papers

Publications (17)

math-ph2015

A mathematical framework for exact milestoning

David Aristoff, Juan M. Bello-Rivas, Ron Elber

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process…

q-bio.QM2022

Data-driven Discovery of Chemotactic Migration of Bacteria via Machine Learning

Yorgos M. Psarellis, Seungjoon Lee, Tapomoy Bhattacharjee +3

E. coli chemotactic motion in the presence of a chemoattractant field has been extensively studied using wet laboratory experiments, stochastic computational models as well as part…

cs.LG2023

Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems

Ellis R. Crabtree, Juan M. Bello-Rivas, Ioannis G. Kevrekidis

A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of th…

stat.ML2021

On the Correspondence between Gaussian Processes and Geometric Harmonics

Felix Dietrich, Juan M. Bello-Rivas, Ioannis G. Kevrekidis

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research…

math.DS2018

Manifold learning for parameter reduction

Alexander Holiday, Mahdi Kooshkbaghi, Juan M. Bello-Rivas +3

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that re…

quant-ph2025

Roadmap to fault tolerant quantum computation using topological qubit arrays

David Aasen, Morteza Aghaee, Zulfi Alam +179

We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap e…

cs.LG2023

GANs and Closures: Micro-Macro Consistency in Multiscale Modeling

Ellis R. Crabtree, Juan M. Bello-Rivas, Andrew L. Ferguson +1

Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in m…

quant-ph2025

A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes

David Aasen, Matthew B. Hastings, Vadym Kliuchnikov +8

Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance o…

cs.LG2025

Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations

Trung V. Phan, George A. Kevrekidis, Soledad Villar +2

The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of…

cs.LG2023

Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling

Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas +2

We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We…

cs.LG2023

Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points

Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui +4

We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipp…

math.DS2023

Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles

Nikolaos Evangelou, Felix Dietrich, Juan M. Bello-Rivas +4

We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained…

cs.LG2022

Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds

Juan M. Bello-Rivas, Anastasia Georgiou, John Guckenheimer +1

We introduce a method to successively locate equilibria (steady states) of dynamical systems on Riemannian manifolds. The manifolds need not be characterized by an a priori known a…

cs.LG2025

Generative Learning for Slow Manifolds and Bifurcation Diagrams

Ellis R. Crabtree, Dimitris G. Giovanis, Nikolaos Evangelou +2

In dynamical systems characterized by separation of time scales, the approximation of so called ``slow manifolds'', on which the long term dynamics lie, is a useful step for model…

cs.LG2024

Identifying Equivalent Training Dynamics

William T. Redman, Juan M. Bello-Rivas, Maria Fonoberova +3

Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior. While a detailed understanding o…

math.DS2023

Gentlest ascent dynamics on manifolds defined by adaptively sampled point-clouds

Juan M. Bello-Rivas, Anastasia Georgiou, Hannes Vandecasteele +1

Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems. Gentlest ascent dynamics (GAD) i…

quant-ph2025

Fault-tolerant quantum computation with a neutral atom processor

Ben W. Reichardt, Adam Paetznick, David Aasen +69

Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and ha…