Related papers: Structural Preprocessing Method for Nonlinear Diff…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…
In this paper, we propose a globally convergent Newton type method to solve $\ell_0$ regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…
Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many efficient algorithms have been proposed. First order methods are…
With the recent proliferation of open-source packages for computing, power system differential-algebraic equation (DAE) modeling and simulation are being revisited to reduce the programming efforts. Existing open-source tools require manual…
We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph $G=(V, E)$ with edge weights in $\{1, 2, \dots, M\}$, we need to preprocess it into a data structure, and answer the following queries: given…
Solutions to differential equations, which are used to model physical systems, are computed numerically by solving a set of discretized equations. This set of discretized equations is reduced to a large linear system, whose solution is…
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of algebraic problems often results in nonisolated singular…
In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid)…
Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of…
An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost…
We present the Solar Bayesian Analysis Toolkit (SoBAT) which is a new easy to use tool for Bayesian analysis of observational data, including parameter inference and model comparison. SoBAT is aimed (but not limited) to be used for the…
In the object detection task, merging various datasets from similar contexts but with different sets of Objects of Interest (OoI) is an inexpensive way (in terms of labor cost) for crafting a large-scale dataset covering a wide range of…
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…