according to one specific embodiment. DETAILED DESCRIPTION

[0035] The following detailed description relates to the attached drawings, which illustrate the particular details and aspects of the present disclosure for the purpose of illustration, in which the present invention may be performed. Other aspects may be used, and structural, logical and electrical changes may be implemented without departing from the scope of protection of the present invention. Because some aspects of the present disclosure may be combined with one or more other aspects of the present disclosure to form new aspects, the various aspects of the present disclosure are not necessarily mutually exclusive.

[0036] Various examples are described in more detail below.

[0037] Figure 1 A system 100 is shown having a device 108 which is configured to perform a physical or chemical process.

[0038] The physical or chemical process can be any type of technical process, such as a manufacturing process (e.g. manufacturing a product or an intermediate product), a machining process (e.g. machining a workpiece), a control process (e.g. moving a robot arm) or a measuring process. Such a physical process typically has to be controlled, in particular configured (set), for example, a measuring device has to be calibrated or the like. For example, it may be necessary to set various control parameters of the device (e.g. within a calibration range) in order to implement the physical or chemical process. For example, in the case of a heat treatment with the aid of a furnace, the physical or chemical process may require calibration of the furnace temperature and / or vacuum. The corresponding configuration of the device 108 (i.e. the implementation of the corresponding configuration task) is performed by the control device 106.

[0039] Two physical or chemical processes and thus also corresponding configuration tasks can be related to each other in different ways. For example, two substantially identical processes can be involved, such as drilling or milling of a component, but the process is performed by means of different machines. Even the same process on different machines may also be able to lead to separate results. Two processes performed on the same machine can also be related to each other. For example, one process can be drilling a metal component and another process can be drilling a ceramic component. In general, if the input parameters of the corresponding process or the corresponding configuration task at least partially overlap and the output parameters of the corresponding process or the corresponding configuration task at least partially overlap, the two processes or configuration tasks can be related to each other. Intuitively, two processes related to each other can have one or more identical input parameters (for example, in the case of heat treatment, process temperature, process time and / or vacuum pressure) set in the case of the corresponding configuration task, and can have one or more identical output parameters (for example, hardness, strength, density, microstructure, macrostructure and / or chemical composition in the case of heat treatment). If the corresponding models of the two processes or configuration tasks are suitable for transfer learning, the two processes or configuration tasks are related to each other.

[0040] It is assumed below that the control device 106 is to perform a target (configuration) task, for example, for the configuration of a specific physical or chemical process that is to be implemented by the device 108, and that one or more processes and configuration tasks related to the target task have already been performed together with the system or also with one or more other (at least similar) systems. These are, for example, physical or chemical processes related to specific physical or chemical processes, and the corresponding configuration task is the configuration (for example of the device 108) for implementing these processes. However, the configuration task (instead of setting parameters for the physical or chemical process) can also, for example, be the configuration of a corresponding machine learning model (i.e. setting hyperparameters of, for example, a neural network). Accordingly, the target task is generally referred to as a (target) configuration task for a technical system (wherein the configuration can involve process parameters or hyperparameters for a machine learning model, etc.). The related (i.e. relational) target task can typically be a related (configuration) task (for another ("relevant") technical system, also referred to herein as a "reference" system) or also a so-called "meta" or "reference" (configuration) task (for a previous configuration of a relational process or neural network as described above, e.g. for similar tasks (e.g. classification of objects of a different type than in the case of the target task), etc.).

[0041] Accordingly, the device 108 may be a machine, but may also be a data processing device or a part thereof (eg, a program part implementing a neural network), etc.

[0042] The control device 106 is configured to control the first device 108 as a function of a corresponding (provided) input parameter value 102 of at least one (i.e., exactly one or more than one) input variable (e.g., temperature, exposure time, hyperparameter, etc.). Therefore, an input parameter value 102 is also understood here to be a vector with values, which contains the values ​​of a plurality of adjustable variables (e.g., process parameters).

[0043] Intuitively, the control device 106 may control the interaction of the device 108 with the environment, for example, based on the input parameter value 102 .

