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 …
Clifford neural layers for pde modeling
Partial differential equations (PDEs) see widespread use in sciences and engineering to
describe simulation of physical processes as scalar and vector fields interacting and …
describe simulation of physical processes as scalar and vector fields interacting and …
Towards multi-spatiotemporal-scale generalized pde modeling
Partial differential equations (PDEs) are central to describing complex physical system
simulations. Their expensive solution techniques have led to an increased interest in deep …
simulations. Their expensive solution techniques have led to an increased interest in deep …
Score-based data assimilation
Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem
of identifying plausible state trajectories that explain noisy or incomplete observations of …
of identifying plausible state trajectories that explain noisy or incomplete observations of …
Physics-integrated variational autoencoders for robust and interpretable generative modeling
Integrating physics models within machine learning models holds considerable promise
toward learning robust models with improved interpretability and abilities to extrapolate. In …
toward learning robust models with improved interpretability and abilities to extrapolate. In …
Learning spatiotemporal dynamics with a pretrained generative model
Reconstructing spatiotemporal dynamics with sparse sensor measurement is a challenging
task that is encountered in a wide spectrum of scientific and engineering applications. The …
task that is encountered in a wide spectrum of scientific and engineering applications. The …
Learning to solve pde-constrained inverse problems with graph networks
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 …
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
Abstract Variational Data Assimilation (DA) has been broadly used in engineering problems
for field reconstruction and prediction by performing a weighted combination of multiple …
for field reconstruction and prediction by performing a weighted combination of multiple …
Bayesian spline learning for equation discovery of nonlinear dynamics with quantified uncertainty
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics
of most complex systems is far from being fully understood. Discovering interpretable …
of most complex systems is far from being fully understood. Discovering interpretable …
Efficient high-dimensional variational data assimilation with machine-learned reduced-order models
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 …
from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather …