Related papers: Structure-preserving Method for Reconstructing Unk…
Techniques based on randomized response enable the collection of potentially sensitive data from clients in a privacy-preserving manner with strong local differential privacy guarantees. One of the latest such technologies, RAPPOR, allows…
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern…
This paper deals with developing tests for checking whether an unknown system has certain structural properties. The tests that we are aiming at are in terms of noisy input-state-output data obtained from the unknown system. Since, in…
Learning the unknown Hamiltonian governing the dynamics of a quantum many-body system is a challenging task. In this manuscript, we propose a possible strategy based on repeated measurements on a single time-dependent state. We prove that…
One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard.…
We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…
Identifying unknown Hamiltonians from their quantum dynamics is a pivotal challenge in quantum technologies. In this paper, we introduce Hamiltonian recognition, a framework that bridges quantum hypothesis testing and quantum metrology,…
Given a structured matrix $A$ we study the problem of finding the closest normal matrix with the same structure. The structures of our interest are: Hamiltonian, skew-Hamiltonian, per-Hermitian, and perskew-Hermitian. We develop a…
A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification problem for these…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their…
In this paper, we present a new methodology to develop arbitrary high-order structure-preserving methods for solving the quantum Zakharov system. The key ingredients of our method are: (i) the original Hamiltonian energy is reformulated…
Imaging Inverse problems aim to reconstruct an underlying image from undersampled, coded, and noisy observations. Within the wide range of reconstruction frameworks, the unrolling algorithm is one of the most popular due to the synergistic…
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…
In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…