Gradient-Guided Physics-Informed Multi-Fidelity U-Mamba for Discontinuous Flow Field Prediction

Surrogate modeling of strong discontinuities, such as shock waves and contact discontinuities, in compressible flows remains challenging: high-resolution numerical schemes are computationally prohibitive on fine grids, purely data-driven operators lack physical consistency and induce Gibbs oscillations, and standard physics-informed neural networks (PINNs) break down where strong-form differential residuals become ill-defined. We propose PIMUG, a Gradient-Guided Physics-Informed Multi-Fidelity U-Mamba framework coupling three complementary branches: (1) a multi-fidelity trunk extracting spatio-temporal features from multi-resolution, multi-timestep inputs; (2) an explicit gradient branch supervising directional derivatives to sharpen discontinuity fronts without oversmoothing; and (3) a coordinate-conditioned physics branch with a divergence-adaptive residual loss that enforces Euler conservation while relaxing ill-posed penalties at shock fronts. An Input Compression Module (ICM) suppresses spatio-temporal redundancy across fidelity levels. On 2D Riemann benchmarks spanning slip lines, rarefactions, and shock collisions, PIMUG preserves sharp discontinuity profiles without visible Gibbs oscillations. As a multi-fidelity field corrector, PIMUG consumes low-fidelity numerical solutions at the target time—a richer input regime than instance-wise pointwise PINNs (PINN-WE), which solve from initial and boundary conditions alone; under this setting, PIMUG reduces self-enforced Euler residuals by two to four orders of magnitude relative to PINN-WE with millisecond amortized inference. Compared to Fourier Neural Operators (FNO) on identical inputs, PIMUG eliminates Gibbs blurring while retaining physical consistency; augmenting FNO with the same residual loss merely induces degenerate over-smoothing while degrading data accuracy by two orders of magnitude, isolating PIMUG's gains as architectural rather than a loss artifact.