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Found 11 papers, 2 papers with code
A Learnable Prior Improves Inverse Tumor Growth Modeling
Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients.
Subsampling Error in Stochastic Gradient Langevin Diffusions
Indeed, we introduce and study the Stochastic Gradient Langevin Diffusion (SGLDiff), a continuous-time Markov process that follows the Langevin diffusion corresponding to a data subset and switches this data subset after exponential waiting times.
Can Physics-Informed Neural Networks beat the Finite Element Method?
In terms of solution time and accuracy, physics-informed neural networks have not been able to outperform the finite element method in our study.
Losing momentum in continuous-time stochastic optimisation
This model is a piecewise-deterministic Markov process that represents the particle movement by an underdamped dynamical system and the data subsampling through a stochastic switching of the dynamical system.
Joint reconstruction-segmentation on graphs
Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations.
Gradient flows and randomised thresholding: sparse inversion and classification
Sparse inversion and classification problems are ubiquitous in modern data science and imaging.
A Continuous-time Stochastic Gradient Descent Method for Continuous Data
Optimization problems with continuous data appear in, e. g., robust machine learning, functional data analysis, and variational inference.
Analysis of Stochastic Gradient Descent in Continuous Time
After introducing it, we study theoretical properties of the stochastic gradient process: We show that it converges weakly to the gradient flow with respect to the full target function, as the learning rate approaches zero.
Certified and fast computations with shallow covariance kernels
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators.
On the well-posedness of Bayesian inverse problems
The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems.
A practical example for the non-linear Bayesian filtering of model parameters
Importantly, the particle filters enable the adaptive updating of the estimate for $g$ as new observations become available.
Computation Numerical Analysis
