TY - JOUR
T1 - Failure-Informed Adaptive Sampling for PINNs, Part III: Applications to Inverse Problems
AU - Liu , Wenbin
AU - Yan , Liang
AU - Zhou , Tao
AU - Zhou , Yuancheng
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 636
EP - 670
PY - 2024
DA - 2024/08
SN - 5
DO - http://doi.org/10.4208/csiam-am.SO-2023-0059
UR - https://global-sci.org/intro/article_detail/csiam-am/23311.html
KW - Inverse problem, FI-PINNs, Gaussian mixture model.
AB - <p style="text-align: justify;">In this paper, we present a novel adaptive sampling strategy for enhancing the performance of physics-informed neural networks (PINNs) in addressing inverse problems with low regularity and high dimensionality. The framework is based
on failure-informed PINNs, which was recently developed in [Gao et al., SIAM J. Sci.
Comput., 45(4), 2023]. Specifically, we employ a truncated Gaussian mixture model to
estimate the failure probability; this model additionally serves as an error indicator in
our adaptive strategy. New samples for further computation are also produced using
the truncated Gaussian mixture model. To describe the new framework, we consider
two important classes of inverse problems: the inverse conductivity problem in electrical impedance tomography and the inverse source problem in a parabolic system. The
effectiveness of our method is demonstrated through a series of numerical examples.</p>