Related papers: Variationally consistent Hamiltonian model reducti…

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model…

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

We build upon recent work on using Machine Learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning where the…

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…

Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…

In this technical note, we introduce a novel approach to studying consensus of continuous-time nonlinear systems with varying topology based on Hilbert metric. We demonstrate that this metric offers significant flexibility in analyzing…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…

Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…

We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…

A perturbative approach is used to quantify the effect of noise in data points on fitted parameters in a general homogeneous linear model, and the results applied to the case of conic sections. There is an optimal choice of normalisation…

We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…

We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…

Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…

In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically…

A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…

The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…

In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…