Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

S Cheng, C Quilodrán-Casas, S Ouala… - IEEE/CAA Journal of …, 2023‏ - ieeexplore.ieee.org
Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

Clifford neural layers for pde modeling

J Brandstetter, R Berg, M Welling, JK Gupta - arxiv preprint arxiv …, 2022‏ - arxiv.org
Partial differential equations (PDEs) see widespread use in sciences and engineering to
describe simulation of physical processes as scalar and vector fields interacting and …

Towards multi-spatiotemporal-scale generalized pde modeling

JK Gupta, J Brandstetter - arxiv preprint arxiv:2209.15616, 2022‏ - arxiv.org
Partial differential equations (PDEs) are central to describing complex physical system
simulations. Their expensive solution techniques have led to an increased interest in deep …

Score-based data assimilation

F Rozet, G Louppe - Advances in Neural Information …, 2023‏ - proceedings.neurips.cc
Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem
of identifying plausible state trajectories that explain noisy or incomplete observations of …

Physics-integrated variational autoencoders for robust and interpretable generative modeling

N Takeishi, A Kalousis - Advances in Neural Information …, 2021‏ - proceedings.neurips.cc
Integrating physics models within machine learning models holds considerable promise
toward learning robust models with improved interpretability and abilities to extrapolate. In …

Learning spatiotemporal dynamics with a pretrained generative model

Z Li, W Han, Y Zhang, Q Fu, J Li, L Qin… - Nature Machine …, 2024‏ - nature.com
Reconstructing spatiotemporal dynamics with sparse sensor measurement is a challenging
task that is encountered in a wide spectrum of scientific and engineering applications. The …

Learning to solve pde-constrained inverse problems with graph networks

Q Zhao, DB Lindell, G Wetzstein - arxiv preprint arxiv:2206.00711, 2022‏ - arxiv.org
Learned graph neural networks (GNNs) have recently been established as fast and accurate
alternatives for principled solvers in simulating the dynamics of physical systems. In many …

[HTML][HTML] Efficient deep data assimilation with sparse observations and time-varying sensors

S Cheng, C Liu, Y Guo, R Arcucci - Journal of Computational Physics, 2024‏ - Elsevier
Abstract Variational Data Assimilation (DA) has been broadly used in engineering problems
for field reconstruction and prediction by performing a weighted combination of multiple …

Bayesian spline learning for equation discovery of nonlinear dynamics with quantified uncertainty

L Sun, D Huang, H Sun… - Advances in neural …, 2022‏ - proceedings.neurips.cc
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics
of most complex systems is far from being fully understood. Discovering interpretable …

Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

R Maulik, V Rao, J Wang, G Mengaldo… - Geoscientific Model …, 2022‏ - gmd.copernicus.org
Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts
from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather …