[HTML][HTML] Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

S Perez, S Maddu, IF Sbalzarini, P Poncet - Journal of Computational …, 2023 - Elsevier
In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian
Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it …

Efficient Sobolev approximation of linear parabolic PDEs in high dimensions

P Cheridito, F Rossmannek - arXiv preprint arXiv:2306.16811, 2023 - arxiv.org
In this paper, we study the error in first order Sobolev norm in the approximation of solutions
to linear parabolic PDEs. We use a Monte Carlo Euler scheme obtained from combining the …

Particle and data-driven approaches for reactive micrometric processes: application to CO2 mineral storage with uncertainty quantification.

S Perez - 2023 - theses.hal.science
Studying reactive flows in porous media is essential to manage the geochemical effects of
CO2 capture and storage in natural underground reservoirs. Through homogenization of the …

Neural Tangent Kernel Analysis and Filtering for Robust Fourier Feature Embedding

M Ma, Q Zhu, Y Zhan, Z Yin, H Wang, J Zhao, Y Zheng - openreview.net
Implicit Neural Representations (INRs) employ neural networks to represent continuous
functions by mapping coordinates to the corresponding values of the target function, with …