相关论文: Identification of slow molecular order parameters …

The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite…

Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…

We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…

Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…

Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more…

Understanding the long-time dynamics of complex physical processes depends on our ability to recognize patterns. To simplify the description of these processes, we often introduce a set of reaction coordinates, customarily referred to as…

Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential…

Investigating processes in complex molecular systems, which are characterized by many variables, is a crucial problem in computational physics. These systems can be reduced to a few meaningful degrees of freedom known as collective…

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…

Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose…

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…

Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond to individual 'processes' or 'fluxes'. Frequently, these…

A tipping point can be defined as an abrupt shift in the properties or behaviour of a system. Tipping points in complex systems from a wide variety of scientific disciplines have been compared to phase transitions in physics, but consistent…

We use machine learning algorithms to detect the crystalline phase in undercooled melts in molecular dynamics simulations. Our classification method is based on local conformation and environmental fingerprints of individual monomers. In…

We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for…

Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…

Currently, identification of crystallization pathways in polymers is being carried out using molecular simulation-based data on a preset cut-off point on a single order parameter (OP) to define nucleated or crystallized regions. Aside from…

Markov state models (MSMs) are a widely used method for approximating the eigenspectrum of the molecular dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomolecular systems.…

We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…