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A two-stage batch estimation algorithm for solving a class of nonlinear, static parameter estimation problems that appear in aerospace engineering applications is proposed. It is shown how these problems can be recast into a form suitable…
Backward error initialization and parasitic mode control are well-suited for use in algorithms that arise from a discrete variational principle on phase-space dynamics. Dynamical systems described by degenerate Lagrangians, such as those…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
We discuss two ways in which parton shower algorithms can be supplemented by matrix-element corrections to ensure the correct hard limit: by using complementary phase-space regions, or by modifying the shower itself. In the former case,…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in…
We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…
We have investigated instability of a superconducting quantum computer by continuously monitoring the qubit output. We found that qubits exhibit a step-like change in the error rates. This change is repeatedly observed, and each step…
Stochastic optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. Although various algorithms have been extensively studied for AUPRC optimization, the generalization is only guaranteed…
Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
This work considers the optimal covariance steering problem for systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as a…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
We discuss some issues arising in the evaluation of confidence intervals in the presence of nuisance parameters (systematic uncertainties) by means of direct Neyman construction in multi-dimensional space. While this kind of procedure…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard…