Rafael Wisniewski

Christoffer Sloth, Rafael Wisniewski

In this report proofs are presented for a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse-Smale systems and complete and refinable abstractions for linear systems are proved.

Deividas Eringis, John Leth, Zheng-Hua Tan et al.

In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. In particular, with the bound derived in this paper relates future average prediction errors with the prediction error generated by the model on the data used for learning. In turn, this allows us to provide finite-sample error bounds for a wide class of learning/system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

Christoffer Sloth, Rafael Wisniewski

This paper proposes a method for abstracting control systems by timed game automata, and is aimed at obtaining automatic controller synthesis. The proposed abstraction is based on partitioning the state space of a control system using positive and negative invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the control system is transversal to the facets of the cells, which induces some desirable properties of the abstraction. To allow a rich class of control systems to be abstracted, the update maps of the timed game automaton are extended. Conditions on the partitioning of the state space and the control are set up to obtain sound abstractions. Finally, an example is provided to demonstrate the method applied to a control problem related to navigation.

Keivan Faghih Niresi, Christian Møller Jensen, Carsten Skovmose Kallesøe et al.

Intelligent operation of thermal energy networks aims to improve energy efficiency, reliability, and operational flexibility through data-driven control, predictive optimization, and early fault detection. Achieving these goals relies on sufficient observability, requiring continuous and well-distributed monitoring of thermal and hydraulic states. However, district heating systems are typically sparsely instrumented and frequently affected by sensor faults, limiting monitoring. Virtual sensing offers a cost-effective means to enhance observability, yet its development and validation remain limited in practice. Existing data-driven methods generally assume dense synchronized data, while analytical models rely on simplified hydraulic and thermal assumptions that may not adequately capture the behavior of heterogeneous network topologies. Consequently, modeling the coupled nonlinear dependencies between pressure, flow, and temperature under realistic operating conditions remains challenging. In addition, the lack of publicly available benchmark datasets hinders systematic comparison of virtual sensing approaches. To address these challenges, we propose a heterogeneous spatial-temporal graph neural network (HSTGNN) for constructing virtual smart heat meters. The model incorporates the functional relationships inherent in district heating networks and employs dedicated branches to learn graph structures and temporal dynamics for flow, temperature, and pressure measurements, thereby enabling the joint modeling of cross-variable and spatial correlations. To support further research, we introduce a controlled laboratory dataset collected at the Aalborg Smart Water Infrastructure Laboratory, providing synchronized high-resolution measurements representative of real operating conditions. Extensive experiments demonstrate that the proposed approach significantly outperforms existing baselines.

Jaron Skovsted Gundersen, Bulut Kuskonmaz, Rafael Wisniewski

A common approach of system identification and machine learning is to generate a model by using training data to predict the test data instances as accurate as possible. Nonetheless, concerns about data privacy are increasingly raised, but not always addressed. We present a secure protocol for learning a linear model relying on recently described technique called real number secret sharing. We take as our starting point the PAC Bayesian bounds and deduce a closed form for the model parameters which depends on the data and the prior from the PAC Bayesian bounds. To obtain the model parameters one needs to solve a linear system. However, we consider the situation where several parties hold different data instances and they are not willing to give up the privacy of the data. Hence, we suggest to use real number secret sharing and multiparty computation to share the data and solve the linear regression in a secure way without violating the privacy of data. We suggest two methods; a secure inverse method and a secure Gaussian elimination method, and compare these methods at the end. The benefit of using secret sharing directly on real numbers is reflected in the simplicity of the protocols and the number of rounds needed. However, this comes with the drawback that a share might leak a small amount of information, but in our analysis we argue that the leakage is small.

Katrine Tjell, Rafael Wisniewski

Privacy preservation in distributed computations is an important subject as digitization and new technologies enable collection and storage of vast amounts of data, including private data belonging to individuals. To this end, there is a need for a privacy preserving computation framework that minimises the leak of private information during computations while being efficient enough for practical usage. This paper presents a step towards such a framework with the proposal of a real number secret sharing scheme that works directly on real numbers without the need for conversion to integers which is the case in related schemes. The scheme offers computations like addition, multiplication, and division to be performed directly on secret shared data (the cipher text version of the data). Simulations show that the scheme is much more efficient in terms of accuracy than its counterpart version based on integers and finite field arithmetic. The drawback with the proposed scheme is that it is not perfectly secure. However, we provide a privacy analysis of the scheme, where we show that the leaked information can be upper bounded and asymptotically goes to zero. To demonstrate the scheme, we use it to perform Kalman filtering directly on secret shared data.

Katrine Tjell, Jaron Skovsted Gundersen, Rafael Wisniewski

This work is inspired by the outbreak of COVID-19, and some of the challenges we have observed with gathering data about the disease. To this end, we aim to help collect data about citizens and the disease without risking the privacy of individuals. Specifically, we focus on how to determine the density of the population across the country, how to trace contact between citizens, how to determine the location of infections, and how to determine the timeline of the spread of the disease. Our proposed methods are privacy-preserving and rely on an app to be voluntarily installed on citizens' smartphones. Thus, any individual can choose not to participate. However, the accurateness of the methods relies on the participation of a large percentage of the population.