Method for assessing model uncertainties by means of a neural network and an architecture of the neural network

Abstract

The invention relates to a computer-implemented method (100) for assessing uncertainties by means of a neural network (200), in particular a neural process, in a model, wherein the model models a technical system and / or system behaviour of the technical system, and an architecture of the neural network (200) for assessing uncertainties.

Description

[0001] Description

[0002] Method for estimating model uncertainties using a neural network and an architecture of the neural network

[0003] State of the art

[0004] The disclosure relates to a method for estimating uncertainties using a neural network and an architecture of the neural network.

[0005] In technical systems, especially safety-critical technical systems, models, especially models for active learning, reinforcement learning or extrapolation, can be used to predict uncertainties, for example using neural networks.

[0006] Recently, neural processes have been increasingly used to predict model uncertainty. Neural processes are essentially a family of neural network-based architectures that produce probabilistic predictions for regression problems. They automatically learn inductive biases tailored to a class of objective functions with some kind of common structure, such as quadratic functions or dynamic models of a particular physical system with varying parameters. Neural processes are trained using so-called multi-task training techniques, where one function corresponds to one task. The resulting model provides accurate predictions about unknown objective functions based on only a few contextual observations.

[0007] A so-called aggregation mechanism is used to feed the context observations into the architecture. This mechanism allows one context tuple at a time, i.e., an input-output pair (x, y) from the objective function, to be passed through an encoder network that maps each context tuple to a latent observation r. All latent observations are then aggregated using a type of contraction operation. Traditionally, neural processes use mean aggregation, i.e., the aggregation mechanism takes the mean across all latent observations. Bayesian context aggregation is also known to be used in neural processes.In contrast to mean aggregation, which assigns a uniform weight of 1 / N to all latent observations, where N is the size of the context set, Bayesian context aggregation allows for weighting of the latent observations according to a learned measure of task ambiguity. This is relevant because different context tuples contain different amounts of information about the identity of the target function. If the context tuple is located in an area of ​​the xy-space with high task ambiguity, i.e., it could be generated by many functions from the underlying function class, the amount of information conveyed by this context tuple is small. Therefore, the weight of the corresponding latent observation in the aggregated set must also be small, and conversely, if the amount of information is high, the weight must also be high.In Bayesian context aggregation, task-ambiguity-dependent weighting is achieved by adding a second encoder network. The second encoder network learns to quantify the task ambiguity of each context tuple using the variance of the latent observation. This encoder output then modulates the weight of the corresponding latent observation according to a Bayesian observation model. Fundamentally, experimental results show that Bayesian context aggregation improves the predictive performance of neural processes compared to traditional mean aggregation.

[0008] An object of the present disclosure is to provide a method and architecture that can at least maintain or improve the predictive performance of Bayesian context aggregation and the advantages, for example, the uneven weighting of the latent observations in the aggregation, while being more parameter efficient than Bayesian context aggregation.

[0009] Disclosure of the invention This object is achieved by a method according to the described embodiments.

[0010] One embodiment relates to a computer-implemented method for estimating uncertainties by means of a neural network, in particular a neural process, in a model, wherein the model models a technical system and / or a system behavior of the technical system, wherein in a step based on a number N of latent observations r n , with n=1... N, a model uncertainty a z2 as the variance of a latent Gaussian distribution and a mean . z the latent Gaussian distribution, where the model uncertainty a z 2 and the mean . z depending on the latent observations r n and a hyperparameter T and in a further step the latent Gaussian distribution is determined by the variance a z 2 and the mean . z parameterized. It should be noted that the model was created based on measurements of the technical system.

[0011] The introduction of the hyperparameter T, also known as softmax temperature, enables uneven weighting of the latent observations without requiring a second encoder network. Using this additional trainable hyperparameter enables so-called "softmax aggregation," which can replace conventional aggregation methods, such as mean aggregation, max aggregation, or Bayesian aggregation, in neural-based architectures.

[0012] The "softmax aggregation" described in the disclosure greatly simplifies the Bayesian aggregation described above, as the "softmax aggregation" has a fixed dependence of the variances o 2 n of the latent observations from the latent observations r n as follows:

[0013] This means that no separate encoder network is needed to calculate o 2 nThis reduces the number of parameters to be learned. The fixed dependence of the variances o 2 n of the I latent observations r n and the hyperparameter T can be used in the well-known Bayesian aggregation equations. The resulting equations then form the "softmax aggregation" equations:

[0014] According to one embodiment, it is provided that the latent observations r n by mapping context data pairs x n ,y n using a neural encoder network to a corresponding latent observation r n are generated. The calculation of o z and y. z according to the described equations and the parameterization of the latent Gaussian distribution with these parameters.

