verify_pde_consistency

Checks that the computed field actually satisfies the equation it claims to solve.

Group: Check the answer.

Parameters

Parameter	Type	Required	Default
solution_files	string	yes
source_term	string	yes
coefficient	string	no	'1.0'
domain	string	no	'[[0,1],[0,1]]'
equation	string	no	''

What the model reads

The text below is the tool's own description, exactly as the AI model receives it.

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Does your field actually satisfy the equation the task stated?

A refinement study CANNOT answer this. Measured over 464 runs, result
sets with a complete set of levels self-converge at a median order
of 1.96 to 1.99 — the discretisation is fine — while a field that
converges cleanly to the WRONG function looks identical in that study.
Your own mesh-independence verdict does not separate them either: it
catches three quarters of the wrong runs and also fires on half the
correct ones.

This checks the weak identity that any solution of
-div(K grad u) = f obeys for a smooth v vanishing on the boundary:

    integral of u * (L* v)  ==  integral of f * v

using ONLY the operator and source from your task and the values you
already wrote. There is no reference solution in it.

Measured separation, by execution: a field that solves the stated
problem drives this residual down by roughly a factor of four per
refinement, from 2.3e-02 to 2.6e-04 over four levels; a field that does
not leaves it FLAT, near 6.4 at every level. The verdict is decided by
whether it falls, not by any particular value.

Args:
    solution_files: comma-separated paths to your solution CSVs, one
        per mesh level, each `x, y, u` (or `x, y, z, u`) with a header.
    source_term: the task's source term, in the task's own Python
        notation, e.g. "36*x**3*y - 20*x**3/3 + 8/3".
    coefficient: "2.5" for a scalar, or a symmetric tensor written as
        "[[3,-1],[-1,2]]". Must match what the task prescribes.
    domain: the box the problem lives on, "[[x0,x1],[y0,y1]]".
    equation: your task's equation, copied from its EQUATION line.
        REQUIRED. This check implements the second-order scalar
        diffusion form only, and it refuses anything else rather than
        answering about an operator it does not model.