FLINT: A Simultaneous Emulator for Discontinuous and Smooth Structures with PINNs

Physics-informed neural networks (PINNs) have made substantial progress on hyperbolic conservation laws containing sharp discontinuities. However, accurately capturing discontinuities while preserving transported fine-scale structure remains a challenge. We show that this failure worsens as the spatial frequency of initial data increases, exposing a core limitation of global space–time PINNs. We introduce FLINT (FLux balance for INitial-data Transport), which combines several recent advances in the PINN literature with our novel contributions: shock-selective residual weighting and variable-height control volumes anchored directly to initial conditions. The PDE residual is down-weighted at points where sharp gradients suggest either a shock or contact discontinuity, while the divergence theorem transforms local conservation into global conservation laws over control volumes, which propagate initial data into later times. We evaluate FLINT on 1D benchmark problems for compressible Euler equations, including the newly proposed Sod-$k$ diagnostic (a shock tube with tunable initial density oscillations), the Shu–Osher problem, and a 1D cylindrical blast wave. Across these benchmarks, FLINT captures wave amplitude and phase while maintaining shock and contact locations and global conservation, outperforming baselines in every metric. On Shu–Osher, FLINT reduces wave-region $L_2$ error by $4-6\times$ and wave amplitude error by $7-31\times$ relative to the stronger baseline, while accurately handling geometric source terms and coordinate singularities in the blast wave. By addressing these 1D transport challenges, FLINT establishes a necessary foundation for scaling global space–time PINNs to complex multi-dimensional compressible flows.