Abstract: A computer-implemented method for predicting a behavior of agents in a dynamic system with a multiplicity of interacting agents depending on the latent state thereof. For a plurality of components and for a plurality of time points up to a prediction time point, a value of a first moment of a first distribution, which models the latent state of the agents, is determined for each component. A value of a second moment of the first distribution is determined. An expected value for a first moment of a second distribution at the prediction time point is determined for each component depending on the value of the first moment of the first distribution at the prediction time point and depending on the value of the second moment of the first distribution at the prediction time point. The second distribution models the behavior of the agents depending on the latent state thereof.

Abstract: A computer-implemented method for generating a control command for an autonomous vehicle. The method includes: capturing sensor data by at least one sensor of the vehicle; generating an input text from the sensor data; interpreting the input text using a machine learning algorithm; and generating a control command for the vehicle from the interpreted input text.

Abstract: A method for determining a model for an unknown function is described comprising training a neural network for selecting inputs at which to evaluate the unknown function. The training includes a plurality of iterations of sampling, from a set of Gaussian processes, at least one initial guess for the unknown function, using the neural network to select inputs and evaluating the selected inputs using the at least one initial guess, determining a value of an objective function from the evaluated selected inputs, adjusting the neural network to improve the value of the objective function and determining the model by evaluating the unknown function at a sequence of inputs given by the trained neural network and fitting the model to the evaluated inputs.

Abstract: Active learning for operating a physical system. The method includes: providing a data set that comprises data points each comprising an input for operating the physical system, and a first and second observation of the physical system; training a multi-output Gaussian process for predicting the first observation for a given input with the data set; training a Gaussian process for predicting the second observation for a given input with the data set; determining with the data set an input for operating the physical system; determining the first and second observations that result from operating the physical system with the determined input; and adding a data point to the data set that comprises the determined input and the determined first and second observations.

Abstract: Generation of a road map, in particular appropriate for use in automated driving (AD) of a vehicle. A method comprises a step of receiving image input data. The image input data includes acquired image data representing at least one area which is drivable by a vehicle. The method includes a step of generating a road map based on the received image input data. The generating of the road map is performed by a trained visual foundation model for road map generation, in particular appropriate for use in AD. The generated road map includes a road layout within the at least one area drivable by a vehicle along with locally allocated contextual information in view of applicable traffic regulations.

Abstract: A device and computer-implemented method for continuous-time interaction modeling of agents. The method includes: providing latent states of first and second agents, respectively; providing a first Gaussian process distribution for a first function for modelling a kinematic behavior of an agent independently of other agents and a second Gaussian process distribution for a second function for modelling an interaction between agents; sampling the first function from the first Gaussian process distribution and the second function from the second Gaussian process distribution, the first function mapping a latent state of one agent to a contribution to a change of its latent state, the second function mapping the latent states of two agents to a contribution to a change of a latent state of one of the two agents; changing the latent state of the first agent.

Abstract: A device and computer-implemented method for machine learning with time-series data representing observations related to a technical system. The comprising includes: providing (the time-series data, and model parameters of a distribution over the time-series data and over a first latent variable and over a second latent variable, and variational parameters of an approximate distribution over a second latent variable, sampling a value of the second latent variable from the approximate distribution over the second latent variable, finding a value of the first latent variable depending on a density of the distribution over the time-series data and over the first latent variable and over the value of the second latent variable, determining a Hessian depending on a second order Taylor approximation of the distribution over the time-series data and the first latent variable and the value of the second latent variable evaluated at the value of the first latent variable.

Abstract: A method for training a target machine learning model for a target system in engineered processes and machines. A multitask Gaussian process implements a joint model of safety values of the target and auxiliary system. A new state is selected for the target system, wherein target safety values are predicted by the multitask Gaussian process.

Abstract: A computer-implemented method of predicting dynamics of objects in a surrounding of a vehicle is disclosed. The method starts with a step of receiving a first data sets characterizing dynamics of the objects respectively. Then, each of the first data sets is propagated through an encoder outputting a latent representation for each of the first data sets. Then, a graph based on the latent representations is generated. Then, the graph is propagated through a Graph Neural Network outputting an updated graph. Based on the updated graph a decoder outputs a predicted dynamic for selected object for a subsequent time step.

