The present disclosure relates to a computer-implemented method for object tracking, the method including the steps of defining a state-space of interest based on a class of objects subject to tracking. Further, the method includes the step of representing the state-space of interest using a FEM representation partitioning the state-space of interest in elements. Further, the method includes initiating a state-space distribution defining a probability density for different states of at least one tracked object in the state-space of interest. Moreover, the method updates the state-space distribution based on evidence, wherein the evidence being at least one of sensor data and external data of at least one tracked object in said class of objects. Furthermore, the method propagates the state-space distribution of the at least one tracked object for a time period.

A system and method for evaluating a subterranean earth formation as well as a method of steering a drill bit in a subterranean earth formation. The system comprises a logging tool that is operable to measure formation data and locatable in a wellbore intersecting the subterranean earth formation. The system also comprises a processor that is in communication with the logging tool. The processor is operable to calculate multiple distance-to-bed-boundary (DTBB) solutions using the measured formation data, identify DTBB solutions that satisfy a threshold, convert the identified solutions into pixelated solutions by dividing the identified solutions into pixels, generate a formation model based on the pixelated solutions, and evaluate the formation using the generated formation model.

A system and method for evaluating a subterranean earth formation as well as a method of steering a drill bit in a subterranean earth formation. The system comprises a logging tool that is operable to measure formation data and locatable in a wellbore intersecting the subterranean earth formation. The system also comprises a processor that is in communication with the logging tool. The processor is operable to calculate multiple distance-to-bed-boundary (DTBB) solutions using the measured formation data, identify DTBB solutions that satisfy a threshold, convert the identified solutions into pixelated solutions by dividing the identified solutions into pixels, generate a formation model based on the pixelated solutions, and evaluate the formation using the generated formation model.

Embodiments determine anomalies in sensor data generated by a sensor by receiving an evaluation time window of clean sensor data generated by the sensor. Embodiments receive a threshold value for determining anomalies. When the clean sensor data has a cyclic pattern, embodiments divide the evaluation time window into a plurality of segments of equal length, wherein each equal length comprises the cyclic pattern. When the clean sensor data does not have the cyclic pattern, embodiments divide the evaluation time window into a pre-defined number of plurality of segments of equal length. Embodiments convert the evaluation time window and each of the plurality of segments into corresponding curves using Kernel Density Estimation (“KDE”). For each of the plurality of segments, embodiments determine a Kullback-Leibler (“KL”) divergence value between corresponding curves of the segment and the evaluation time window to generate a plurality of KL divergence values.

Embodiments determine anomalies in sensor data generated by a sensor by receiving an evaluation time window of clean sensor data generated by the sensor. Embodiments receive a threshold value for determining anomalies. When the clean sensor data has a cyclic pattern, embodiments divide the evaluation time window into a plurality of segments of equal length, wherein each equal length comprises the cyclic pattern. When the clean sensor data does not have the cyclic pattern, embodiments divide the evaluation time window into a pre-defined number of plurality of segments of equal length. Embodiments convert the evaluation time window and each of the plurality of segments into corresponding curves using Kernel Density Estimation (“KDE”). For each of the plurality of segments, embodiments determine a Kullback-Leibler (“KL”) divergence value between corresponding curves of the segment and the evaluation time window to generate a plurality of KL divergence values.

Provided is a technology that optimizes a variable being an optimization target at high speed. A variable optimization apparatus includes a variable update unit configured to, by assuming that w is a variable being an optimization target. G(w)(=G1(w)+G2(w)) is a cost function for optimizing the variable w, calculated by using input data. D is a strictly convex function that is differentiable and satisfies ∇D(0)=0. Ri and Ci are a D-resolvent operator and a D-Cayley operator, respectively and −Gi(w) is a strongly convex function approximating a function Gi(w), recursively calculate a value of the variable w by using the D-resolvent operator Ri and the D-Cayley operator Ci. When the variable update unit calculates ∇D(w), for a D-resolvent operator R1 and a D-Cayley operator C1, T1(w)=∇−G1(w)−∇−G1(0) is used for calculation of ∇D(w), and for a D-resolvent operator R2 and a D-Cayley operator C2, ∇T2(w)=∇−G2(w)−∇−G2(0) is used for calculation of ∇D(w).

Provided is a technology that optimizes a variable being an optimization target at high speed. A variable optimization apparatus includes a variable update unit configured to, by assuming that w is a variable being an optimization target. G(w)(=G1(w)+G2(w)) is a cost function for optimizing the variable w, calculated by using input data. D is a strictly convex function that is differentiable and satisfies ∇D(0)=0. Ri and Ci are a D-resolvent operator and a D-Cayley operator, respectively and −Gi(w) is a strongly convex function approximating a function Gi(w), recursively calculate a value of the variable w by using the D-resolvent operator Ri and the D-Cayley operator Ci. When the variable update unit calculates ∇D(w), for a D-resolvent operator R1 and a D-Cayley operator C1, T1(w)=∇−G1(w)−∇−G1(0) is used for calculation of ∇D(w), and for a D-resolvent operator R2 and a D-Cayley operator C2, ∇T2(w)=∇−G2(w)−∇−G2(0) is used for calculation of ∇D(w).

The disclosure relates to a computer-implemented method for performing a deformation-based physics simulation described by a partial differential equation. The method comprises providing a geometrical model representing a portion of the real world. The method comprises performing a hybrid discretization of the model. The performing of the hybrid discretization comprises discretizing one or more first objects in the portion each with a mesh and one or more second objects in the portion each with a point cloud. The method comprises one or more iterations. Each iteration comprises performing a simulation run based on a discretization of the partial differential equation and on the hybrid discretization. The iteration comprises assessing a deformation as a result of the simulation run. The deformation corresponds to a shape deformation of the one or more second objects. The iteration comprises updating the hybrid discretization to model the deformation by moving points of a point cloud.

The disclosure relates to a computer-implemented method for performing a deformation-based physics simulation described by a partial differential equation. The method comprises providing a geometrical model representing a portion of the real world. The method comprises performing a hybrid discretization of the model. The performing of the hybrid discretization comprises discretizing one or more first objects in the portion each with a mesh and one or more second objects in the portion each with a point cloud. The method comprises one or more iterations. Each iteration comprises performing a simulation run based on a discretization of the partial differential equation and on the hybrid discretization. The iteration comprises assessing a deformation as a result of the simulation run. The deformation corresponds to a shape deformation of the one or more second objects. The iteration comprises updating the hybrid discretization to model the deformation by moving points of a point cloud.

A system for machine learning architecture for time series data prediction. The system may be configured to: maintain a data set representing a neural network having a plurality of weights; obtain time series data associated with a data query; generate, using the neural network and based on the time series data, a predicted value based on a sampled realization of the time series data and a normalizing flow model, the normalizing flow model based on a latent continuous-time stochastic process having a stationary marginal distribution and bounded variance; and generate a signal providing an indication of the predicted value associated with the data query.