Related papers: Formal Verification of Unknown Dynamical Systems v…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…
A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…
We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized…
This paper is concerned with a data-driven technique for constructing finite Markov decision processes (MDPs) as finite abstractions of discrete-time stochastic control systems with unknown dynamics while providing formal closeness…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…
Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often…
Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…
This paper presents a unified framework for uncertainty propagation in dynamical systems involving hybrid aleatory and epistemic uncertainties. The framework accommodates precise probabilistic, imprecise probabilistic, and non-probabilistic…
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…
This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse…
Switching physical systems are ubiquitous in modern control applications, for instance, locomotion behavior of robots and animals, power converters with switches and diodes. The dynamics and switching conditions are often hard to obtain or…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
Markov decision processes (MDPs) are formal models commonly used in sequential decision-making. MDPs capture the stochasticity that may arise, for instance, from imprecise actuators via probabilities in the transition function. However, in…
In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent…
Controlling stochastic systems with unknown dynamics and under complex specifications is specially challenging in safety-critical settings, where performance guarantees are essential. We propose a data-driven policy synthesis framework that…
We present a data-driven approach for producing policies that are provably robust across unknown stochastic environments. Existing approaches can learn models of a single environment as an interval Markov decision processes (IMDP) and…
We present a novel method for accurately auditing the differential privacy (DP) guarantees of DP mechanisms. In particular, our solution is applicable to auditing DP guarantees of machine learning (ML) models. Previous auditing methods…