TY - JOUR
T1 - TSPINN
T2 - Thompson sampling-based adaptive training for physics-informed neural networks
AU - Zhang, Fangyi
AU - Wang, Dianpeng
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.
PY - 2026/4
Y1 - 2026/4
N2 - Physics-Informed Neural Networks (PINNs) offer a powerful framework for solving partial differential equations (PDEs) but often suffer from training inefficiencies. A critical factor is the selection of effective sampling distributions for training points. This work introduces Thompson Sampling PINN (TSPINN), a novel adaptive sampling approach inspired by Thompson Sampling. TSPINN dynamically defines a reward distribution based on recent PDE residuals to guide the adaptive selection of training points, strategically balancing exploration of uncertain regions and exploitation of high-residual zones. Furthermore, we integrate TSPINN with the Causal PINN framework to develop Causal TSPINN, explicitly incorporating temporal and spatial causality into the sampling process. Extensive numerical experiments demonstrate that both TSPINN and Causal TSPINN significantly enhance solution accuracy while requiring fewer training iterations and collocation points compared to existing adaptive sampling techniques (e.g., R3, RAD). These methods demonstrate broad applicability across various PDE types, including Poisson, Helmholtz, and convection equations, among others.
AB - Physics-Informed Neural Networks (PINNs) offer a powerful framework for solving partial differential equations (PDEs) but often suffer from training inefficiencies. A critical factor is the selection of effective sampling distributions for training points. This work introduces Thompson Sampling PINN (TSPINN), a novel adaptive sampling approach inspired by Thompson Sampling. TSPINN dynamically defines a reward distribution based on recent PDE residuals to guide the adaptive selection of training points, strategically balancing exploration of uncertain regions and exploitation of high-residual zones. Furthermore, we integrate TSPINN with the Causal PINN framework to develop Causal TSPINN, explicitly incorporating temporal and spatial causality into the sampling process. Extensive numerical experiments demonstrate that both TSPINN and Causal TSPINN significantly enhance solution accuracy while requiring fewer training iterations and collocation points compared to existing adaptive sampling techniques (e.g., R3, RAD). These methods demonstrate broad applicability across various PDE types, including Poisson, Helmholtz, and convection equations, among others.
KW - Adaptive sampling
KW - Physics-informed neural networks
KW - Thompson sampling
UR - https://www.scopus.com/pages/publications/105028913839
U2 - 10.1007/s11222-026-10824-w
DO - 10.1007/s11222-026-10824-w
M3 - Article
AN - SCOPUS:105028913839
SN - 0960-3174
VL - 36
JO - Statistics and Computing
JF - Statistics and Computing
IS - 2
M1 - 75
ER -