Prompt 19 — Inverse problem and parameter-inference builder

Inputs

FORWARD_MODEL: {{FORWARD_MODEL_JSON}}
DATASET_CARD: {{DATASET_CARD_JSON}}
MEASUREMENT_RECORDS: {{MEASUREMENT_RECORDS_JSON}}
PRIOR_OR_REGULARIZATION_POLICY: {{PRIOR_OR_REGULARIZATION_POLICY_JSON}}
CANDIDATE_INFERENCE_METHODS: {{CANDIDATE_INFERENCE_METHODS_JSON}}
VALIDATION_RECEIPTS: {{VALIDATION_RECEIPTS_JSON}}

Task

Build objects for inverse problems, parameter estimation, state estimation, model calibration, and identifiability analysis.

• define the forward map, observed quantities, latent variables, parameters, nuisance variables, and noise model;
• distinguish structural identifiability, practical identifiability, observability, and numerical conditioning;
• record priors, regularization, constraints, loss or likelihood, and optimization or sampling method;
• keep calibration data separate from held-out and intervention data;
• report parameter covariance, posterior dependence, multimodality, non-identifiability, and sensitivity;
• compare alternative forward models and noise assumptions;
• perform or summarize posterior predictive, residual, bootstrap, cross-validation, or profile checks as supplied;
• record solver seeds, initialization, convergence diagnostics, and stopping rules;
• avoid causal language unless interventions and assumptions support it;
• reject point estimates that conceal unresolved non-identifiability.

Return a physics-library-batch object.