Related papers: Learning Markovian Dynamics with Spectral Maps

The combination of chain-mapping and tensor-network techniques provides a powerful tool for the numerically exact simulation of open quantum systems interacting with structured environments. However, these methods suffer from a quadratic…

The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…

We present a new method that enables the identification and analysis of both transition and metastable conformational states from atomistic or coarse-grained molecular dynamics (MD) trajectories. Our algorithm is presented and studied by…

Deep representation learning is a crucial procedure in multimedia analysis and attracts increasing attention. Most of the popular techniques rely on convolutional neural network and require a large amount of labeled data in the training…

Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate…

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

In this work, we propose a data-driven method to discover the latent space and learn the corresponding latent dynamics for a collisional-radiative (CR) model in radiative plasma simulations. The CR model, consisting of high-dimensional…

Particle accelerators are complex systems that focus, guide, and accelerate intense charged particle beams to high energy. Beam diagnostics present a challenging problem due to limited non-destructive measurements, computationally demanding…

Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables. The free energy…

Learning reduced descriptions of chaotic many-body dynamics is fundamentally challenging: although microscopic equations are Markovian, collective observables exhibit strong memory and exponential sensitivity to initial conditions and…

The ISOKANN (Invariant Subspaces of Koopman Operators Learned by Artificial Neural Networks) framework provides a data-driven route to extract collective variables (CVs) and effective dynamics from complex molecular systems. In this work,…

Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal…

Mapping the surrounding environment is essential for the successful operation of autonomous robots. While extensive research has focused on mapping geometric structures and static objects, the environment is also influenced by the movement…

Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing…

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…

The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…