Abstract: A device and a computer-implemented method for determining a variable of a technical system, using a machine learning model. A kernel for the model is selected from a set of kernels as a function of a selection criterion, and a first data set which includes mutually assigned input variables and output variables of the technical system. The selection criterion is determined for a kernel that is selected from the set of kernels as a function of an acquisition function, the acquisition function being determined as a function of a second data set that includes pairs of kernels from the set of kernels and a selection criterion. The pairs of kernels are determined over respectively one pair of kernels from the set of kernels and as a function of the second data set. Representations of a first and second kernel are provided.

Abstract: A method for operating an injection valve by ascertaining an opening time and/or closing time of the injection valve on the basis of a sensor signal. The method includes: providing an analysis point time series by sampling a sensor signal of a sensor of the injection valve; using a nonlinear, data-based first submodel in order to obtain a first model output on the basis of the analysis point time series; using a linear, data-based second submodel in order to obtain a second model output on the basis of the analysis point time series; ascertaining the opening time and/or closing time as a function of the first and second model outputs.

Abstract: A method for operating an injection valve by determining an opening or closing time of the injection valve based on a sensor signal. The method includes: providing an evaluation point time series by sampling a sensor signal of a sensor of the injection valve; using a non-linear data-based first sub-model to obtain a first output vector based on the evaluation point time series, wherein each element of the first output vector is associated with a specific time; using a linear, data-based second sub-model to obtain a second output vector based on the evaluation point time series, wherein each element of the second output vector is associated with a specific time; limiting the time determined by the first output vector depending on the second output vector in order to obtain the opening or closing time.

Abstract: A method for training a data-based evaluation model to determine an opening or closing time of an injection valve based on a sensor signal. The method includes: measuring an operation of the injection valve in order to determine at least one sensor signal and an associated opening or closing time; sampling the sensor signal at a sampling rate in order to obtain a sensor signal time series with sensor signal values; determining a plurality of training data sets by assigning a plurality of evaluation point time series generated from a sensor signal time series to the opening or closing time associated with the sensor signal, wherein the evaluation point time series has a lower temporal resolution than the sensor signal time series; training the data-based evaluation model depending on the determined training data sets.

Abstract: Apparatus, system and computer-implemented method of operating a technical system. A first variable of the technical system is mapped onto a prediction for a second variable of the technical system using a Gaussian process, and the technical system is operated depending on the prediction. The Gaussian process, depending on a sum of a first Gaussian process, weighted with a first weight function, is determined with a second Gaussian process. The first Gaussian process maps the first variable based onto a first prediction of the second variable, and the second Gaussian process maps the first variable onto a second prediction for the second variable. Sub-domains of a domain and/or a value range of the Gaussian process are determined depending on a numerical representation of a binary tree with leaves and nodes.

Abstract: A computer-implemented method for training a data-based time determining model for determining an opening or closing time of an injection valve based on a sensor signal. The method includes: providing an unlabeled analysis point time series by sampling the sensor signal of a sensor of the injection valve; training the data-based time determining model to assign a time specification which represents a specific opening or closing duration to an analysis point time series, the training process being carried out using a first shifting function to time-shift the analysis point time series and a second shifting function in order to time-shift the time specification. A consistency loss function is used for the training process.

Abstract: A method for operating an injection valve by ascertaining an opening time and/or closing time of the injection valve on the basis of a sensor signal. The method includes: providing an analysis point time series by sampling a sensor signal of a sensor of the injection valve; using a nonlinear, data-based first submodel in order to obtain a first model output on the basis of the analysis point time series; using a linear, data-based second submodel in order to obtain a second model output on the basis of the analysis point time series; ascertaining the opening time and/or closing time as a function of the first and second model outputs.

Abstract: A computer-implemented method for the safe, active training of a computer-aided model for modeling time series of a physical system using Gaussian processes, including the steps of establishing a safety threshold value ?; initializing by implementing safe initial curves as input values on the system, creating an initial regression model and an initial safety model; repeatedly carrying out the steps of updating the regression model; updating the safety model; determining a new curve section; implementing the determined new curve section on the physical system and measuring output variables; incorporating the new output values in the regression model and the safety model until N passes have been carried out; and outputting the regression model and the safety model.

Abstract: A computer-implemented method for ascertaining a closure point in time of an injector of an internal combustion engine using a classifier. The method includes: ascertaining a time series of input signals, each corresponding to a point in time within the time series, and each characterizing a deformation of the injector; ascertaining a plurality of first values using the classifier based on the time series, in each case a first value corresponding to a point in time of the time series, and the first value characterizing a probability that the closure point in time of the injector matches the point in time; ascertaining a plurality of second values, each being a sum of neighboring first values, of a first value and the first value, the second value corresponding to the point in time to which the first value corresponds; ascertaining the closure point in time based on the largest second value.

Abstract: A computer-implemented method for ascertaining a closure point in time of an injector of an internal combustion engine using a classifier. The method includes: ascertaining a time series of input signals, each corresponding to a point in time within the time series, and each characterizing a deformation of the injector; ascertaining a plurality of first values using the classifier based on the time series, in each case a first value corresponding to a point in time of the time series, and the first value characterizing a probability that the closure point in time of the injector matches the point in time; ascertaining a plurality of second values, each being a sum of neighboring first values, of a first value and the first value, the second value corresponding to the point in time to which the first value corresponds; ascertaining the closure point in time based on the largest second value.

Abstract: A computer-implemented method for the safe, active training of a computer-aided model for modeling time series of a physical system using Gaussian processes, including the steps of establishing a safety threshold value ?; initializing by implementing safe initial curves as input values on the system, creating an initial regression model and an initial safety model; repeatedly carrying out the steps of updating the regression model; updating the safety model; determining a new curve section; implementing the determined new curve section on the physical system and measuring output variables; incorporating the new output values in the regression model and the safety model until N passes have been carried out; and outputting the regression model and the safety model.