Physics-Enforced Neural Control via Architectural Constraints

Recent industry roadmaps for “XXLarge” Physics Foundation Models identify the certification gap—the inability to verify black-box neural surrogates for safety- critical engineering—as a primary barrier to deployment (Ashton et al., 2025). We present ATOM, a neuro-symbolic architecture that addresses this gap by embedding physical constraints directly into network structure rather than as soft loss penalties. By combining a Helmholtz-decomposition head that guarantees divergence-free velocity fields (∇ · v ≡ 0 by construction) with a symplectic in- tegrator that bounds energy drift to machine precision (∆H < 10−10), ATOM ensures physical validity architecturally. The “Scientist” module autonomously distills flow dynamics into interpretable symbolic control laws via PySR with split conformal calibration. On preliminary benchmarks (Re= 1000, 64 × 32 × 24 grid), ATOM stabilizes vortex shedding where unconstrained RL fails, discovering control laws structurally consistent with phase-matched blowing strategies known in aerospace literature (Choi et al., 2008). We present this as proof-of-concept evidence that physics-enforced architectures enable meaningful control research on consumer hardware. Compute Transparency: All experiments were conducted on a single MacBook Pro (M4, 24GB RAM). We acknowledge that DNS-resolution validation remains necessary to confirm these preliminary findings. We explicitly invite collaboration from groups with HPC resources to extend this work. The codebase will be released following validation; research groups interested in early access for collaborative validation are invited to request access via the contact email below to discuss potential partnership.