Title: Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Physics-Informed Neural Networks, Stiff PDEs, Hard Constraints, Initial Condition, Ablation Study, Neural Tangent Kernel

Abstract: Training Physics-Informed Neural Networks (PINNs) on stiff time-dependent PDEs remains highly unstable. Through rigorous ablation studies, we identify a surprisingly critical factor: the enforcement of initial conditions.  We present the first systematic ablation of two core strategies, hard initial-condition constraints and adaptive loss weighting. Across challenging benchmarks (sharp transitions, higher-order derivatives, coupled systems, and high frequency modes), we find that exact enforcement of initial conditions (ICs) is not optional but essential. Our study demonstrates that stability and efficiency in PINN training fundamentally depend on ICs, paving the way toward more reliable PINN solvers in stiff regimes.