Abstract: A state-space model which includes one or more neural networks. The state-space model is configured to stochastically model a technical system by modelling uncertainties both in latent states of the technical system and in weights of the one or more neural networks. Thereby, the state-space model may be able to capture both aleatoric uncertainty (inherent unpredictability in observations) and epistemic uncertainty (uncertainty in the model's parameters or weights. During the training and during subsequent use for model-predictive control, moment matching across neural network layers is used, which may ensure that the model's predictions are consistent and close to real system behavior.

Abstract: A method for processing a variance of a Gaussian process prediction of an embedded system is disclosed. A computer program, a device and a storage medium for this purpose is also disclosed.

Abstract: A method for training a neural network system to predict the behavior of a set of interacting agents.

Abstract: A device and computer-implemented method for predicting a state of a technical system. A state of the technical system is detected and a time series is provided which comprises values which characterize a course of the detected state of the technical system. Using a learning-based model for predicting the short-term behavior of the technical system, a first value for the prediction is determined as a function of the values of the time series, and, using a physical model for predicting the long-term behavior of the technical system, a second value for the prediction is determined as a function of the values of the time series, and wherein a value of the prediction is determined as a function of the first value for the prediction and the second value for the prediction.

Abstract: A device and computer-implemented method for predicting a state of a technical system. A state of the technical system is detected. A time series is provided which includes values which characterize a course of the detected state of the technical system. Using a first filter, first filtered values for predicting the short-term behavior of the technical system are determined as a function of the values of the time series. Using a second filter, second filtered values for predicting the long-term behavior of the technical system are determined as a function of the values of the time series. A first value for the prediction is determined as a function of the filtered first values. A second value for the prediction is determined as a function of the filtered second values. A value of the prediction is determined as a function of the first and second values for the prediction.

Abstract: A method for training a machine learning model. The method includes: determining a plurality of training sequences of training-input data elements, wherein for each training sequence each training-input data element contains sensor data for a time point from a time period assigned to the training sequence in which a prespecified event takes place at least once at one or more respective event time points; determining, for each training-input data element, the temporal distance between the time point for which the training-input data element contains sensor data and one of the one or more respective event time points; and training the machine learning model depending on the determined temporal distances.

Abstract: A method for generating additional training data for training a machine learning algorithm is disclosed. The method includes (i) providing training data for training the machine learning algorithm, wherein the training data includes labeled sensor data from at least one sensor, (ii) transforming the training data for training the machine learning algorithm in a graph structure, wherein nodes in the graph structure represent objects represented in the corresponding sensor data, and wherein a starting node of the graph structure represents the position of the at least one sensor with respect to the objects represented in the corresponding sensor data, and (iii) generating additional training data for training the machine learning model by modifying the graph structure.

Abstract: A computer-implemented method of training a model for making time-series predictions of a computer-controlled system. The model uses a stochastic differential equation (SDE) comprising a drift component and a diffusion component. The drift component has a predefined part representing domain knowledge, that is received as an input to the training; and a trainable part. When training the model, values of the set of SDE variables at a current time point are predicted based on their values at a previous time point, and based on this, the model is refined. In order to predict the values of the set of SDE variables, the predefined part of the drift component is evaluated to get a first drift, and the first drift is combined with a second drift obtained by evaluating the trainable part of the drift component.

Abstract: A method for training a deep-learning-based machine learning algorithm. The method includes: providing training data for training the deep-learning-based machine learning algorithm, wherein the training data comprise sensor data; training, by a machine learning method, the deep-learning-based machine learning algorithm based on the training data; and subsequently optimizing at least one parameter of the trained deep-learning-based machine learning algorithm based on a non-differentiable cost function.

Abstract: A computer-implemented method for predicting a behavior of agents in a dynamic system with a multiplicity of interacting agents depending on the latent state thereof. For a plurality of components and for a plurality of time points up to a prediction time point, a value of a first moment of a first distribution, which models the latent state of the agents, is determined for each component. A value of a second moment of the first distribution is determined. An expected value for a first moment of a second distribution at the prediction time point is determined for each component depending on the value of the first moment of the first distribution at the prediction time point and depending on the value of the second moment of the first distribution at the prediction time point. The second distribution models the behavior of the agents depending on the latent state thereof.

Abstract: Active learning for operating a physical system. The method includes: providing a data set that comprises data points each comprising an input for operating the physical system, and a first and second observation of the physical system; training a multi-output Gaussian process for predicting the first observation for a given input with the data set; training a Gaussian process for predicting the second observation for a given input with the data set; determining with the data set an input for operating the physical system; determining the first and second observations that result from operating the physical system with the determined input; and adding a data point to the data set that comprises the determined input and the determined first and second observations.