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Include velocity and density multipliers needed by advection and continuity. Invert only the strictly positive density, rather than velocities which cross zero. Match periodic spatial boundaries and resolve the early time transient. Use the STLSQ threshold from the reported workflow for this nondimensional example. Correct the displayed variable-density equations and name the third state rho consistently. Related to dynamicslab#589.
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Related to #589. The current
howto_PDEexample cannot represent its own advection or continuity equations: its nonlinear library contains only reciprocals, so terms such asu u_1andrho v_2are absent. Inverting velocities also creates singular features where the flow crosses zero.Include
u,v,rhoand only1/rho. Match the simulator's periodic spatial boundaries, use 100 time samples to resolve the initial transient, and use the reported STLSQ setup for this nondimensional example. Correct the displayed variable-density equations and label density consistently. Regenerate and execute the paired notebook so the rendered tutorial includes the corrected code and results.Executed the actual tutorial's data generation and both PDE fits on base and head. Both fits now select exactly the expected 14 coupled momentum/continuity terms, with no extras. The largest coefficient error is
8.73e-4for PDE-FIND and5.05e-3for WeakSINDy. Both Burgers coefficient arrays remain exact in matched-seed source replays.A separate NumPy periodic-difference implementation generates a flow with different initial phases and amplitudes and evaluates the learned equations against its RHS:
These are simulated-workload checks, not measured-fluid accuracy or a general discovery guarantee. The 2.1.0 version of the reporter's original library already recovers the expected terms with and without the stated noise; this PR repairs the separate configuration problem in the current tutorial and does not close the historical report.
The full tutorial script completes on its simulated data with open CVXPY solvers, including its later Trapping/plotting sections; those sections are smoke checks, not an accuracy claim. The project notebook test also passes, and 171 feature-library/weak-form checks pass with one skip. The standard full-suite attempt has the same 35 failing nodes on unchanged main and this head, primarily the installed GUROBI solver rejecting
max_iter; the alternative environment cannot collect the full optimizer suite without optional MIOSR. Pre-commit passes. Strict Sphinx HTML builds complete without warnings on base and head.