Discovering Physical Representation Languages

2026-09-20

AI Summary

本文解决了从匿名控制实验中直接恢复隐藏物理本体的问题，提出了一种可识别理论和多项式时间过程来恢复测量类型、非可逆细化语义等。

Abstract

Before a machine can discover a physical law, it must discover what its measurements are: which observations live on cells, which are intensive or extensive, which sectors are dual, and which distinctions are merely gauge. We introduce physical representation-language discovery, the problem of recovering this hidden ontology directly from anonymous controlled experiments. We give an identifiability theory and constructive polynomial-time procedure that recovers a carrier and differential sequence, measurement types and orientation twist, noninvertible refinement semantics, primal-dual Maxwell diagrams, and the residual equivalences that no permitted experiment can break. The theory turns material nuisance into a commutant, uses refinement to separate quantities from coordinates, and selects physics only after its representation has been recovered. For a certified finite experiment family, we prove an end-to-end two-stage measurement bound and a matching minimax rate in dimension, accuracy, and confidence. Blind Maxwell experiments recover complete primal/relative-dual ontologies on regular and unstructured carriers under jointly corrupted observations; an independent unstructured RLC system demonstrates that the result is not specific to Maxwell. The framework scales to tens of thousands of cells per carrier, while stress audits demonstrate robustness across severe physical regimes - including non-Markovian memory, nonlinearities, nonlocality, and complex constitutive hysteresis. A public FDTD audit demonstrates the emergence of anonymous curl structure from incomplete field data, while characterizing the informational prerequisites for complete recovery. The goal is to move scientific ML from learning laws in a human-supplied language to discovering the language in which laws become expressible, establishing exact theoretical limits on observational identifiability.

Problem

• Physical Representation
• Ontology Recovery
• Controlled Experiments
• Measurement Types
• Observational Identifiability

Innovation

• Physical Representation-Language Discovery
• Identifiability Theory
• Polynomial-Time Procedure
• Commutant
• Refinement Semantics