arXiv subjects

Oliver Schön

Publications and source records attributed to Oliver Schön.

14 recordsLinked to original sources

arXiv2026

Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning

The reliability of autonomous systems depends on their robustness, i.e., their ability to meet their objectives under uncertainty. In this paper, we study spatiotemporal robustness of temporal logic specifications evaluated over discrete-time signals. Existing work has proposed robust semantics that capture not only Boolean satisfiability, but also the geometric distance from unsatisfiability, corresponding to admissible spatial perturbations of a given signal. In contrast, we propose spatiotemporal robustness (STR), which captures admissible spatial and temporal perturbations jointly. This notion is particularly informative for interacting systems, such as multi-agent robotics, smart cities, and air traffic control. We define STR as a multi-objective reasoning problem, formalized via a partial order over spatial and temporal perturbations. This perspective has two key advantages: (1) STR can be interpreted as a Pareto-optimal set that characterizes all admissible spatiotemporal perturbations, and (2) STR can be computed using tools from multi-objective optimization. To navigate computational challenges, we propose robust semantics for STR that are sound in the sense of suitably under-approximating STR while being computationally tractable. Finally, we present monitoring algorithms for STR using these robust semantics. To the best of our knowledge, this is the first work to deal with robustness across multiple dimensions via multi-objective reasoning.

cs.AI↗

arXiv2026

Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations

We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being \emph{reusable}: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the \emph{semantic basis}, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a \emph{rolling prediction monitor} that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.

cs.LG↗

arXiv2026

Safety Certification is Classification

The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons $T$. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the $T$-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.

cs.AI↗

arXiv2026

Kernel-Based Learning of Safety Barriers

The rapid integration of AI algorithms in safety-critical applications such as autonomous driving and healthcare is raising significant concerns about the ability to meet stringent safety standards. Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems and lack the flexibility needed to scale to the complexity of real-world applications. In this paper, we present a data-driven approach for safety verification and synthesis of black-box systems with discrete-time stochastic dynamics. We employ the concept of control barrier certificates, which can guarantee safety of the system, and learn the certificate directly from a set of system trajectories. We use conditional mean embeddings to embed data from the system into a reproducing kernel Hilbert space (RKHS) and construct an RKHS ambiguity set that can be inflated to robustify the result to out-of-distribution behavior. We provide the theoretical results on how to apply the approach to general classes of temporal logic specifications beyond safety. For the data-driven computation of safety barriers, we leverage a finite Fourier expansion to cast a typically intractable semi-infinite optimization problem as a linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. Our work moves beyond restrictive assumptions on system dynamics and uncertainty, as demonstrated on two case studies including a black-box system with a neural network controller.

cs.AI↗

arXiv2025

LUCID: Learning-Enabled Uncertainty-Aware Certification of Stochastic Dynamical Systems

Ensuring the safety of AI-enabled systems, particularly in high-stakes domains such as autonomous driving and healthcare, has become increasingly critical. Traditional formal verification tools fall short when faced with systems that embed both opaque, black-box AI components and complex stochastic dynamics. To address these challenges, we introduce LUCID (Learning-enabled Uncertainty-aware Certification of stochastIc Dynamical systems), a verification engine for certifying safety of black-box stochastic dynamical systems from a finite dataset of random state transitions. As such, LUCID is the first known tool capable of establishing quantified safety guarantees for such systems. Thanks to its modular architecture and extensive documentation, LUCID is designed for easy extensibility. LUCID employs a data-driven methodology rooted in control barrier certificates, which are learned directly from system transition data, to ensure formal safety guarantees. We use conditional mean embeddings to embed data into a reproducing kernel Hilbert space (RKHS), where an RKHS ambiguity set is constructed that can be inflated to robustify the result to out-of-distribution behavior. A key innovation within LUCID is its use of a finite Fourier kernel expansion to reformulate a semi-infinite non-convex optimization problem into a tractable linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. LUCID thus offers a robust and efficient verification framework, able to handle the complexities of modern black-box systems while providing formal guarantees of safety. These unique capabilities are demonstrated on challenging benchmarks.

