A Ghadami, BI Epureanu - Philosophical Transactions of …, 2022 - royalsocietypublishing.org
In recent years, we have witnessed a significant shift toward ever-more complex and ever- larger-scale systems in the majority of the grand societal challenges tackled in applied …
All physical laws are described as mathematical relationships between state variables. These variables give a complete and non-redundant description of the relevant system …
M Raissi - Journal of Machine Learning Research, 2018 - jmlr.org
We put forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time. Specifically …
M Raissi, GE Karniadakis - Journal of Computational Physics, 2018 - Elsevier
While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial …
K Champion, B Lusch, JN Kutz… - Proceedings of the …, 2019 - National Acad Sciences
The discovery of governing equations from scientific data has the potential to transform data- rich fields that lack well-characterized quantitative descriptions. Advances in sparse …
The integration of data and scientific computation is driving a paradigm shift across the engineering, natural, and physical sciences. Indeed, there exists an unprecedented …
We propose a sparse regression method capable of discovering the governing partial differential equation (s) of a given system by time series measurements in the spatial …
T Qin, K Wu, D Xiu - Journal of Computational Physics, 2019 - Elsevier
We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual …
Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long …