Antti Solonen

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.

Alessio Spantini, Antti Solonen, Tiangang Cui et al.

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to characterize and approximate the posterior distribution of the parameters. We first investigate approximation of the posterior covariance matrix as a low-rank update of the prior covariance matrix. We prove optimality of a particular update, based on the leading eigendirections of the matrix pencil defined by the Hessian of the negative log-likelihood and the prior precision, for a broad class of loss functions. This class includes the Förstner metric for symmetric positive definite matrices, as well as the Kullback-Leibler divergence and the Hellinger distance between the associated distributions. We also propose two fast approximations of the posterior mean and prove their optimality with respect to a weighted Bayes risk under squared-error loss. These approximations are deployed in an offline-online manner, where a more costly but data-independent offline calculation is followed by fast online evaluations. As a result, these approximations are particularly useful when repeated posterior mean evaluations are required for multiple data sets. We demonstrate our theoretical results with several numerical examples, including high-dimensional X-ray tomography and an inverse heat conduction problem. In both of these examples, the intrinsic low-dimensional structure of the inference problem can be exploited while producing results that are essentially indistinguishable from solutions computed in the full space.