We present a machine learning framework bridging manifold learning, neural networks,
Gaussian processes, and Equation-Free multiscale approach, for the construction of …

The data-driven discovery of partial differential equations (PDEs) consistent with
spatiotemporal data is experiencing a rebirth in machine learning research. Training deep …

Abstract We present an Equation/Variable free machine learning (EVFML) framework for the
control of the collective dynamics of complex/multiscale systems modeled via …

We introduce a machine-learning framework named statistics-informed neural network
(SINN) for learning stochastic dynamics from data. This new architecture was theoretically …

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

In this work, we propose a method to learn multivariate probability distributions using sample
path data from stochastic differential equations. Specifically, we consider temporally …

With the rapid development of computational techniques and scientific tools, great progress
of data-driven analysis has been made to extract governing laws of dynamical systems from …

We construct a reduced, data-driven, parameter dependent effective stochastic differential
equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from …

The dynamical behavior of social systems can be described by agent-based models.
Although single agents follow easily explainable rules, complex time-evolving patterns …

Deriving closed-form analytical expressions for reduced-order models, and judiciously
choosing the closures leading to them, has long been the strategy of choice for studying …