Promising directions of machine learning for partial differential equations
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
Sparse model identification enables the discovery of nonlinear dynamical systems purely
from data; however, this approach is sensitive to noise, especially in the low-data limit. In this …
from data; however, this approach is sensitive to noise, especially in the low-data limit. In this …
Learning dynamical models of single and collective cell migration: a review
Single and collective cell migration are fundamental processes critical for physiological
phenomena ranging from embryonic development and immune response to wound healing …
phenomena ranging from embryonic development and immune response to wound healing …
Deeptime: a Python library for machine learning dynamical models from time series data
Generation and analysis of time-series data is relevant to many quantitative fields ranging
from economics to fluid mechanics. In the physical sciences, structures such as metastable …
from economics to fluid mechanics. In the physical sciences, structures such as metastable …
Parsimony as the ultimate regularizer for physics-informed machine learning
Data-driven modeling continues to be enabled by modern machine learning algorithms and
deep learning architectures. The goals of such efforts revolve around the generation of …
deep learning architectures. The goals of such efforts revolve around the generation of …
Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches
Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to
understand and describe their behavior. However, there is a scarcity of plasma models of …
understand and describe their behavior. However, there is a scarcity of plasma models of …
Benchmarking sparse system identification with low-dimensional chaos
Sparse system identification is the data-driven process of obtaining parsimonious differential
equations that describe the evolution of a dynamical system, balancing model complexity …
equations that describe the evolution of a dynamical system, balancing model complexity …
Sparse nonlinear models of chaotic electroconvection
Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a
fluid is driven, for example, by a thermal gradient or an electric potential. Modelling …
fluid is driven, for example, by a thermal gradient or an electric potential. Modelling …
Machine learning for partial differential equations
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and multi …
descriptions of natural physical laws, capturing a rich variety of phenomenology and multi …
An empirical mean-field model of symmetry-breaking in a turbulent wake
Improved turbulence modeling remains a major open problem in mathematical physics.
Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that …
Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that …