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The numerical simulation of the time-dependent Schr\"odinger equation for quantum systems is a very active research topic. Yet, resolving the solution sufficiently in space and time is challenging and mandates the use of modern…

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…

In this paper, we propose to estimate the forward dynamics equations of mechanical systems by learning a model of the inverse dynamics and estimating individual dynamics components from it. We revisit the classical formulation of rigid body…

Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be…

Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…

The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…

We present a practical algorithm based on symplectic splitting methods to integrate numerically in time the Schr\"odinger equation. When discretized in space, the Schr\"odinger equation can be recast as a classical Hamiltonian system…

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

A method for time-reversible numerical integration of the deterministic Landau-Lifshitz Gilbert equation by means of a second order Suzuki-Trotter decomposition is presented and tested against commonly used second order predictor-corrector…

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…

The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…

We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to…

Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…

The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…

In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth…

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…

Langevin and Brownian simulations play a prominent role in computational research, and state of the art integration algorithms provide trajectories with different stability ranges and accuracy in reproducing statistical averages. The…