DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains
Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed neural networks (PINNs), as uniform collocation sampling becomes increasingly ineffective in high-dimensional spatiotemporal domains. In this work, a deep adaptive sampling framework for PINNs is extended to the time-dependent setting by treating space and time as a unified domain without any explicit time marching. A normalising flow neural network model effectively learns the distribution induced by the PDE residual and generates new collocation points concentrated in regions where the solution is most difficu...
| Authors | Anshima Singh, David J. Silvester |
|---|---|
| Primary category | math.NA |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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