Related papers: Learning Markovian Dynamics with Spectral Maps
It is shown how S-matrix theory and the concept of continuous quantum measurements can be combined to yield Markovian master equations which describe the environmental interaction non-perturbatively. The method is then applied to obtain the…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic…
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete…
A spectral method for identifying lumping in large Markov chains is presented. Identification of meta stable states is treated as a special case. The method is based on spectral analysis of a self-adjoint matrix that is a function of the…
Learning graph representations is a fundamental task aimed at capturing various properties of graphs in vector space. The most recent methods learn such representations for static networks. However, real world networks evolve over time and…
Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and the general form of the underlying balance law model, we perform a detailed…
Slow Feature Analysis is a unsupervised representation learning method that extracts slowly varying features from temporal data and can be used as a basis for subsequent reinforcement learning. Often, the behavior that generates the data on…
Autonomous robots operating in complex, unstructured environments face significant challenges due to latent, unobserved factors that obscure their understanding of both their internal state and the external world. Addressing this challenge…
We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to…