Promising directions of machine learning for partial differential equations
SL Brunton, JN Kutz - Nature Computational Science, 2024 - nature.com
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 …
Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review
Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …
Interpretable machine learning for science with PySR and SymbolicRegression. jl
M Cranmer - arXiv preprint arXiv:2305.01582, 2023 - arxiv.org
PySR is an open-source library for practical symbolic regression, a type of machine learning
which aims to discover human-interpretable symbolic models. PySR was developed to …
which aims to discover human-interpretable symbolic models. PySR was developed to …
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 …
[HTML][HTML] A new family of Constitutive Artificial Neural Networks towards automated model discovery
For more than 100 years, chemical, physical, and material scientists have proposed
competing constitutive models to best characterize the behavior of natural and man-made …
competing constitutive models to best characterize the behavior of natural and man-made …
Reconstructing computational system dynamics from neural data with recurrent neural networks
Computational models in neuroscience usually take the form of systems of differential
equations. The behaviour of such systems is the subject of dynamical systems theory …
equations. The behaviour of such systems is the subject of dynamical systems theory …
Pysindy: a python package for the sparse identification of nonlinear dynamics from data
BM de Silva, K Champion, M Quade… - arXiv preprint arXiv …, 2020 - arxiv.org
PySINDy is a Python package for the discovery of governing dynamical systems models
from data. In particular, PySINDy provides tools for applying the sparse identification of …
from data. In particular, PySINDy provides tools for applying the sparse identification of …
State estimation of a physical system with unknown governing equations
State estimation is concerned with reconciling noisy observations of a physical system with
the mathematical model believed to predict its behaviour for the purpose of inferring …
the mathematical model believed to predict its behaviour for the purpose of inferring …
Discovering governing equations from partial measurements with deep delay autoencoders
A central challenge in data-driven model discovery is the presence of hidden, or latent,
variables that are not directly measured but are dynamically important. Takens' theorem …
variables that are not directly measured but are dynamically important. Takens' theorem …
Hypothesis learning in automated experiment: application to combinatorial materials libraries
Abstract Machine learning is rapidly becoming an integral part of experimental physical
discovery via automated and high‐throughput synthesis, and active experiments in …
discovery via automated and high‐throughput synthesis, and active experiments in …