[0044] The term "control device" (also referred to as "control device") may be understood as any type of logic implementation unit, which may, for example, include a circuit and / or a processor, which is capable of executing software, firmware or a combination thereof stored in a storage medium and which may, for example, distribute instructions to devices for executing the process in this example. The control device may, for example, be set up by program code (e.g., software) for controlling the operation and / or setting (e.g., calibration) of a control system, such as a production system, a processing system, a robot, etc.

[0045] An input parameter value as used herein may be a parameter value describing an input quantity, such as a physical or chemical parameter, an applied voltage, an opening of a valve, etc. For example, the input parameter may be a process-related property of one or more materials, such as hardness, thermal conductivity, electrical conductivity, density, microstructure, macrostructure, chemical composition, etc. However, as mentioned above, the input parameter value may also be a hyperparameter (e.g. the number of layers of a neural network or their size) or the like.

[0046] When or after the target task or the corresponding related task is executed according to the corresponding input parameter value 102 , the result of the corresponding task is determined.

[0047] For this purpose, the system 100 may, for example, have one or more sensors 110. One or more first sensors 110 may be set up to capture the result of a target task, in particular a physical or chemical process. The result of the process may, for example, be the properties of the manufactured product or the processed workpiece (e.g. hardness, strength, density, microstructure, macrostructure, chemical composition, etc.), the success or failure of the robot's skills (e.g. picking up an object), the resolution of an image recorded by means of a camera, etc. The result of the process may be described by means of at least one (i.e. exactly one or more than one) output variable. One or more first sensors 110 may be set up to capture at least one output variable and thus determine a result value 112. Like the input parameter value, the result value may be a vector with multiple components, for example, the corresponding value of each of the multiple output variables may be captured.

[0048] As described herein, the results of the acquisition process by means of one or more sensors can be performed during the execution of the process (in situ) and / or after the execution of the process (non-in situ). For example, the model can describe the relationship between one or more input parameters and at least two output parameters, wherein the output value of one of the at least two output parameters can be acquired during the process, and the output value of another of the at least two output parameters can be acquired after the execution of the process. As an illustrative example for acquiring output values ​​after the execution of the process, the process can be to harden the workpiece in a furnace with temperature as an input parameter. In this case, the output parameter can be the hardness of the workpiece at room temperature after the hardening process. The output parameter can have an application-specific quality standard. The output parameter can be a parameter related to the component, such as a scale or layer thickness, or can be a parameter related to the material, such as hardness, thermal conductivity, electrical conductivity, density, chemical composition, etc.

[0049] In the case where the respective task is the configuration of a respective neural network, output value 112 can also be determined without sensors, for example by evaluating the accuracy of a neural network that has been configured as a function of the respective input parameter values.

[0050] The result value may be a value describing an output parameter of a process. The output parameter of a process may be a characteristic of a product, a workpiece, a recorded image or other result. However, the output parameter of the process may also be a success or failure (e.g. of a robot's skill). Intuitively, the result value 112 is obtained from the input parameter value 102.

[0051] However, the relationship between input parameter values ​​102 and result values ​​112 is typically very complex and unknown. A pair consisting of an input parameter value 102 and an associated result value 112 constitutes an observation (or “data point”) 130 .

[0052] If x represents an input parameter value 102 and y represents a result value 112, then for the target task (indicated by the index t for "target") y = f t (x), and for the related tasks (indicated by the index m for "meta") y = f m (x), where not only f t And f m It's all unknown.

[0053] The typical task now proposed is to maximize f t (It is assumed below that the result value has only real number components), that is, to find the result value x that is as good as possible (e.g., the largest). In order to improve the efficiency of such optimization, according to various embodiments, the knowledge of related tasks is used, that is, the so-called "meta-learning" (or "transfer learning") is used, which can greatly reduce the number of experiments required for the target task. It should be noted that it is not necessary that the goal here is to optimize f t , but it is also possible to expect to find t In the following, however, it is assumed that f should be optimized (in particular maximized) t .

