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This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems.…
In this paper, we present a robust and adaptive model predictive control (MPC) framework for uncertain nonlinear systems affected by bounded disturbances and unmodeled nonlinearities. We use Gaussian Processes (GPs) to learn the uncertain…
Falsification is the basis for testing existing hypotheses, and a great danger is posed when results incorrectly reject our prior notions (false positives). Though nonparametric and nonlinear exploratory methods of uncovering coupling…
One of the key challenges that Reinforcement Learning (RL) faces is its limited capability to adapt to a change of data distribution caused by uncertainties. This challenge arises especially in RL systems using deep neural networks as…
Computational models providing accurate estimates of their uncertainty are crucial for risk management associated with decision making in healthcare contexts. This is especially true since many state-of-the-art systems are trained using the…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of a domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
The recently proposed non-iterative load flow method, called the holomorphic embedding method, may encounter the precision issue, i.e. nontrivial round-off errors caused by the limit of digits used in computation when calculating the…
We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real…
Deep learning offers promising new ways to accurately model aleatoric uncertainty in robotic state estimation systems, particularly when the uncertainty distributions do not conform to traditional assumptions of being fixed and Gaussian. In…
We investigate the use of data-driven likelihoods to bypass a key assumption made in many scientific analyses, which is that the true likelihood of the data is Gaussian. In particular, we suggest using the optimization targets of flow-based…
Accurate path following is challenging for autonomous robots operating in uncertain environments. Adaptive and predictive control strategies are crucial for a nonlinear robotic system to achieve high-performance path following control. In…
Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…
Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
This is the second part of a two-part paper on data-based distributionally robust stochastic optimal power flow (OPF). The general problem formulation and methodology have been presented in Part I [1]. Here, we present extensive numerical…