Lassi Roininen

Neil K. Chada, Marco A. Iglesias, Lassi Roininen et al.

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.

Victoria Jorry, Zina-Sabrina Duma, Tuomas Sihvonen et al.

In the domain of rotating machinery, bearings are vulnerable to different mechanical faults, including ball, inner, and outer race faults. Various techniques can be used in condition-based monitoring, from classical signal analysis to deep learning methods. Based on the complex working conditions of rotary machines, multivariate statistical process control charts such as Hotelling's $T^2$ and Squared Prediction Error are useful for providing early warnings. However, these methods are rarely applied to condition monitoring of rotating machinery due to the univariate nature of the datasets. In the present paper, we propose a multivariate statistical process control-based fault detection method that utilizes multivariate data composed of Fourier transform features extracted for fixed-time batches. Our approach makes use of the multidimensional nature of Fourier transform characteristics, which record more detailed information about the machine's status, in an effort to enhance early defect detection and diagnosis. Experiments with varying vibration measurement locations (Fan End, Drive End), fault types (ball, inner, and outer race faults), and motor loads (0-3 horsepower) are used to validate the suggested approach. The outcomes illustrate our method's effectiveness in fault detection and point to possible broader uses in industrial maintenance.

Teemu Härkönen, Sara Wade, Kody Law et al.

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance matrix. To circumvent this, mixtures of Gaussian process experts have been considered where data points are assigned to independent experts, reducing the complexity by allowing inference based on smaller, local covariance matrices. Moreover, mixtures of Gaussian process experts substantially enrich the model's flexibility, allowing for behaviors such as non-stationarity, heteroscedasticity, and discontinuities. In this work, we construct a novel inference approach based on nested sequential Monte Carlo samplers to simultaneously infer both the gating network and Gaussian process expert parameters. This greatly improves inference compared to importance sampling, particularly in settings when a stationary Gaussian process is inappropriate, while still being thoroughly parallelizable.

Emma Hannula, Jana de Wiljes, Matthew T. Moores et al.

Bayesian inference is a powerful tool for parameter estimation and uncertainty quantification in dynamical systems. However, for nonlinear oscillator networks such as Kuramoto models, widely used to study synchronization phenomena in physics, biology, and engineering, inference is often computationally prohibitive due to high-dimensional state spaces and intractable likelihood functions. We present an amortized Bayesian inference approach that learns a neural approximation of the posterior from simulated phase dynamics, enabling fast, scalable inference without repeated sampling or optimization. Applied to synthetic Kuramoto networks, the method shows promising results in approximating posterior distributions and capturing uncertainty, with computational savings compared to traditional Bayesian techniques. These findings suggest that amortized inference is a practical and flexible framework for uncertainty-aware analysis of oscillator networks.

Emma Hannula, Arttu Häkkinen, Antti Solonen et al.

Making the control of building heating systems more energy efficient is crucial for reducing global energy consumption and greenhouse gas emissions. Traditional rule-based control methods use a static, outdoor temperature-dependent heating curve to regulate heat input. This open-loop approach fails to account for both the current state of the system (indoor temperature) and free heat gains, such as solar radiation, often resulting in poor thermal comfort and overheating. Model Predictive Control (MPC) addresses these drawbacks by using predictive modeling to optimize heating based on a building's learned thermal behavior, current system state, and weather forecasts. However, current industrial MPC solutions often employ simplified physics-inspired indoor temperature models, sacrificing accuracy for robustness and interpretability. While purely data-driven models offer superior predictive performance and therefore more accurate control, they face challenges such as a lack of transparency. To bridge this gap, we propose a partially stochastic deep learning (DL) architecture, dubbed LSTM+BNN, for building-specific indoor temperature modeling. Unlike most studies that evaluate model performance through simulations or limited test buildings, our experiments across a comprehensive dataset of 100 real-world buildings, under various weather conditions, demonstrate that LSTM+BNN outperforms an industry-proven reference model, reducing the average prediction error measured as RMSE by more than 40% for the 48-hour prediction horizon of interest. Unlike deterministic DL approaches, LSTM+BNN offers a critical advantage by enabling pre-assessment of model competency for control optimization through uncertainty quantification. Thus, the proposed model shows significant potential to improve thermal comfort and energy efficiency achieved with heating MPC solutions.

Arttu Arjas, Lassi Roininen, Mikko J. Sillanpää et al.

Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the convolution kernel to recover an accurate reconstruction and additionally prior assumptions on the regularity of the signal are needed. To overcome these limitations, we parametrise the convolution kernel and prior length-scales, which are then jointly estimated in the inversion procedure. The proposed framework of blind hierarchical deconvolution enables accurate reconstructions of functions with varying regularity and unknown kernel size and can be solved efficiently with an empirical Bayes two-step procedure, where hyperparameters are first estimated by optimisation and other unknowns then by an analytical formula.