[0054] Next, we therefore consider the meta-learning case, where the goal is to efficiently maximize the function (where D is the corresponding space of possible input parameter values ​​for the configuration), where f t is unknown (e.g., a sample from an unknown distribution of functions). In order to maximize f t , the parameters (i.e. input parameter values) x can be evaluated sequentially n , in order to obtain the noisy observation y n =f t (x n )+ωn , where ω n ~N(0,σ t 2 ) is Gaussian noise with zero mean and is independent and identically distributed. It should be noted that the approach described here is not limited to applications that satisfy this assumption. In practice, this assumption is often violated, but methods with regression of Gaussian processes still often work well. For example, this assumption is made even in the case of linear regression by means of the method of least squares.

[0055] For this purpose, the target task can be used The number of previously executed N t observations so that f t Create a probability model. According to various embodiments, a Gaussian process is used as a model, i.e. A Gaussian process models different function values ​​on a common Gaussian distribution parameterized by a mean vector and a covariance matrix.

[0056] By targeting f t Use the mean function m(·) and the kernel (i.e., covariance function) k(·,·) in the data The posterior Gaussian process (hereinafter referred to as the posterior) formed by conditioning the prior Gaussian process (hereinafter referred to as the prior) is a Gaussian process with mean and covariance, and the mean and covariance are determined by

[0057]

[0058] Given, where Know is the vector of corresponding noisy result values.

[0059] In Bayesian optimization, we use the posterior represented by (1) to sequentially query for new parameters As a result, the new parameters inform f t The optimal value of is obtained by solving an auxiliary optimization problem based on the acquisition function α

[0060]

[0061] The power of such a scheme typically depends on the quality of the prior. In particular, according to various embodiments, a method is provided that enables the determination of a prior with good quality. To this end, observations (“metadata”) from the related tasks are used. The relationship between the input parameters 102 and the result values ​​112 for the related tasks is given by the function f m Given (the function is for example derived from f t same function distribution).

[0062] Therefore, assume that for each related task (index m, There is a corresponding dataset The dataset is based on the N m A noisy observation y m，n =f m (X m，n )+ω m，n , the data sets have different noise levels These datasets together constitute the metadata

[0063] Metadata can be included in Gaussian process modeling by considering a common model for the target task and related tasks. Such a multi-task GP model (MTGP) is defined by an extended kernel that additionally models the similarities between tasks,

[0064]

[0065] where km is an arbitrary kernel function and W m is a positive semidefinite matrix, called a colocalization matrix, because its entries [W m ](v, v′) models the covariance between two tasks v and v′. and Conditioning this common model (i.e., “conditioning” in the sense of conditional probability), we can obtain the GP equation for f through (1) t However, these multi-task GP models are not only computationally intensive (cubic in the number of all meta-points and task points), but also difficult to train in practice due to the large number of hyperparameters.

[0066] For simplicity, the target task is referred to as the M+1th task below, i.e., t=M+1. The central challenge in learning the MTGP model with (3) is that it is difficult to learn the covariance based on a small number of data points, which usually leads to poor performance. For this reason, the joint use of hyperparameters is often introduced in practice. However, this does not reduce the computational cost for evaluating the model.

[0067] The following describes an MTGP meta-learning model that can not only be trained efficiently but also evaluated. Instead of the typical parameter partitioning, two assumptions are introduced for the common GP model of (3), which restrict learning to the most important covariances and lead to a modular GP posterior model that can be evaluated efficiently.

[0068] First, the correlations between meta-tasks are ignored, since it may be difficult (or even impossible) to learn such correlations when there is only a small amount of metadata for each meta-task, respectively. For simplicity, regarding the covariance between the tasks used, we write

[0069] Cov(f m , f m )=c, for c≥0,

[0070] Instead of the more explicit Cov(f m (x), f m (x)) = ck m (x, x).

[0071] Assumption 1: Cov(f 1：M , f 1：M )=I.