[0015] It can be provided that the hyperparameter T is determined by means of the neural encoder network to map the context data pairs x n ,y n is generated.

[0016] For example, it may be advantageous if the hyperparameter T together with parameters of the neural encoder network for mapping the context data pairs x n ,y n is learned, for example in a collaborative learning process.

[0017] According to a further embodiment, the hyperparameter T is determined independently by hyperparameter optimization.

[0018] According to a further embodiment, it is provided that by means of a neural decoder network based on the latent Gaussian distribution, in particular based on an input point x and based on a latent sample z derived from the Gaussian distribution, a variance of an output of the model, also output variance oy 2, is determined. The neural decoder network can thus calculate predictions about target variables y at locations x based on samples z from the latent Gaussian distribution. According to a further embodiment, it is provided that a mean fiy of the output of the model is determined by means of a further neural decoder network based on the latent Gaussian distribution, in particular based on an input location x and based on a latent sample z derived from the Gaussian distribution. The mean / / y, in particular in combination with the output variance, provides an estimate of target variables y.

[0019] Further embodiments relate to an architecture of a neural network, in particular of a neural process, wherein the neural network is designed to carry out steps of a method according to the described embodiments for estimating uncertainties in a model, wherein the model models a technical system and / or a system behavior of the technical system.

[0020] According to one embodiment, the neural network comprises at least one neural encoder network and / or at least one neural decoder network, wherein the neural encoder network is trained to, based on context data pairs x n , y n latent observations r n to generate and / or wherein the neural decoder network is trained to generate a variance of an output of the model based on the latent Gaussian distribution, also output variance oy 2 , and / or a mean . yto determine the output of the model.

[0021] Further embodiments relate to a device comprising a neural network, in particular a neural process, with an architecture according to the described embodiments, wherein the device is designed to carry out steps of a method according to the described embodiments.

[0022] Further embodiments relate to the use of a method according to the described embodiments and / or a neural network, in particular a neural process, with an architecture according to the described embodiments, for determining a, in particular impermissible, deviation of a system behavior of a technical system from a standard value range. It should be noted that, depending on a determined deviation, the technical system can be switched to a safe operating mode or a warning can be issued.

[0023] When determining the deviation of the technical system, an artificial neural network is used, which is fed with input and output data from the technical device during a learning phase. By comparing the input and output data of the technical system, the corresponding connections are created in the artificial neural network, and the neural network is trained on the system behavior of the technical system.

[0024] In a prediction phase following the learning phase, the neural network can be used to reliably predict the system behavior of the technical system. For this purpose, input data from the technical system is fed to the neural network in the prediction phase, and output comparison data is calculated in the neural network and compared with the output data of the technical system. If this comparison shows that the difference between the output data of the technical system, which is preferably recorded as measured values, deviates from the output comparison data of the neural network and the deviation exceeds a limit, this constitutes an inadmissible deviation of the system behavior of the technical system from the standard value range. Suitable measures can then be taken, for example, a warning signal can be generated or stored, or partial functions of the technical system can be deactivated (degradation of the technical device).If necessary, alternative technical equipment may be used in the event of an inadmissible deviation.

[0025] Using the method described above, a real technical system can be continuously monitored. During the learning phase, the neural network is fed with sufficient information from both the input and output sides of the technical system so that the technical system can be mapped and simulated in the neural network with sufficient accuracy. This allows the technical system to be monitored in the subsequent prediction phase and a deterioration in system behavior to be predicted. In this way, the remaining service life of the technical system can be predicted.

[0026] Further features, possible applications, and advantages of the disclosure will become apparent from the following description of exemplary embodiments of the invention, which are illustrated in the figures of the drawing. All described or illustrated features, individually or in any combination, constitute the subject matter of the disclosure, regardless of their summary in the patent claims or their references, as well as regardless of their wording or representation in the description or in the drawing. The drawing shows:

[0027] Fig. 1 schematically shows a method for estimating uncertainties according to an embodiment, and

[0028] Fig. 2 shows an architecture of a neural process according to an embodiment.

[0029] In the following, a computer-implemented method for estimating uncertainties by means of a neural network, in particular a neural process, in a model, wherein the model models a technical system and / or a system behavior of the technical system, is described with reference to the figures.

[0030] The method 100 comprises a step 110, wherein in step 110 based on a number N of latent observations r n , with n=1... N, a model uncertainty a z 2 as the variance of a latent Gaussian distribution and a mean . z the latent Gaussian distribution, where the model uncertainty a z 2 and the mean . z depending on the latent observations r n and a hyperparameter T.

