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We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

By preparing a sensor system around isolated exceptional points, one can obtain a great enhancement of the sensitivity benefiting from the non-Hermiticity. However, this comes at the cost of reduction of the flexibility of the system, which…

Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

Data-driven emulators are increasingly being used to learn and emulate physics-based simulations, reducing computational expense and run time. Here, we present a structured way to improve the quality of these high-dimensional emulated…

We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, towards efficient quantum computing of molecular electronic structure calculations.…

A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. Specifically, spectral and topological data is used to build an appropriate discrete model that accurately replicates these…

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…

Reconstructing Hamiltonians from local measurements is key to enabling reliable quantum simulation: both validating the implemented model, and identifying any left-over terms with sufficient precision is a problem of increasing importance.…

We show that it is possible to initialize and manipulate in a deterministic manner protected qubits using time varying Hamiltonians. Taking advantage of the symmetries of the system, we predict the effect of the noise during the…

The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…

The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one…

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…

In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…

As Machine Learning (ML) is now widely applied in many domains, in both research and industry, an understanding of what is happening inside the black box is becoming a growing demand, especially by non-experts of these models. Several…

We revisit an algorithm by Skeel et al. for computing the modified, or shadow, energy associated with the symplectic discretization of Hamiltonian systems. By rephrasing the algorithm as a Richardson extrapolation scheme arbitrary high…

In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…

We develop an efficient and robust approach to Hamiltonian identification for multipartite quantum systems based on the method of compressed sensing. This work demonstrates that with only O(s log(d)) experimental configurations, consisting…

Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a…