[0072] Note that while this limits the information transfer between meta-tasks, each meta-task can still influence the target task. After conditioning on the observations, the meta-task may still be relevant. Assume Cov(f m , f m ) = 1 (for m = 1 ... M) ensures that each kernel k in (3) m is the corresponding meta-task f m The model of models the boundary distribution. Taken together, these two properties are decisive for the fact that the provided model can also be efficiently learned for a large number M of meta-tasks, since it allows to learn a model independently for each meta-task, which are then combined into a prior for the target task.

[0073] Second, the proposed model is restricted as follows, assuming that f t is additive in the function of the meta-task, that is, in the function that is perfectly (anti-)correlated with the meta-task model. The shorthand Corr(f m , f m )=Corr(f m (x), f m (x)).

[0074] Assumption 2: Function f t It can be written as follows:

[0075] in

[0076] Know For all

[0077] In particular, for the MTGP model in (3) it is applicable that

[0078] By constraining the components of the target task model Making the components perfectly related to the meta-task model directly models the intuition that parts of the meta-task functions should be reflected in the target task. Thus, only the scaling of these functions remains as free parameters that can be learned.

[0079] This leads to the conclusion that the provided model has a structured prior for the target task. It is independent of the meta-task and aims to model all parts of the target task that cannot be explained by metadata.

[0080] Assumptions 1 and 2 together enforce the structuring of the colocalization matrix in (3). Assumption 1 enforces that: if m≠m′, then [w m ](m,m) is zero, while Assumption 2 directly forces [W]m,m=1, so that the change of each meta-task is directly determined by the corresponding kernel k m Modeling. The assumption about the correlation additionally leads to the matrix W m , the matrix for each meta-task By a single scalar and unconstrained parameter is parameterized. Specifically, except

[0081]

[0082] The matrix elements are all zero.

[0083] For example, for meta-task M=1,

[0084]

[0085] From this example, it can be easily verified that both matrices are positive semidefinite and

[0086]

[0087] Therefore, in the case of the provided model, the meta-task f m The function and target task f t The corresponding component in the function is constrained to be perfectly correlated, and w m The size of determines the extent to which the meta-task is related to the target task: μ1 and Given for f t The priors for , and in the limit w1→0 they are modeled as unrelated. The same reasoning applies to multiple tasks, since the assumptions yield valid kernels, i.e., we can show that:

[0088] With of Assumptions 1 and 2 provide an efficient multitasking kernel, which is given by

[0089]

[0090] When v = t, g m (v) is equal to w m ; 1 when v = m; and zero otherwise. δ i＝j is the Dirac delta. According to (5), an effective common kernel for the meta-task and the target task is available, which is expressed by the scalar parameter (weight) parameterization. While this successfully limits the number of parameters, the resulting model generally has the same inference complexity as every other MTGP. However, the common kernel in (5) additionally leads to a specific posterior distribution that allows each meta-task to be modeled as a separate Gaussian process and evaluated efficiently. It can be shown that:

[0091] In the case of a Gaussian process prior with zero mean and a multi-task kernel given by (5), the posterior conditioned on the metadata is given by Given, where

[0092]

[0093] where μ m (x) and ∑ m (x, x) are the mean and covariance of the posterior for the corresponding meta-task according to (1) (with index m rather than t because (1) is expressed with respect to the target task, but (6) involves a meta-task), which depends only on

[0094] Therefore, each meta-task m can be based on the kernel k m A separate Gaussian process is used to model and determine the posterior mean μ for each meta-task m and the posterior covariance ∑m in a way that is based on (only) the corresponding meta-task The metadata of the corresponding Gaussian process is conditioned. For the target task f t The GP prior distribution derived from it is given by the weighted sum of the meta-task posteriors according to (6). It should be noted here that the kernel matrix is ​​precious The result of the inversion can be stored intermediately for each meta-task, since it depends only on fixed metadata Therefore, the scheme is suitable for parallelization and efficient evaluation.

[0095] Therefore, we obtain the prior for the target task, which can be obtained by (1) according to is conditioned to obtain a posterior for the target task

[0096]

[0097] This not only enables a fully Bayesian treatment of uncertainty, but also enables the determination of the meta-task weights w by maximum likelihood methods m .

