Related papers: Learning Markovian Dynamics with Spectral Maps
This paper studies how to find compact state embeddings from high-dimensional Markov state trajectories, where the transition kernel has a small intrinsic rank. In the spirit of diffusion map, we propose an efficient method for learning a…
This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. Due to the complex nature of mixing in heterogeneous and…
Understanding kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to…
We introduce a method for elucidating and modifying the functionality of systems dominated by rare events that relies on the automated tuning of their underlying free energy surface. The proposed approach seeks to construct collective…
Turbulence plays a key role in star formation in molecular clouds, affecting star cluster primordial properties. As modelling present-day objects hinges on our understanding of their initial conditions, better constraints on turbulence can…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
Extending spatio-temporal scale limitations of models for complex atomistic systems considered in biochemistry and materials science necessitates the development of enhanced sampling methods. The potential acceleration in exploring the…
Deep functional map frameworks are widely employed for 3D shape matching. However, most existing deep functional map methods cannot adaptively capture important frequency information for functional map estimation in specific matching…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
Deep spatiotemporal models are used in a variety of computer vision tasks, such as action recognition and video object segmentation. Currently, there is a limited understanding of what information is captured by these models in their…
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is…
Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems.…
Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…
Network Markov Decision Processes (MDPs), a popular model for multi-agent control, pose a significant challenge to efficient learning due to the exponential growth of the global state-action space with the number of agents. In this work,…
This paper proposes a dynamic network framework for uncovering latent community paths in high-dimensional VAR-type models. By embedding a degree-corrected stochastic co-blockmodel (ScBM) into the transition matrices of VAR-type systems, we…
Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to…
Current and upcoming generations of visible-shortwave infrared (VSWIR) imaging spectrometers promise unprecedented capacity to quantify Earth System processes across the globe. However, reliable cloud screening remains a fundamental…