{"root_cause":"The dimensional PINN objective is severely ill-conditioned. Mixing length near 1e-3 m with temperature near 500 K makes the PDE and boundary residuals numerically incomparable; the nine-order gradient-norm gap indicates that optimization can reduce the PDE residual while providing negligible effective pressure to satisfy the boundary conditions.","confidence":0.9,"evidence":["Observation: the PDE residual loss is below 1e-7.","Observation: boundary values remain physically wrong.","Observation: input and output scales differ substantially: length is about 1e-3 m and temperature about 500 K.","Observation: per-loss gradient norms differ by about nine orders of magnitude.","Inference: the small dimensional PDE loss is not evidence that the full boundary-value problem is solved.","Inference: the gradient disparity is consistent with unit-induced conditioning failure and one loss term dominating parameter updates."],"competing_hypotheses":["The boundary-condition implementation, target values, point locations, or derivative coordinates are wrong.","Boundary points are sampled or weighted too sparsely relative to interior collocation points.","The network architecture cannot represent the boundary behavior, although this is less likely than scaling given the nine-order gradient disparity.","Derivative computation uses normalized coordinates without the required chain-rule scale factors."],"first_action":"Rewrite one cheap run in dimensionless coordinates and fields, including explicit chain-rule factors, then measure the initial and early-training PDE and boundary losses, physical boundary errors, and per-term parameter-gradient norms using the same seed. The prediction is about conditioning; this experiment does not require choosing a gradient aggregation method.","prediction_if_true":"Nondimensionalization will shrink the gradient-norm gap by several orders of magnitude, and boundary error will fall while the dimensionless PDE residual remains controlled.","prediction_if_false":"The gradient gap or boundary failure will persist after correct nondimensionalization, shifting priority to auditing boundary targets/collocation and coordinate-chain-rule implementation, followed by a tiny boundary-value overfit test.","immediate_changes":[],"fallback_logic":[]}