[0098] Figure 2 Clarify the model provided.

[0099] The individual meta-task posteriors 201 are combined with the test task kernel kt in a weighted sum to obtain the target task prior 202 according to (6). The prior is calculated based on the target task data according to (1). is conditioned to obtain a posteriori 203 for the target task.

[0100] In the above example, suppose the kernel hyperparameters θ in the kernel functions km for various tasks are given m and the target task hyperparameter θ t , which contains k t The parameters and weights w m However, according to various embodiments, in practice the kernel hyperparameter θ m and the target task hyperparameter θ t From the data and is determined by likelihood estimation. Directly evaluating the likelihood of the observed data for the common task model according to (5) is computationally intensive. in However, every model that satisfies Assumption 1 can exploit the model structure to scale with the number of meta-tasks M, since

[0101]

[0102] The second term is given by θ m The sum of the logarithmic probabilities of the corresponding metadata belonging to the meta-task under the parameterized corresponding meta-task model can be used to calculate the cost To calculate, the first term is the prior likelihood of the target task. Given the inverted meta-task kernel matrix, the target task input value X t The computation and complexity of the posterior meta-task covariance Together with the obtained target task likelihood, we can get The total complexity of X is linear in the number of metatasks M and thus enables scalable optimization. t The number of input parameters in θ is typically significantly smaller than the number of available metadata, since the meta-prior already contains important information. This leads to the meta-model parameters θ m and the result y of the target task t This is especially true for the provided model, since the margin per-task model depends only on k m , and thus with θ t Not relevant.

[0103] Accordingly, according to various embodiments, the provided model is modularized in such a way that θ m and θ t Conditional independence between:

[0104] Assumption 3: For all meta-tasks Applicable to

[0105]

[0106] Assumption 1 gives independence between meta-tasks, while Assumption 3 continues one step further and allows independence from the target task hyperparameters θ t Derive meta-task hyperparameters θ m Therefore, the meta-task Gaussian process can be run in parallel based on (only) its individual data

[0107]

[0108] is optimized (i.e. “fitted”).

[0109] If the corresponding meta-task Gaussian process has been fitted to the data of the corresponding meta-task Then input parameter X for the target task t Calculate the posterior mean μ of the meta-task Gaussian process m (X t ) and the covariance matrix ∑ m (X t , X t ) and store them in intermediate storage. Since the prior for the target task according to (6) depends on these parameters, and due to Assumption 3, these parameters do not depend on θ t , so the parameters θ of the model for the target task can be determined by likelihood estimation t :

[0110]

[0111] The cost of this is This can be especially true in the case of M≈Nt Since the meta-task Gaussian process is independent of the target task, it can be calculated once and used again for each new target task. In summary, this enables scalable meta-learning with Gaussian processes.

[0112] Algorithm 1 summarizes the t The training of the model.

[0113]

[0114]

[0115] Algorithm 1

[0116] The training starts in line 2 by training a separate Gaussian process model for each meta-task, which is combined into a target task prior in line 3. On this basis, in line 4, the hyperparameters for the target task are optimized in a cost-effective manner with the help of (7). Finally, in line 5, the hyperparameters for the target task are optimized by (1) according to Conditioning is performed to determine the posterior.

[0117] As described above, equation (6) therefore provides a scalable and structured approach to incorporating information from the meta-task into the new prior for the target task. The key component to this can be seen in Assumption 2, which is based on an additive model. These models reflect many real-world situations, while more flexible meta-learning models based on neural networks are in principle able to learn more complex relationships between meta-tasks and target tasks. However, by relaxing the model assumptions, these methods also require significantly more data. Therefore, the above approach is most suitable when the amount of data for each task is relatively small. The overall scheme scales linearly with the number of meta-tasks and enables parallel optimization, while each individual model is still a standard Gaussian process that scales cubically with the number of data points for each task. For a large number of data points per task, N m or Nt, a scalable GP approximation can be used to obtain efficient inference.

