We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs).
Often, this requires high-resolution or adaptive discretization grids to capture relevant spatio-temporal features in the PDE solution, e. g., in applications like turbulence, combustion, and shock propagation.
Bile, the central metabolic product of the liver, is secreted by hepatocytes into bile canaliculi (BC), tubular subcellular structures of 0. 5-2 $\mu$m diameter which are formed by the apical membranes of juxtaposed hepatocytes.
We propose a statistical learning framework based on group-sparse regression that can be used to 1) enforce conservation laws, 2) ensure model equivalence, and 3) guarantee symmetries when learning or inferring differential-equation models from measurement data.
The identification of singular points or topological defects in discretized vector fields occurs in diverse areas ranging from the polarization of the cosmic microwave background to liquid crystals to fingerprint recognition and bio-medical imaging.
We show that in particular the combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast, parameter-free, and robust computational framework for PDE inference that outperforms previous algorithmic approaches with respect to recovery accuracy, amount of data required, and robustness to noise.
Life science today involves computational analysis of a large amount and variety of data, such as volumetric data acquired by state-of-the-art microscopes, or mesh data resulting from analysis of such data or simulations.
We provide motivation for this choice from different points of view, and we fully validate the resulting prior for use on biomedical images by showing its stability and correlation with image quality.
We show how particle methods as applied to image segmentation allow for a simple and computationally efficient implementation of Sobolev gradients.