CoSGF: 4D Scientific Gaussian Fields for High-Resolution Reconstruction from Complementary Observations

High-fidelity numerical simulations resolve the spatiotemporal structures needed to study complex physical systems, but generating and retaining long high-resolution trajectories can be computationally and storage intensive. Existing approaches reduce data requirements through augmentation, few-shot learning, flexible representations, or physical priors, but reconstruction is often organized around a dominant observation pathway; increasing model capacity or adding auxiliary constraints alone cannot recover information that is not identifiable from coarse measurements. We instead formulate scientific-field reconstruction as the joint inference of a shared physical field from heterogeneous but complementary scientific evidence. We instantiate this formulation with a 4D Scientific Gaussian Field whose primitives encode physical variables rather than appearance. Numerical measurements and retained scientific visualizations constrain the same field through their corresponding forward processes, while dataset-specific physical and geometric knowledge further restricts residual ambiguity. Rather than treating physics as an unrestricted third loss, physics-driven optimizer displacements are coordinated using the local sensitivity of active observations and finite forward verification, so refinement preferentially acts on weakly observed degrees of freedom while preserving evidence-supported content. The HR field remains inaccessible during reconstruction and is used only for evaluation, while the framework directly produces an analysis-ready high-resolution scientific field. In the reported comparison over four single-phase datasets at $4\times$ and $8\times$ reconstruction ratios, CoSGF achieves the highest mean PSNR among the compared methods.