[0118] According to one embodiment, the weights are implemented is computed directly (rather than as part of the likelihood estimate according to (7) or rather by means of a separate optimization problem (in the space spanned by the weights)).

[0119] This can be very advantageous in particular in the case of a large number of meta-tasks and / or a large number of data points for each meta-task. The weights thus found can then either be used directly or can serve as a starting point for a local optimization of the weights.

[0120] The solution to this is to consider the posterior mean of the meta-task model evaluated at the target task input parameter values As a basis in the space spanned by possible observations of the target task. If the basis is likely to be orthogonal, then one can simply project the observed target task result yt onto the basis and obtain the weight as the component of the target data vector expressed through the corresponding basis

[0121] w m =y t ·μ m (X t ) (8)

[0122] However, are not usually orthogonal, and therefore not orthonormal. However, this problem can be solved using a simple algorithm as described below.

[0123] We begin by introducing the vector auxiliary variable y=yt.

[0124] In the first step, determine in In the second step, the part of y described by this first projection is subtracted: the result is the residual For all remaining These two steps are repeated or until the norm of the auxiliary variable falls below a previously determined value. This value can be given in particular by the desired model accuracy. The norm can be given in particular by the L2 or highest norm.

[0125] Since the two basis vectors usually strongly overlap, the weights of the first meta-task model obtained using this method are generally much larger than those corresponding to m>>1. In order to obtain balanced weights, we can use μ m (X t ) are repeated multiple times in different orders and then the weighted average is constructed.

[0126] Algorithm 2 summarizes the approach of directly calculating (or estimating) weights. Common English keywords for, do, and end are used here.

[0127]

[0128] Algorithm 2

[0129] As described above, the above-described approach can be used to optimize the configuration of a target system 100 (eg, a device 108 such as a machine). An example of a process for optimizing and for operating such a target system is given below.

[0130] 1. Parameterize the target system with a series of parameters X (= parameter vector), where individual parameters are also possible. For each parameter, a minimum and a maximum value are defined. This specification defines the search range S.

[0131] a. Example: Parameters characterizing the laser welding process (e.g. laser power, focus position relative to the workpiece)

[0132] b. Parameters characterize the neural network (e.g. number of layers, learning rate)

[0133] c. Variant: The minimum and / or maximum allowed value of a parameter may depend on the values ​​of other parameters.

[0134] d. Variant: The value range specified for a parameter can consist of multiple intervals.

[0135] 2. There are M meta-tasks, which are represented by m=1..M. A Gaussian process model is constructed for each meta-task. Then, according to the corresponding metadata (For each meta-task) train and condition this Gaussian process model to obtain the posterior mean μ of the meta-task m and covariance∑ m .

[0136] a. Specification: A Gaussian process is typically characterized by a kernel, which is usually parameterized with hyperparameters that are optimized during training of the Gaussian process model.

[0137] i. Example: The target kernel is a square exponential kernel or a matrix kernel

[0138] ii. Hyperparameters are length scale and signal variance

[0139] 3. Define the hyperparameter θ t Parameterized target kernel k t .

[0140] 4. Combine all observed target task data points into a target dataset Where n is the number of data points in the dataset.

[0141] 5. According to (6), construct a Gaussian process model for the target task using the kernel. This is the target task prior.

[0142] 6. If the target task dataset is empty, set all weights to w m =1 / M, set k t =0.

[0143] Otherwise, according to (7), the likelihood of the target task data point is maximized by jointly changing the weights w of the target task kernel m and hyperparameter θ t .

[0144] a. Variant: Using Algorithm 2 to directly calculate the weights, a particularly computationally beneficial variant is N iterationen(迭代) =1.

[0145] 7. If the target task dataset is empty, then in this case the target task prior is used for the target task (i.e. for f t ) model.

[0146] Otherwise, the target task prior is conditioned according to the target task dataset to obtain the target task posterior, which in this case is for the target task (i.e., for f t ) model.

