Non-linearities in Gaussian processes with integral observations

Gaussian processes (GP) can be used for inferring latent continuous functions also based on aggregate observations corresponding to integrals of the function, for example to learn daily rate of new infections in a population based on cumulative observations collected only weekly. We extend these approaches to cases where the observations correspond to aggregates of arbitrary non-linear transformations of a GP. Such models are needed, for example, when the latent function of interest is known to be non-negative or bounded. We present a solution based on Markov chain Monte Carlo with numerical integration for aggregation, and demonstrate it in binned Poisson regression and in non-invasive detection of fouling using ultrasound waves.Peer reviewe

Ultrasonic Fouling Detector Powered by Machine Learning

Guided waves can be used to monitor structural health in industrial pipelines, and e.g. allow detection of accumulated precipitation on the surface of pipe. Propagation of guided waves in a tubular structure carrying possible fouling can be separated from a clean structure due to variation in wave propagation properties at the fouled area. In addition, multiple propagation paths around the tubular structure allow locating the fouled areas. In this study, we obtained dispersion curves of a tubular structure loaded with a local fouling layer of different thickness by using numerical simulations. We combined the dispersion curve information with simulated and measured times-of-arrival of guided wave propagation to second order helicoidal paths and used a Gaussian Process machine learning approach to estimate location of fouling on a steel pipe.Peer reviewe

Localizing a target inside an enclosed cylinder with a single chaotic cavity transducer augmented with supervised machine learning

Ultrasound is employed in, e.g., non-destructive testing and environmental sensing. Unfortunately, conventional single-element ultrasound probes have a limited acoustic aperture. To overcome this limitation, we employ a modern method to increase the field-of-view of a commercial transducer and to test the approach by localizing a target. In practice, we merge the transducer with a chaotic cavity to increase the effective aperture of the transducer. In conventional pulse-echo ultrasound signal analysis, location estimation is based on determining the time-of-flight with known propagation speed in the medium. In the present case, the dispersing field induces complexity to this inverse problem, also in 2D. To tackle this issue, we use a convolutional neural network-based machine learning approach to study the feasibility of employing one single chaotic cavity transducer to localize an object in 2D. We show that we indeed can localize an inclusion inside a water-filled cylinder. The localization accuracy is one diameter of the inclusion. The area that we can infer increases by 49% in comparison to using the same transducer without applying the proposed chaotic cavity method. (C) 2021 Author(s).Peer reviewe

Traversing Time with Multi-Resolution Gaussian Process State-Space Models

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic differential equations, but inference for long sequences with fast and slow transitions is difficult. Fast transitions need tight discretizations whereas slow transitions require backpropagating the gradients over long subtrajectories. We propose a novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution, to model effects on different timescales. The combined model allows traversing time on adaptive scales, providing efficient inference for arbitrarily long sequences with complex dynamics. We benchmark our novel method on semi-synthetic data and on an engine modeling task. In both experiments, our approach compares favorably against its state-of-the-art alternatives that operate on a single time-scale only.Peer reviewe

Sensor Placement for Spatial Gaussian Processes with Integral Observations

Gaussian processes (GP) are a natural tool for estimating unknown functions, typically based on a collection of point-wise observations. Interestingly, the GP formalism can be used also with observations that are integrals of the unknown function along some known trajectories, which makes GPs a promising technique for inverse problems in a wide range of physical sensing problems. However, in many real world applications collecting data is laborious and time consuming. We provide tools for optimizing sensor locations for GPs using integral observations, extending both model-based and geometric strategies for GP sensor placement. We demonstrate the techniques in ultrasonic detection of fouling in closed pipes.Peer reviewe