Related papers: Finite-sample guarantees for data-driven forward-b…
The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to a sequential testing procedure (STP) that…
This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration two implicit-explicit second order backward differentiation…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…
We introduce a simulation-free method to estimate the fidelity of large quantum circuits based on the order statistics of measured output probabilities from highly entangled, chaotic states. The approach requires only the…
We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and let \(R(p)\) be the finite-dimensional quantity to be…
We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general…
We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…
This paper addresses learning safe output feedback control laws from partial observations of expert demonstrations. We assume that a model of the system dynamics and a state estimator are available along with corresponding error bounds,…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
In this paper, we describe a novel approach for checking safety specifications of a dynamical system with exogenous inputs over infinite time horizon that is guaranteed to terminate in finite time with a conclusive answer. We introduce the…
In this paper, we study a safe control design for dynamical systems in the presence of uncertainty in a dynamical environment. The worst-case error approach is considered to formulate robust Control Barrier Functions (CBFs) in an…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
In threshold-based anomaly detection, we want to tune the threshold of a detector to achieve an acceptable false alarm rate. However, tuning the threshold is often a non-trivial task due to unknown detector output distributions. A detector…
Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
Forward reachability analysis is a dominant approach for verifying reach-avoid specifications in neural feedback systems, i.e., dynamical systems controlled by neural networks, and a number of directions have been proposed and studied. In…
We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence…
When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the…
Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…