# structural causal model

Constitutive model discovery now asks which environmental variable drives which mechanism, not merely which candidate terms fit the response. A constitutive model with internal variables is written as a time-unrolled structural causal model, candidate graphs are scored by a weak-form equilibrium gap through the boundary value problem, and climate-chamber protocols count as interventions. On a synthetic perforated plate at about 0.01 px displacement noise, interventional data recover the true graph exactly in 7 of 10 runs, with no attribution error; correlated observational data never do.

Constitutive model discovery now asks which environmental variable drives which mechanism, not merely which candidate terms fit the response. A constitutive model with internal variables is written as a time-unrolled structural causal model, candidate graphs are scored by a weak-form equilibrium gap through the boundary value problem, and climate-chamber protocols count as interventions. On a synthetic perforated plate at about 0.01 px displacement noise, interventional data recover the true graph exactly in 7 of 10 runs, with no attribution error; correlated observational data never do.

The authors present SHERLOCK, an interpretable deep generative framework that represents genetic and pharmacological perturbations as structured interventions on a latent baseline cellular state, learns correlated and sparse perturbation representations, enables counterfactual estimation of downstream transcriptional effects under explicit identifiability assumptions, quantifies condition-dependent responses, and compositionally models combinatorial perturbations; across genome-scale CRISPR, chemical, and spatial perturbation datasets, it recovers perturbation relationships concordant with known biological pathways and pharmacological properties, identifies condition-dependent responses, and predicts combinatorial perturbation effects.

The authors present SHERLOCK, an interpretable deep generative framework that represents genetic and pharmacological perturbations as structured interventions on a latent baseline cellular state, learns correlated and sparse perturbation representations, enables counterfactual estimation of downstream transcriptional effects under explicit identifiability assumptions, quantifies condition-dependent responses, and compositionally models combinatorial perturbations; across genome-scale CRISPR, chemical, and spatial perturbation datasets, it recovers perturbation relationships concordant with known biological pathways and pharmacological properties, identifies condition-dependent responses, and predicts combinatorial perturbation effects.