ATOM: A Neuro-Symbolic Architecture for Physics-Constrained Control and Autonomous Law Discovery in Computational Fluid Dynamics

We introduce ATOM, a neuro-symbolic agent architecture for physics-constrained control and autonomous scientific discovery. Unlike Physics-Informed Neural Networks (PINNs) that enforce physical laws via soft loss penalties, ATOM embeds hard constraints directly into the network architecture through Helmholtz-projected Fourier Neural Operators (guaranteed mass conservation, ∇·v ≈ 10⁻⁹) and symplectic integrators (energy drift ≈ 10⁻¹⁶, machine epsilon).Applied to active flow control of vortex shedding at Re=1000, ATOM demonstrates three key capabilities: (1) 99.99% sample efficiency versus traditional deep reinforcement learning, converging in ~100 steps versus 10⁶; (2) multi-modal Pareto frontier exploration, autonomously discovering three distinct physical control mechanisms—reactive linear damping, energy-based quadratic scheduling, and preventative inverse-law pressure maintenance; and (3) symbolic law extraction, distilling learned policies into compact, human-interpretable equations that recover known aerodynamic principles. The architecture generalizes without modification to extreme physics regimes, including supersonic analog gravity simulations (Mach 1.2) exhibiting spontaneous acoustic Hawking radiation. We report state-of-the-art lift variance reduction of 41.3% at Re=1000, compared to 8% drag reduction at Re=100 in prior work (Rabault et al., 2019). Full ablation studies validate that symplectic dynamics reduce control stress by 531% versus unconstrained baselines. Code and technical documentation: https://culturiq.ai