Compact Conditional Neural Fields for PDE Surrogates with Depth-Adapted Shared Operators

Learning PDE surrogates requires compact models that retain both global sample information and spatially localized context. We introduce a compact conditional neural field architecture in which a task encoder produces distributed query context together with a pooled sample condition, and a coordinate-conditioned decoder reconstructs the physical field. To reduce parameter storage without removing iterative refinement, repeated transformations share a base operator while using lightweight depth-specific low-rank adaptations. This design preserves node- or grid-level information paths while allowing a compact global condition to modulate the field decoder. Across standard PDE benchmarks, the resulting models achieve competitive accuracy with substantially fewer parameters: $0.00572$ relative $L_2$ on Elasticity using $0.624$M parameters, and $0.00523$, $0.00338$, and $0.00548$ on Airfoil, Pipe, and Darcy using fewer than $0.875$M parameters each. Relative to published Transolver-profile parameter counts, our models reduce parameter storage by approximately $54$–$84$, while maintaining errors close to strong published baselines under the reported protocols. Ablations show that compact global conditioning is most valuable when distributed communication is restricted, whereas full token or convolutional context can already carry substantial sample-specific information. The results support a parameter-efficient conditional-field route for PDE surrogate modeling that avoids forcing the solution through a single global bottleneck.