Related papers: Some fundamental problems for an energy conserving…
Molecular dynamics (MD) is a widely-used tool for simulating the molecular and materials properties. It is a common wisdom that molecular dynamics simulations should obey physical laws and, hence, lots of effort is put into ensuring that…
This work introduces a formulation of model predictive control (MPC) which adaptively reasons about the complexity of the model based on the task while maintaining feasibility and stability guarantees. Existing MPC implementations often…
We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the…
The optimization of dynamic problems is both widespread and difficult. When conducting dynamic optimization, a balance between reinitialization and computational expense has to be found. There are multiple approaches to this. In parallel…
Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…
Simulation schemes that allow to change molecular representation in a subvolume of the simulation box while preserving the equilibrium with the surrounding introduce conceptual problems of thermodynamic consistency. In this work we present…
Here we present a program aimed at free-energy calculations in molecular systems. It consists of a series of routines that can be interfaced with the most popular classical molecular dynamics (MD) codes through a simple patching procedure.…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
This paper concerns applications of genetic algorithms and genetic programming to tasks for which it is difficult to find a representation that does not map to a highly complex and discontinuous fitness landscape. In such cases the standard…
We describe the adaptive resolution multiscale method AdResS. The conceptual evolution as well as the improvements of its technical efficiency are described step by step, with an explicit reference to current limitations and open problems.
Atomistic foundation models (AFMs) have great promise as accurate interatomic potentials, and have enabled data-efficient molecular dynamics simulations with near quantum mechanical accuracy. However, AFMs remain markedly slower at…
Molecular dynamics simulations are typically constrained to have a fixed number of particles, which limits our capability to simulate chemical and physical processes where the composition of the system changes during the simulation time.…
The rapidly changing landscapes of modern optimization problems require algorithms that can be adapted in real-time. This paper introduces an Adaptive Metaheuristic Framework (AMF) designed for dynamic environments. It is capable of…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions for which it is possible to identify a priori a slow reaction coordinate. In…
In molecular dynamics (MD), systems are molecules made up of atoms, and the aim is to determine their evolution over time. MD is based on a numerical resolution algorithm, whose role is to apply the forces generated by the various…
A theoretical scheme for the treatment of an open molecular system with electrons and nuclei is proposed. The idea is based on the Grand Canonical description of a quantum region embedded in a classical reservoir of molecules. Electronic…