相关论文: Lagrangian uncertainty quantification and informat…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Significant uncertainty appears when the flow field is inferred…
The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self--gravitating flows in which the dynamics is described in…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
Multifields datasets are common in a large number of research and engineering applications of computational science. The effective visualization of the corresponding datasets can facilitate their analysis by elucidating the complex and…
We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it…
Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of whether the flow is turbulent or laminar, the particle dynamics…
In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…
We construct sub-grid scale models of incompressible fluids by considering expectations of semi-martingale Lagrangian particle trajectories. Our construction is based on the Lagrangian decomposition of flow maps into mean and fluctuation…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density…
Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
The high dynamics and heterogeneous interactions in the complicated urban systems have raised the issue of uncertainty quantification in spatiotemporal human mobility, to support critical decision-makings in risk-aware web applications such…