Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

We propose an approach to learn effective evolution equations for large systems of
interacting agents. This is demonstrated on two examples, a well-studied system of coupled …

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

In statistical modelling with Gaussian process regression, it has been shown that combining
(few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy …

Systems of coupled dynamical units (eg, oscillators or neurons) are known to exhibit
complex, emergent behaviors that may be simplified through coarse-graining: a process in …

We propose a local conformal autoencoder (LOCA) for standardized data coordinates.
LOCA is a deep learning-based method for obtaining standardized data coordinates from …

Before we attempt to (approximately) learn a function between two sets of observables of a
physical process, we must first decide what the inputs and outputs of the desired function are …

We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of
large systems of coupled heterogeneous agents. These coordinates then serve as an …

Circadian rhythmicity lies at the center of various important physiological and behavioral
processes in mammals, such as sleep, metabolism, homeostasis, mood changes, and more …

Equations governing physico-chemical processes are usually known at microscopic spatial
scales, yet one suspects that there exist equations, eg, in the form of partial differential …