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.

Scientists increasingly use artificial intelligence to predict how physical systems evolve over time—for example, how air flows around a supersonic jet, how traffic congestion forms and disperses, or how weather systems move across the globe. However, current AI approaches often face a trade-off: purely data-driven models require large amounts of expensive simulation data, while physics-based models can become difficult to optimize and may struggle to adapt across different tasks. We developed APIC, a hybrid AI framework that learns from both observational data and physical structure at the same time. The system is designed so that the physics-guided component and the data-driven component can cooperate without excessively interfering with each other during training. We also introduce a flexible mathematical operator framework that can be adapted to a wide range of spatiotemporal prediction problems, including fluid dynamics, weather forecasting, and urban traffic modeling. Across multiple scientific forecasting tasks, APIC achieves accurate predictions while using substantially less training data than existing methods. By combining physical structure with modern machine learning, this work aims to make scientific AI models more data-efficient, stable, and broadly applicable to real-world forecasting problems.