Related papers: An Exact Bitwise Reversible Integrator
Solving mathematical equations faster and more efficiently has been a Holy Grail for centuries for scientists and engineers across all disciplines. While electronic digital circuits have revolutionized equation solving in recent decades, it…
Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory cost. Here, we introduce a class of algebraically reversible…
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems,…
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…
Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of the unpredictable behavior of…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
For a periodically shaken optical lattice, effective time-reversal is investigated numerically. For interacting ultra-cold atoms, the scheme of [J. Phys. B 45, 021002 (2012)] involves a quasi-instantaneous change of both the…
We present a new symplectic integrator designed for collisional gravitational $N$-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves 9 integrals of motion of the $N$-body problem to machine…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
The parareal in time algorithm allows to efficiently use parallel computing for the simulation of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…
We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes…
Bit reset is a basic operation in irreversible computing. This costs work and dissipates energy in the computer, creating a limit on speeds and energy efficiency of future irreversible computers. It was recently shown in [Phys. Rev. Lett.…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
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…
Reversible algorithms are algorithms in which each step represents a partial injective function; they are useful for performance optimization in reversible systems. In this study, using Janus, a reversible imperative high-level programming…