Optimal Transport Based Refinement of Physics-Informed Neural Networks
- Computer ScienceArXiv
A novel training strategy for solving the FPKE using OT-based sampling to supplement the existing PINNs framework is presented, an iterative approach that induces a network trained on a small dataset to add samples to its training dataset from regions where it nominally makes the most error.
SHOWING 1-10 OF 24 REFERENCES
On Kalman Filtering With Nonlinear Equality Constraints
- MathematicsIEEE Transactions on Signal Processing
This paper proposes a new method that utilizes the projection method twice-once to constrain the entire distribution and once to Constrain the statistics of the distribution, and illustrates these algorithms in a tracking system that uses unit quaternions to encode orientation.
Unscented filtering for equality-constrained nonlinear systems
- Engineering, Mathematics2008 American Control Conference
This paper addresses the state-estimation problem for nonlinear systems in a context where prior knowledge, in addition to the model and the measurement data, is available in the form of an equality…
An optimal transport formulation of the linear feedback particle filter
- Mathematics2016 American Control Conference (ACC)
A key difference between the optimal control law and the one in the original FPF, is the replacement of noise term with a deterministic term that serves to decrease the simulation variance.
State estimation for linear and non-linear equality-constrained systems
- MathematicsInt. J. Control
The equality-constrained Kalman filter (KF) is derived as the maximum-a-posteriori solution to the equality- Constrained state-estimation problem for linear and Gaussian systems and is compared to alternative algorithms.
Kalman filtering with state constraints: a survey of linear and nonlinear algorithms
The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For…
Kalman Filtering with State Constraints
- Engineering, Mathematics
The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear…
A Tutorial on Particle Filtering and Smoothing: Fifteen years later
- Computer Science
A complete, up-to-date survey of particle filtering methods as of 2008, including basic and advanced particle methods for filtering as well as smoothing.
A Nonparametric Ensemble Transform Method for Bayesian Inference
- Computer Science, MathematicsSIAM J. Sci. Comput.
This paper proposes another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions and is based on solving an optimal transportation problem for discrete random variables.