🤖 AI Summary
This work addresses the lack of theoretical grounding in the trade-off between fidelity and preservation of physical observables in physics-informed compression. The authors propose an analytical framework based on the local geometry of latent spaces, revealing that anisotropic distributions of compression noise induce an inherent conflict between physical alignment loss and conventional distortion metrics. Key contributions include a rate–distortion theory formulated on tangent spaces, an alignment diagnostic tool grounded in principal eigensubspace overlap, and a geometric alignment strategy integrating latent-space sensitivity analysis, entropy modeling, and physics-gradient guidance. Experiments across multiple scientific datasets demonstrate that the proposed metrics accurately predict the actual performance trade-offs between physical consistency and data-space reconstruction fidelity.
📝 Abstract
In AI for Science, physics-informed losses are increasingly used to train learned compressors for scientific data, but their rate-distortion implications remain poorly understood. At fixed bitrate, these objectives often improve preservation of a target physical observable while degrading standard reconstruction fidelity. We develop a local geometric theory showing that this tradeoff is governed by the interaction of latent-space sensitivities induced by the entropy model, the physical observable, and the distortion metric. At each operating point, these induce preferred directions along which compression noise should be suppressed, yielding an anisotropic error-allocation mechanism. When these directions are misaligned, improving the observable at fixed rate necessarily worsens standard distortion, establishing a fundamental limit on simultaneous preservation. We formalise this through a local tangent-space rate-distortion law and introduce a practical alignment diagnostic based on dominant eigenspace overlap. Experiments across scientific domains test the theory and validate that the alignment diagnostic correlates with observed data- and physics-space trade-offs.