[0031] The dependence of the variances o 2 n of the latent observations from the latent observations rn and the hyperparameter T is prescribed as follows: The fixed dependence of the variances o 2 n of the I latent observations r n and the hyperparameter T can be converted into known Bayesian aggregation equations The resulting equations then form the "softmax aggregation" equations:

[0032] In the resulting equations, n zfi = 0 and G Z 0 oo provided.

[0033] The use of the additional trainable hyperparameter T enables so-called "softmax aggregation," which can replace conventional aggregation methods, such as mean aggregation, max aggregation, or Bayesian aggregation, in neural process-based architectures. It can be advantageous that "softmax aggregation" combines traditional mean and max aggregation: mean aggregation is restored in the limit T—>°° and max aggregation in the limit T—>0.

[0034] The method further comprises a step 120, wherein in step 120 the latent Gaussian distribution is determined by the variance a z 2 and the mean . z According to one embodiment, the latent observations r n by mapping context data pairs x n ,y nusing a neural encoder network to a corresponding latent observation r n be generated, see step 130. Then the calculation of o z and y. z according to the described equations, see step 110, and the parameterization of the latent Gaussian distribution with these parameters, see step 120.

[0035] The hyperparameter is determined, for example, in one of the training and / or optimization processes preceding the method 100, see step 140. It can be provided that the hyperparameter T is determined by means of the neural encoder network for mapping the context data pairs x n ,y n For example, it may be advantageous if the hyperparameter T together with parameters of the neural encoder network for mapping the context data pairs x n ,y nis learned, for example, in a joint learning process. According to a further embodiment, the hyperparameter T is determined independently by hyperparameter optimization.

[0036] According to a further embodiment, it is provided that by means of a neural decoder network based on the latent Gaussian distribution, in particular based on an input point x and based on a latent sample z derived from the Gaussian distribution, a variance of an output of the model, also output variance oy 2 , is determined, see step 150. The neural decoder network can thus calculate predictions about target variables y at locations x based on samples z from the latent Gaussian distribution.

[0037] According to a further embodiment, it is provided that a mean value fiy of the output of the model is determined by means of a further neural decoder network based on the latent Gaussian distribution, in particular based on an input point x and based on a latent sample z derived from the Gaussian distribution, cf. step 150. The mean value / z y , in particular in combination with the output variance, provides an estimate of target variable y. Fig. 2 shows an architecture of a neural network 200, in particular a neural process, wherein the neural network 200 is designed to carry out steps of a method 100 according to the described embodiments for estimating uncertainties in a model, wherein the model models a technical system and / or a system behavior of the technical system.

[0038] The neural network 200 comprises, according to Fig. 2, a neural encoder network 210. The neural encoder network 210 is trained to convert the latent observations r n by mapping context data pairs x n ,y n to a corresponding latent observation r n to generate.

[0039] The neural network 200 comprises, according to Fig. 2, a first neural decoder network 220, wherein the first neural decoder network 220 is trained to calculate the variance of an output of the model, also output variance a, on an input point x and a latent sample z. y 2 , to determine.

[0040] According to Fig. 2, the neural network 200 comprises a further neural decoder network 230, wherein the further neural decoder network 230 is trained to determine a mean value based on an input point x and a latent sample z. y of the output. The mean / z y, especially in combination with the output variance, provides an estimate of target variable y.

[0041] Further embodiments relate to the use of the method 100 according to the described embodiments and / or a neural network 200, in particular a neural process, with an architecture according to the described embodiments for determining a, in particular inadmissible, deviation of a system behavior of a technical system from a standard value range.

[0042] When determining the deviation of the technical system, an artificial neural network is used, which is fed with input and output data from the technical device during a learning phase. By comparing the input and output data of the technical system, the corresponding connections are created in the artificial neural network, and the neural network is trained on the system behavior of the technical system.

[0043] A plurality of training data sets used in the learning phase can comprise input variables measured on the technical system and / or calculated for the technical system. The plurality of training data sets can contain information relating to operating states of the technical system. Additionally or alternatively, the plurality of training data sets can contain information relating to the environment of the technical system. In some examples, the plurality of training data sets can contain sensor data. The computer-implemented machine learning system can be trained for a specific technical system in order to process data (e.g., sensor data) arising in this technical system and / or in its environment and to calculate one or more output variables relevant for monitoring and / or controlling the technical system. This can happen during the design of the technical system.In this case, the computer-implemented machine learning system can be used to calculate the corresponding output variables depending on the input variables. The obtained data can then be incorporated into a monitoring and / or control device for the technical system. In other examples, the computer-implemented machine learning system can be used in the operation of the technical system to perform monitoring and / or control tasks.

