APIC: Orthogonalized Neuro-Symbolic Modeling for Nonlinear Dissipative Dynamics

Current data-driven scientific modeling struggles with a functional dichotomy: neural operators exhibit spectral bias in high-frequency regimes, while physics-constrained paradigms suffer from optimization pathologies. To bridge this gap, we propose Adaptive Physics-Informed Computing (APIC), a neuro-symbolic meta-architecture designed with structural reconfigurability to encode diverse domain priors. Crucially, APIC integrates a gradient isolation strategy that reduces interference between the optimization paths of parameter identification and residual correction, effectively mitigating gradient conflicts. By instantiating this framework for nonlinear dissipative systems, we derive the Generalized Kuramoto-Sivashinsky-Cahn-Hilliard (G-KSCH) kernel, providing a unified representation for sparse dynamic identification. Extensive experiments demonstrate that APIC establishes new benchmarks in 3D compressible supersonic shock wave prediction, surpassing diverse architectures (e.g., CNNs and Transformers) by substantial margins in predictive accuracy. Notably, APIC achieves Pareto-optimal performance, delivering superior precision with reduced computational overhead compared to SOTA models, while exhibiting strong cross-task adaptability across meteorological and urban traffic datasets.