Related papers: Improving the predictive power of empirical shell-…

We construct valence-space Hamiltonians for use in shell-model calculations, where the residual two-body interaction is based on symmetry principles and the low-momentum expansion from chiral effective field theory. In addition to the usual…

We present a machine-learning method for predicting sharp transitions in a Hamiltonian phase diagram by extrapolating the properties of quantum systems. The method is based on Gaussian Process regression with a combination of kernels chosen…

Experimental calibration of dynamic thermal models is required for model predictive control and characterization of building energy performance. In these applications, the uncertainty assessment of the parameter estimates is decisive; this…

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively…

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…

This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…

This work proposes a novel approach for non-deterministic extension of experimental data that considers structural model inadequacy for conditions other than the calibration scenario while simultaneously resolving any significant prior-data…

Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…

Improving the accuracy of forecast models for physical systems such as the atmosphere is a crucial ongoing effort. Errors in state estimation for these often highly nonlinear systems has been the primary focus of recent research, but as…

External controls from historical trials or observational data can augment randomized controlled trials when large-scale randomization is impractical or unethical, such as in drug evaluation for rare diseases. However, non-randomized…

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…

Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…

Recent advances in machine learning, specifically transformer architecture, have led to significant advancements in commercial domains. These powerful models have demonstrated superior capability to learn complex relationships and often…

Forecasts in cosmology, both with Monte-Carlo Markov-chain methods and with the Fisher matrix formalism, depend on the choice of the fiducial model because both the signal strength of any observable as well as the model nonlinearities…

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…

A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the…