Learning Physics-Constrained Collocation Samplers for Dual-Cone Optimization in Physics Informed Neural Networks

Physics-informed neural networks (PINNs) are highly sensitive to the choice of collocation points used to enforce PDE residuals and boundary conditions, particularly when trained with modern optimization methods such as dual cone gradient descent that rely on stable gradient geometry. Existing sampling strategies are largely heuristic and fail to adapt to the optimization dynamics induced by these optimizers, leading to poor sample efficiency and unstable training in high-dimensional and complex PDEs. We propose CoDyS (Collocation for Dynamic Sampling), a framework that learns physics-constrained collocation samplers to optimize PINN training under a fixed dual cone gradient descent optimizer. CoDyS formulates sampler design as a bi-level learning problem in which a generator agent proposes structured, physics-valid sampling programs, a PINN agent executes training with a fixed architecture and optimizer, and a critic agent evaluates candidate samplers using held-out PDE residual and boundary losses together with dual-cone stability diagnostics. Final performance is then reported with an independent relative L2 error metric on a disjoint test set. Without modifying the PINN or optimizer, CoDyS consistently improves sample efficiency and training stability compared to space-filling and adaptive sampling baselines across benchmark and high-dimensional PDEs, while remaining compatible with consumer-grade local workstations for open-weight models and lightweight API access for proprietary generators, without requiring model fine-tuning.