[0044] In a prediction phase following the learning phase, the neural network can be used to reliably predict the system behavior of the technical system. For this purpose, input data from the technical system is fed to the neural network in the prediction phase, and output comparison data is calculated in the neural network and compared with the output data of the technical system. If this comparison shows that the difference between the output data of the technical system, which is preferably recorded as measured values, deviates from the output comparison data of the neural network and the deviation exceeds a limit, this constitutes an inadmissible deviation of the system behavior of the technical system from the standard value range. Suitable measures can then be taken, for example, a warning signal can be generated or stored, or partial functions of the technical system can be deactivated (degradation of the technical device).If necessary, alternative technical equipment may be used in the event of an inadmissible deviation.

[0045] Using the method described above, a real technical system can be continuously monitored. During the learning phase, the neural network is fed with sufficient information from both the input and output sides of the technical system so that the technical system can be mapped and simulated in the neural network with sufficient accuracy. This allows the technical system to be monitored in the subsequent prediction phase and a deterioration in system behavior to be predicted. In this way, the remaining service life of the technical system can be predicted.

[0046] Specific applications include applications in various technical devices and systems. For example, computer-implemented machine learning systems can be used to control and / or monitor a device.

[0047] A first example relates to the design of a technical device or a technical system. In this context, the training data sets can contain measurement data and / or synthetic data and / or software data that play a role in the operating states of the technical device or a technical system. The input or output data can be state variables of the technical device or a technical system and / or control variables of the technical device or a technical system. In one example, generating the computer-implemented probabilistic machine learning system (e.g., a probabilistic regressor or classifier) ​​can comprise mapping an input vector of one dimension (H ) to an output vector of a second dimension (IR m). Here, for example, the input vector can represent elements of a time series for at least one measured input state variable of the device. The output vector can represent at least one estimated output state variable of the device, which is predicted based on the generated a posteriori predictive distribution. In one example, the technical device can be a machine, e.g. a motor (e.g. an internal combustion engine, an electric motor, or a hybrid motor). In other examples, the technical device can be a fuel cell. In one example, the measured input state variable of the device can include a rotational speed, a temperature, or a mass flow rate. In other examples, the measured input state variable of the device can include a combination thereof. In one example, the estimated output state variable of the device can include a torque, an efficiency, a pressure ratio.In other examples, the estimated output state variable may include a combination thereof.

[0048] The various input and output variables in a technical device can exhibit complex non-linear dependencies during operation. In one example, the computer-implemented machine learning systems of this disclosure can be used to model a parameterization of a characteristic map for the device (e.g., for an internal combustion engine, an electric motor, a hybrid engine, or a fuel cell). The modeled characteristic map of the method according to the invention makes it possible, above all, to quickly and accurately provide the correct relationships between the various state variables of the device during operation. The characteristic map modeled in this way can, for example, be used during operation of the device (e.g., the engine) to monitor and / or control the engine (e.g., in an engine control device). In one example, the characteristic map can indicate how a dynamic behavior (e.g., energy consumption) of a machine (e.g.,of an engine) depends on various state variables of the machine (e.g. speed, temperature, mass flow, torque, efficiency and pressure ratio).

[0049] The computer-implemented machine learning systems can be used to classify a time series, in particular the classification of image data (i.e., the technical device is an image classifier). The image data can be, for example, camera, lidar, radar, ultrasound, or thermal image data (e.g., generated by corresponding sensors). In some examples, the computer-implemented machine learning systems can be designed for a monitoring device (e.g., of a manufacturing process and / or for quality assurance) or for a medical imaging system (e.g., for analyzing diagnostic data) or can be used in such a device.

[0050] In other examples (or additionally), the computer-implemented machine learning systems can be designed or used to monitor the operating state and / or the environment of an at least partially autonomous robot. The at least partially autonomous robot can be an autonomous vehicle (or another at least partially autonomous means of locomotion or transport). In other examples, the at least partially autonomous robot can be an industrial robot. For example, using data from position and / or speed and / or torque sensors, in particular of a robot arm, a precise probabilistic estimate of position and / or speed, in particular of the robot arm, can be determined by means of the described regression. In other examples, the technical device can be a machine or a group of machines (e.g., an industrial plant). For example, an operating state of a machine tool can be monitored.In these examples, the output data y may contain information regarding the operating state and / or environment of the respective technical device.

