| # Restore the stochastic sampling and discretization contract |
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|
| A computational physics group is maintaining the supplied historical py-pde |
| source. Complete stochastic `PDE.solve()` calculations remain numerically |
| stable because the current implementation compensates one scaling choice with |
| another. The defect is instead at the reusable interface between Gaussian |
| sampling and spatial discretization. |
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| The backend Gaussian primitive is a standard-normal sampling service. For the |
| same backend, seed, dtype, and array shape, its draw must not change when only |
| the physical grid measure changes. Cell volumes belong to the discretization |
| of a stochastic field: a variance-based solver converts continuum noise |
| variance to a cell increment using the inverse cell measure. Keeping these |
| responsibilities separate lets the primitive remain reusable across fields and |
| backends while solvers consistently interpret the public noise variance. |
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| The package also documents a lower-level direct-realization interface. A user |
| who chooses that route supplies the complete spatially discretized realization, |
| including any required measure factor. That does not change the contract of the |
| backend standard-normal primitive used by variance-based solvers. |
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| Run the offline reproduction, inspect the task context and complete source |
| snapshot, and repair the implementation so that both sides of this contract |
| hold for all supported valid inputs. Preserve deterministic PDE |
| behavior, public APIs, stochastic interpretations, supported backends, device |
| and dtype behavior, and unrelated functionality. |
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| Do not hard-code the public grids, seeds, controlled draw, lifecycle status, or |
| generated report. The public experiment states the architecture being studied |
| but does not name a target source file or prescribe a patch shape. Hidden tests |
| vary geometry, backend, solver, noise interpretation, and realization route. |
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