BibTeX

@article{2405.14558v2,
Author        = {Levi E. Lingsch and Dana Grund and Siddhartha Mishra and Georgios Kissas},
Title         = {FUSE: Fast Unified Simulation and Estimation for PDEs},
Eprint        = {2405.14558v2},
ArchivePrefix = {arXiv},
PrimaryClass  = {cs.LG},
Abstract      = {The joint prediction of continuous fields and statistical estimation of the
underlying discrete parameters is a common problem for many physical systems,
governed by PDEs. Hitherto, it has been separately addressed by employing
operator learning surrogates for field prediction while using simulation-based
inference (and its variants) for statistical parameter determination. Here, we
argue that solving both problems within the same framework can lead to
consistent gains in accuracy and robustness. To this end, We propose a novel
and flexible formulation of the operator learning problem that allows jointly
predicting continuous quantities and inferring distributions of discrete
parameters, and thus amortizing the cost of both the inverse and the surrogate
models to a joint pre-training step. We present the capabilities of the
proposed methodology for predicting continuous and discrete biomarkers in
full-body haemodynamics simulations under different levels of missing
information. We also consider a test case for atmospheric large-eddy simulation
of a two-dimensional dry cold bubble, where we infer both continuous
time-series and information about the systems conditions. We present
comparisons against different baselines to showcase significantly increased
accuracy in both the inverse and the surrogate tasks.},
Year          = {2024},
Month         = {May},
Url           = {http://arxiv.org/abs/2405.14558v2},
File          = {2405.14558v2.pdf}
}