[0051] In further examples, the system to be monitored may be a communications network. In some examples, the network may be a telecommunications network (e.g., a 5G network). In these examples, the input data x may contain utilization data in nodes of the network, and the output data y may contain information regarding the allocation of resources (e.g., channels, bandwidth in network channels, or other resources). In other examples, a network malfunction may be detected.

[0052] In other examples (or in addition), the computer-implemented machine learning systems can be designed or used to control (or regulate) a technical device. The technical device can in turn be one of the devices discussed above (or below) (e.g., an at least partially autonomous robot or a machine). In these examples, the output data y can contain a control variable of the respective technical system.

[0053] In still other examples (or in addition), the computer-implemented machine learning systems may be configured or deployed to filter a signal. In some cases, the signal may be an audio signal or a video signal. In these examples, the output data y may include a filtered signal.

[0054] The methods for creating and applying computer-implemented machine learning systems of the present disclosure may be performed on a computer-implemented system. The computer-implemented system may include at least one processor, at least one memory (which may contain programs that, when executed, perform the methods of the present disclosure), and at least one interface for inputs and outputs. The computer-implemented system may be a stand-alone system or a distributed system that communicates over a network (e.g., the Internet).

[0055] The present disclosure also relates to computer-implemented machine learning systems generated using the methods of the present disclosure. The present disclosure also relates to computer programs configured to perform all the steps of the methods of the present disclosure. Furthermore, the present disclosure relates to machine-readable storage media (e.g., optical storage media or read-only memory, e.g., FLASH memory) on which computer programs configured to perform all the steps of the methods of the present disclosure are stored.

Claims

Claims 1. Computer-implemented method (100) for estimating uncertainties by means of a neural network (200, 300), in particular a neural process, in a model, wherein the model models a technical system and / or a system behavior of the technical system, wherein in a step (110) based on a number N of latent observations (r„), with n=1... N, a model uncertainty (o- z 2 ) as the variance of a latent Gaussian distribution and a mean ( z z ) of the latent Gaussian distribution, where the model uncertainty (o- z 2 ) and the mean ( z z ) is determined depending on the latent observations (r„) and a hyperparameter (T) and in a further step (120) the latent Gaussian distribution is determined by the variance (o- z 2 ) and the mean ( z z ) is parameterized.

2. The method (100) according to claim 1, wherein the latent observations (r„) are generated by mapping context data pairs (x n ,y n ) can be generated using a neural encoder network to a corresponding latent observation (r„).

3. The method (100) according to claim 2, wherein the hyperparameter (T) is determined by means of the neural encoder network (210) for mapping the context data pairs (x n ,y n ) is generated.

4. Method (100) according to one of claims 1 to 3, wherein the hyperparameter (T) together with parameters of the neural encoder network (210) for mapping the context data pairs (x n ,y n ) is learned.

5. The method (100) of claim 1 or 2, wherein the hyperparameter (T) is determined independently by hyperparameter optimization.

6. Method (100) according to one of the preceding claims, wherein by means of a first neural decoder network (220) based on the latent Gaussian distribution, in particular based on an input point (x) and based on a latent sample (z) derived from the Gaussian distribution, a variance of an output of the model, also output variance (o- y 2 ), is determined.

7. Method (100) according to one of the preceding claims, wherein by means of a further neural decoder network (230) based on the latent Gaussian distribution, in particular based on an input point (x) and based on a latent sample (z) derived from the Gaussian distribution, a mean value ( / z y ) of the model's output.

8. Architecture of a neural network (200), in particular of a neural process, wherein the neural network (200) is designed to carry out steps of a method (100) according to one of claims 1 to 7 for estimating uncertainties in a model, wherein the model models a technical system and / or a system behavior of the technical system.

9. The architecture of claim 8, wherein the neural network (200) comprises at least one neural encoder network (210) and / or at least one neural decoder network (220, 230), wherein the neural encoder network (210) is trained to, based on context data pairs (x n ,y n ) to generate latent observations (r„) and / or wherein a neural decoder network (220, 230) is trained to generate a variance of an output of the model, also output variance (oy 2 ), and / or a mean . yto determine the output of the model.

10. Device comprising a neural network (200), in particular a neural process, with an architecture according to one of claims 7 to 9, wherein the device is designed to carry out steps of a method (100) according to one of claims 1 to 6. Use of a method according to one of claims 1 to 6 and / or a neural network (200), in particular a neural process, with an architecture according to one of claims 8 to 9 for determining a, in particular inadmissible, deviation of a system behavior of a technical system from a standard value range.

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