Oleksii Molodchyk

Johannes Teutsch, Oleksii Molodchyk, Marion Leibold et al.

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this work, we propose novel non-asymptotic probabilistic uniform error bounds for kernel-based regression. Compared to related bounds in the literature that are restricted to (conditionally) independent sub-Gaussian noise, our bounds allow to consider a broad class of non-Gaussian distributions, such as sub-Gaussian, bounded, sub-exponential, and variance/moment-bounded noise. Moreover, our results apply to correlated and uncorrelated noise. We compare our proposed error bounds with existing results in terms of the induced uncertainty region and their performance in safe control, demonstrating the tightness of the proposed bounds.

Oleksii Molodchyk, Omid Mokhtari, Samuel Chevalier et al.

Real-time control of distribution networks requires accurate information about the system state. In practice, however, such information is difficult to obtain because real-time measurements are available only at a limited number of locations. This paper proposes a novel data-driven power flow (DDPF) framework for balanced radial distribution networks. The proposed algorithm combines the behavioral approach with the DistFlow model and leverages offline historical data to solve power flow problems using only a limited set of real-time measurements. To design DDPF under sparse measurement conditions, we develop a sensor placement problem based on optimal network reductions. This allows us to determine sensor locations subject to a predefined sensor budget and to explicitly account for the radial nature of distribution networks. Unlike approaches that rely on full observability, the proposed framework is designed for practical distribution grids with sparse measurement availability. This enables data-driven power flow for real-time operation while reducing the number of required sensors. On several test cases, the proposed DDPF algorithm could demonstrate accurate voltage magnitude predictions, with a maximum error less than 0.001 p.u., with as little as 25% of total locations equipped with sensors.

Srimanta Santra, Oleksii Molodchyk, Matti Noack et al.

This paper studies the certification of a fixed candidate trajectory on a finite certification grid under parametric uncertainty. For each constraint-time pair, we define a scalar measure of constraint violation and aggregate the resulting pointwise chance constraints into a worst-case Value-at-Risk (VaR) margin. The goal is not to generate a new trajectory, but to assess online whether a trajectory produced by a planner or predictive controller is sufficiently safe on the certification grid. Direct evaluation requires repeated uncertainty propagation and is often too expensive for computationally demanding models. We therefore adopt an offline-online scheme: offline, a surrogate of the constraint violation map along the candidate trajectory is constructed using polynomial chaos expansion (PCE) when the uncertainty law is known, or kernel regression when only sampled input-output data are available; online, the surrogate is sampled to evaluate conservative VaR bounds at low computational cost. On the theoretical side, we derive a finite-sample upper bound for the grid-based VaR margin using empirical quantiles, the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality, and a union bound over all constraint-time pairs, without assuming a parametric family for the underlying violation distribution. We also show how a uniform surrogate error bound transfers to the certified VaR margin. The approach is illustrated on a crystallization population balance model, where the surrogate-based risk estimates track direct Monte Carlo results while substantially reducing online evaluation time.

Oleksii Molodchyk, Timm Faulwasser

Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.

Oleksii Molodchyk, Johannes Teutsch, Timm Faulwasser

Bayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic error bounds related to the uncertainty surrounding the surrogate model. For the case of Gaussian Process surrogates and Gaussian measurement noise, we present a novel error bound based on the recently proposed Wiener kernel regression. We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature, leading to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.