[0147] 8. Maximize the acquisition function α using the target model as the backup model. The value of the parameter vector that maximizes the acquisition function is x n+1 .

[0148] a. Example: The acquisition function can be expected improvement, probability of improvement, or upper confidence limit

[0149] b. Example: For the above acquisition function, the maximum can be found efficiently by gradient descent with multiple restarts from different starting points.

[0150] 9. Using the input parameter value x n+1 Configure the target system and observe the resulting data n+1 (The resulting data enables evaluation).

[0151] a. Example: The result of the optimization of a neural network may be the accuracy of its predictions, which is evaluated based on a target data set.

[0152] b. For example, the results of the laser welding process can be evaluated by the width and depth of the resulting weld cross section.

[0153] 10. Determine the scalar value (result value) y n+1 , a scalar value characterizing the desirability of the results described by the result data.

[0154] a. In the case of neural networks, higher prediction accuracy is usually desirable.

[0155] b. In the case of laser welding methods, the difference between the observed width and depth of the weld cross section and the desired reference values ​​should be small.

[0156] c. It may be advantageous to model various pressing requirements separately. In this case, multiple target task datasets and target task models are created. The acquisition function uses all models collectively as backup models.

[0157] 11. Construct the (n+1)th data point as p n+1 =(x n+1 ,y n+1 ) and add it to the target dataset.

[0158] 12. Determine if optimization is complete. If not, continue with step 3.

[0159] a. Example: The maximum number of evaluations on the target system can be specified in the preparation phase.

[0160] 13. Select the best input parameter value set (i.e., the input parameter value set with the best result value) in the target task data set, and run the target system using the configuration given by the input parameters.

[0161] a. Example: The optimal parameter may be the parameter for which the scalar value characterizing the desirability of the observed outcome is already the largest.

[0162] In the context of active learning, the process remains essentially the same. The acquisition function in step 8 is selected such that it minimizes the uncertainty of the target model. For example, an acquisition function with an upper confidence limit of a very large exploration margin, or a more demanding acquisition function such as the entropy of the backup model, may be used. In step 13, instead of selecting the best parameters, the backup model itself is returned and then used for the desired application, for example for controlling a motor based on the model.

[0163] In summary, according to various embodiments, there is provided Figure 3 The method shown in .

[0164] Figure 3 A flow chart 300 is shown which represents a method for configuring a technical system to be configured according to one specific embodiment.

[0165] In 301, for each one or more technical reference systems, reference observations of the results of the reference system are collected (measured) for different values ​​of the configuration parameters. It should be noted in this case that the values ​​of the configuration parameters (and their number) on which the reference observations are based can be different in the case of each reference system. If, for example, there is only one configuration parameter p1, then, for example, reference system 1 can be evaluated for p1={0,1; 0,2; 0,5} and, for example, reference system 2 can be evaluated for p1={0,3; 0,6}.

[0166] At 302 , for each reference system, a corresponding reference system model for a relationship between values ​​of configuration parameters and results provided by the reference system is conditioned on reference observations collected for the reference system.

[0167] In 303 , observations of results of the technical system to be configured are collected (eg measured) for various values ​​of configuration parameters of the technical system to be configured.

[0168] In 304, an a priori model for the relationship between the value of the configuration parameter and the result provided by the technical system to be configured is adapted to the observations collected for the technical system to be configured, wherein the a priori model consists of a weighted combination of the conditioned reference system model (e.g., as in the above example, supplemented with a residual term k t , see equation (5)) (i.e., the prior model contains a weighted combination of the conditioned reference system model).

[0169] In 305, an a posteriori model for the relationship between values ​​of configuration parameters (considered to be configuration parameters for the technical system to be configured - for the entire range of values ​​of the configuration parameters (i.e. not only for different values ​​of the configuration parameters, observations of the results have been collected)) and the results provided by the technical system to be configured is conditioned by conditioning the adapted a priori model based on observations collected for the technical system to be configured.

[0170] In 306 , the technical system to be configured is configured using the determined a posteriori model.

