相关论文: "Proper" Shift Rules for Derivatives of Perturbed-…

A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…

In many computer vision classification tasks, class priors at test time often differ from priors on the training set. In the case of such prior shift, classifiers must be adapted correspondingly to maintain close to optimal performance.…

Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…

We address optimal control of semilinear evolution equations on Banach spaces with finitely many control channels, a framework encompassing a broad class of infinite-dimensional dynamical systems, arising in many applications. For this…

We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global…

In this paper, we develop reliable a posteriori error estimates for numerical approximations of scalar hyperbolic conservation laws in one space dimension. Our methods have no inherent small-data limitations and are a step towards error…

Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully…

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…

Accurate calculation of switching events is important for electromagnetic transient simulation to obtain reliable results. The common presumption of continuous differential state variables could prevent the accurate calculation, thus…

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision,…

In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the…

We introduce a new quantum noise deconvolution technique that does not rely on the complete knowledge of noise and does not require partial noise tomography. In this new method, we construct a set of observables with completely correctable…

In statistical mechanics, evaluating finite-size macroscopic fluctuations typically relies on Edgeworth expansions. However, these perturbative methods append additive polynomial corrections that inevitably break down in the large deviation…

An inherent challenge in computing fully-explicit generalization bounds for transformers involves obtaining covering number estimates for the given transformer class $T$. Crude estimates rely on a uniform upper bound on the local-Lipschitz…

We study the problem of estimating the value function of discrete-time switched systems under arbitrary switching. Unlike the switched LQR problem, where both inputs and mode sequences are optimized, we consider the case where switching is…

The theory of optimal quantum control serves to identify time-dependent control Hamiltonians that efficiently produce desired target states. As such, it plays an essential role in the successful design and development of quantum…

In a ubiquitous $SU(2)$ dynamics, achieving the simultaneous optimal estimation of multiple parameters is significant but difficult. Using quantum control to optimize this $SU(2)$ coding unitary evolution is one of solutions. We propose a…

Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are…

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…

Trajectory prediction models that can infer both finite future trajectories and their associated uncertainties of the target vehicles in an online setting (e.g., real-world application scenarios) is crucial for ensuring the safe and robust…