eess.SY↗

arXiv2025

Formal Control for Uncertain Systems via Contract-Based Probabilistic Surrogates (Extended Version)

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making with formal correctness and performance guarantees. Focusing on probabilistic simulation relations and surrogate models of stochastic systems, we propose an approach that significantly enhances the scalability and practical applicability of such simulation relations by eliminating the need to compute error bounds directly. As a result, we provide an abstraction-based technique that scales effectively to higher dimensions while addressing complex nonlinear agent-environment interactions with infinite-horizon temporal logic guarantees amidst uncertainty. Our approach trades scalability for conservatism favorably, as demonstrated on a complex high-dimensional vehicle intersection case study.

eess.SY↗

arXiv2024

Data-Driven Abstractions via Binary-Tree Gaussian Processes for Formal Verification

To advance formal verification of stochastic systems against temporal logic requirements for handling unknown dynamics, researchers have been designing data-driven approaches inspired by breakthroughs in the underlying machine learning techniques. As one promising research direction, abstraction-based solutions based on Gaussian process (GP) regression have become popular for their ability to learn a representation of the latent system from data with a quantified error. Results obtained based on this model are then translated to the true system via various methods. In a recent publication, GPs using a so-called binary-tree kernel have demonstrated a polynomial speedup w.r.t. the size of the data compared to their vanilla version, outcompeting all existing sparse GP approximations. Incidentally, the resulting binary-tree Gaussian process (BTGP) is characteristic for its piecewise-constant posterior mean and covariance functions, naturally abstracting the input space into discrete partitions. In this paper, we leverage this natural abstraction of the BTGP for formal verification, eliminating the need for cumbersome abstraction and error quantification procedures. We show that the BTGP allows us to construct an interval Markov chain model of the unknown system with a speedup that is polynomial w.r.t. the size of the abstraction compared to alternative approaches. We provide a delocalized error quantification via a unified formula even when the true dynamics do not live in the function space of the BTGP. This allows us to compute upper and lower bounds on the probability of satisfying reachability specifications that are robust to both aleatoric and epistemic uncertainties.

cs.LO↗

arXiv2024

Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings

Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on exact models of the underlying systems. Since this assumption can rarely be met in practice, models have to be inferred from measurement data or are bypassed completely. Whilst former usually requires the model structure to be known a-priori and immense amounts of data to be available, latter gives rise to a plethora of restrictive mathematical assumptions about the unknown dynamics. In a pursuit of developing scalable formal verification algorithms without shifting the problem to unrealistic assumptions, we employ the concept of barrier certificates, which can guarantee safety of the system, and learn the certificate directly from a compact set of system trajectories. We use conditional mean embeddings to embed data from the system into a reproducing kernel Hilbert space (RKHS) and construct an RKHS ambiguity set that can be inflated to robustify the result w.r.t. a set of plausible transition kernels. We show how to solve the resulting program efficiently using sum-of-squares optimization and a Gaussian process envelope. Our approach lifts the need for restrictive assumptions on the system dynamics and uncertainty, and suggests an improvement in the sample complexity of verifying the safety of a system on a tested case study compared to a state-of-the-art approach.

eess.SY↗

arXiv2024

Bayesian Formal Synthesis of Unknown Systems via Robust Simulation Relations

This paper addresses the problem of data-driven computation of controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. With a focus on continuous-space stochastic systems with parametric uncertainty, we propose a two-stage approach that decomposes the problem into a learning stage and a robust formal controller synthesis stage. The first stage utilizes available Bayesian regression results to compute robust credible sets for the true parameters of the system. For the second stage, we introduce methods for systems subject to both stochastic and parametric uncertainties. We provide simulation relations for enabling correct-by-design control refinement that are founded on coupling uncertainties of stochastic systems via sub-probability measures. The presented relations are essential for constructing abstract models that are related to not only one model but to a set of parameterized models. The results are demonstrated on three case studies, including a nonlinear and a high-dimensional system.

eess.SY↗

arXiv2023

Verifying the Unknown: Correct-by-Design Control Synthesis for Networks of Stochastic Uncertain Systems

In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems with additive stochastic noise and model parametric uncertainty. Such settings arise when multiple systems interact in an uncertain environment and only observational data is available. We address two limitations of existing approaches for formal synthesis of controllers for networks of uncertain systems satisfying complex temporal specifications. Firstly, whilst existing approaches rely on the stochasticity to be Gaussian, the heterogeneous nature of composed systems typically yields a more complex stochastic behavior. Secondly, exact models of the systems involved are generally not available or difficult to acquire. To address these challenges, we show how abstraction-based control synthesis for uncertain systems based on sub-probability couplings can be extended to networked systems. We design controllers based on parameter uncertainty sets identified from observational data and approximate possibly arbitrary noise distributions using Gaussian mixture models whilst quantifying the incurred stochastic coupling. Finally, we demonstrate the effectiveness of our approach on a nonlinear package delivery case study with a complex specification, and a platoon of cars.

eess.SY↗

arXiv2023

SySCoRe: Synthesis via Stochastic Coupling Relations

We present SySCoRe, a MATLAB toolbox that synthesizes controllers for stochastic continuous-state systems to satisfy temporal logic specifications. Starting from a system description and a co-safe temporal logic specification, SySCoRe provides all necessary functions for synthesizing a robust controller and quantifying the associated formal robustness guarantees. It distinguishes itself from other available tools by supporting nonlinear dynamics, complex co-safe temporal logic specifications over infinite horizons and model-order reduction. To achieve this, SySCoRe generates a finite-state abstraction of the provided model and performs probabilistic model checking. Then, it establishes a probabilistic coupling to the original stochastic system encoded in an approximate simulation relation, based on which a lower bound on the satisfaction probability is computed. SySCoRe provides non-trivial lower bounds for infinite-horizon properties and unbounded disturbances since its computed error does not grow linearly in the horizon of the specification. It exploits a tensor representation to facilitate the efficient computation of transition probabilities. We showcase these features on several benchmarks and compare the performance of the tool with existing tools.

eess.SY↗

arXiv2022

Correct-by-Design Control of Parametric Stochastic Systems

This paper addresses the problem of computing controllers that are correct by design for safety-critical systems and can provably satisfy (complex) functional requirements. We develop new methods for models of systems subject to both stochastic and parametric uncertainties. We provide for the first time novel simulation relations for enabling correct-by-design control refinement, that are founded on coupling uncertainties of stochastic systems via sub-probability measures. Such new relations are essential for constructing abstract models that are related to not only one model but to a set of parameterized models. We provide theoretical results for establishing this new class of relations and the associated closeness guarantees for both linear and nonlinear parametric systems with additive Gaussian uncertainty. The results are demonstrated on a linear model and the nonlinear model of the Van der Pol Oscillator.

eess.SY↗

arXiv2022

Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose a physics-guided hybrid approach for modeling non-autonomous systems under control. Starting from a traditional physics-based model, this is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy yielding physically plausible models. While purely data-driven methods fail to produce satisfying results, experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model.

eess.SY↗

arXiv2022

Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order

In the present paper we take a step towards the generalization of the post-Newtonian formalism to tensor-multi-scalar theories. These are theories where we have more than one scalar field being mediators of the gravitational interaction in addition to the spacetime metric. They are very natural extensions of Einstein's gravity allowing for the existence of new classes of compact objects and offering interesting phenomenology reaching far beyond the single scalar field theories. We calculate the expansion up to 2.5 post-Newtonian order in the near zone using the so-called direct integration of the relaxed Einstein equations formalism and derive the equation of motion. This work is the first step towards the calculation of gravitational waveforms in tensor-multi-scalar theories.

gr-qc↗