[0171] The result can be collected in the form of one or more output parameters. In the case of multiple output parameters, a separate model can be created for each output parameter, and then the union of these models can be used as a model. In order to jointly consider different goals in the acquisition function, a common goal can be defined. For example, a cost function is defined, and then the cost function should be minimized by setting input parameters with the help of the acquisition function. The cost function combines all target parameters in a single scalar function. For example, the cost function can be a sum. The target parameter that should be minimized is included in the total with a positive sign. The target parameter that should be maximized is correspondingly included with a negative sign. For the target parameter that should reach a specific value, the distance between the target parameter and the expected value is included in the cost function. Then the individual contributions can also be weighted.

[0172] Figure 3The method can be implemented by one or more computers having one or more data processing units. The term "data processing unit" can be understood as any type of entity that enables processing of data or signals. For example, data or signals can be processed according to at least one (i.e., one or more than one) specific function implemented by a data processing unit. The data processing unit may include an analog circuit, a digital circuit, a logic circuit, a microprocessor, a microcontroller, an integrated circuit of a central unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), a programmable gate array (FPGA), or any combination thereof or constructed thereof. Any other means for implementing the corresponding functions described in more detail here can also be understood as a data processing unit or a logic circuit device. One or more of the method steps described in detail here can be performed (e.g., implemented) by a data processing unit through one or more specific functions, and the specific functions are implemented by the data processing unit.

[0173] According to various embodiments, the method is therefore in particular computer-implemented.

[0174] Various embodiments may receive and use (e.g. for observation) time series of sensor data from various sensors, such as video, radar, lidar, ultrasound, motion, thermal imaging, current, voltage, temperature, etc. Based on the sensor data, various technical systems, physical devices, etc. may be configured, for example by corresponding control devices.

Claims

1. A method for configuring a technical system (108) to be configured, comprising: For each one or more technical reference systems, collecting reference observations of results of the reference system for different values ​​of configuration parameters (130); For each reference system, conditioning a corresponding reference system model for the relationship between values ​​of configuration parameters and results provided by the reference system according to reference observations (130) collected for the reference system; For the technical system to be configured (108), collecting observations (130) of results of the technical system to be configured (108) for various values ​​of configuration parameters; Adapting an a priori model (202) of the relationship between values ​​of configuration parameters and results provided by the technical system (108) to be configured to observations (130) collected for the technical system (108) to be configured, wherein the a priori model (202) is composed of a weighted combination of conditioned reference system models (201); determining an a posteriori model (203) for the relationship between values ​​of configuration parameters and results provided by the technical system (108) to be configured by conditioning the adapted a priori model (202) on observations (130) collected for the technical system (108) to be configured; and The technical system (108) to be configured is configured using the determined a posteriori model (203).

2. The method of claim 1, wherein adapting the a priori model (202) comprises adapting weights of a weighted combination of the conditioned reference system models (201).

3. The method according to claim 1 or 2, wherein the conditioned reference system model (201) and the prior model (202) for the system (108) to be configured are Gaussian processes.

4. The method according to claim 3, wherein the covariance function of the prior model (202) is composed of a weighted sum of the covariance of the reference system model and a residual covariance function, wherein adapting the prior model (202) includes adapting the residual covariance function.

5. A method according to claim 3 or 4, wherein the weight of the first reference system model of the reference system model is determined by projecting the observations (130) collected for the technical system (108) to be configured onto the mean of the first reference system model, and the weight of the second reference system model of the reference system model is determined by projecting the residuals of the observations (130) collected for the technical system (108) to be configured onto the mean of the second reference system model.

6. The method according to any one of claims 1 to 5, comprising: For each reference system, a reference system model is generated by fitting a corresponding reference a priori model to observations (130) acquired for the reference system. 7 . A data processing device configured to carry out the method according to claim 1 . 8 . A computer program comprising instructions which, when executed by a processor, cause the processor to carry out the method according to claim 1 .

9. A computer readable medium storing instructions which, when executed by a processor, cause the processor to implement the method according to any one of claims 1 to 6.

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