Related papers: Learning Markovian Dynamics with Spectral Maps
We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive)…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration,…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or…
We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a…
We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive)…
The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…
A method for detecting intrinsic slow variables in high-dimensional stochastic chemical reaction networks is developed and analyzed. It combines anisotropic diffusion maps (ADM) with approximations based on the chemical Langevin equation…
Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the…
Vibrational spectroscopy is a powerful technique to characterize the near-equilibrium dynamics of molecules in the gas- and the condensed-phase. This contribution summarizes efforts from computer-based methods to gain insight into the…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
A large number of biological systems - from bacteria to sheep - can be described as ensembles of self-propelled agents (active particles) with a complex internal dynamic that controls the agent's behavior: resting, moving slow, moving fast,…
In this paper, we study statistical classification accuracy of two different Markov field environments for pixelwise image segmentation, considering the labels of the image as hidden states and solving the estimation of such labels as a…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
A variety of enhanced sampling methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is…
Metadynamics is a commonly used and successful enhanced sampling method. By the introduction of a history dependent bias which depends on a restricted number of collective variables(CVs) it can explore complex free energy surfaces…