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Better int - #122
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pcpet wants to merge 194 commits into
Open
Better int#122pcpet wants to merge 194 commits into
pcpet wants to merge 194 commits into
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…eriori-estimator Add PINN a posteriori estimator notebook for unit-square Poisson problem
…eriori-estimator Add interval Hessian evaluation and Sobolev order-2 support, plus PINN a posteriori notebook
…eriori-estimator-egyu8b Add Hessian enclosures and Sobolev order=2 support (API, docs, tests, notebook)
…eriori-estimator
Add Hessian enclosures and W^{2,p} support (eval_hessian, propagation, docs, tests, notebook)
…eriori-estimator Add Hessian interval enclosures and Sobolev order=2 (Hessian-aware norms), docs, notebook, and tests
…rent-output Plot PDE residual in panel (b) of Poisson PINN notebook
…rent-output Notebook: cache interval power bounds, certify residual L2, and visualize residuals
…rent-output notebooks: cache interval power bounds, add autograd flag, and visualize residuals in Poisson PINN notebook
…rent-output notebooks: autograd fix, caching and visualization updates in Poisson PINN a-posteriori notebook
…rent-output-ie0k4z Modal Poisson source, autograd control, and cached certified residuals with visualization tweaks
…norm-computations Add PZ two-jet norm diagnostics
…-rendering Handle tuple-backed PZ trace components
…ynomial-zonotopes Prune zero polynomial zonotope terms
…book-for-diagnostics Clean up affine PZ two-jet notebook diagnostics
Avoids naively squaring the polynomial zonotope enclosures for the neural network 2 jet, as was done with pz_symmetric_hessian_sum_squares(jet.H). This speeds up computation of W22 norm but also L2 and W12.
…red-function Optimize direct PZ two-jet squared integration
Replace the dependent interval-product enclosure with the same outward-rounded scalar endpoint/extrema routine added to main. Preserve PyTorch float32 padding and the known sign. Add the scalar API, the rounding argument, high-precision regressions and Hessian integration tests. Affine PZ enclosures are unchanged. Validation: targeted interval/PZ tests, 236 passed; full better-int suite, 277 passed.
Use the outward-rounded stable 4*q/(1+q)^2 endpoint formula with q=exp(-2*abs(x)). Select extrema by distance to zero, preserve exact zero-domain value 1, clip bounds to [0,1], and handle underflow conservatively. Apply the scalar helper to the interval Jacobian/Hessian path and deep hybrid derivative interval factors, rounding again after tensor conversion. Expose tanh_prime_bounds, document the rounding argument, and fix the optional PyTorch import guard so scalar activation bounds work without PyTorch. Validation: all 333 tests passed, including high-precision references, saturated-tail regressions, subnormal inputs/outputs, tensor dtype conversion, and import without PyTorch.
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added hessian computations and an example to compute a residual assiciated to a PINN.