analiza aiqbench
A certified upper bound on reconstruction error is not the same as a measured reduction in actual error, so the framework's "no-harm" guarantee depends on how well its stability assumptions and residual calibration hold in practice. The paper's selector rejects candidates that look unreliable and defaults to the baseline in strongly ill-posed settings, which is useful for practitioners wary of hallucinated reconstructions. Readers should weigh the reported numerical tests on a few PDE problems against the conditional nature of the guarantees and the need for independent validation on broader cases.
No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty
arXiv:2606.07153v2 Announce Type: replace-cross Abstract: Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify. This paper develops a no-harm certification-and-selection framework for physics-informed inverse learning. A learned reconstruction is accepted only when its residual-calibrated radius is no worse than the baseline radius, namely when $$R_{\mathrm{learn}}\le R_{\mathrm{base}}+\varepsilon_{\mathrm{safe}};$$otherwise, the method returns the baseline. The certificate combines data, physics, boundary or initial-condition, and optimization residuals. Under a conditional stability estimate, these residuals yield an a posteriori reconstruction-error bound and a deterministic uncertainty radius. A high-probability certificate is also derived for physics residuals estimated from independent random collocation points. Numerical tests on Poisson source recovery, inverse heat reconstruction, limited-angle tomography, elliptic coefficient identification, and stochastic residual validation show that the selector accepts certified improvements, rejects shifted, hallucinated, or unfinished candidates, and becomes conservative in strongly ill-posed regimes. The framework is therefore a certification-and-selection layer, not another reconstruction architecture.
Abstract:Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify. This paper develops a no-harm certification-and-selection framework for physics-informed inverse learning. A learned reconstruction is accepted only when its residual-calibrated radius is no worse than the baseline radius, namely when $$R_{\mathrm{learn}}\le R_{\mathrm{base}}+\varepsilon_{\mathrm{safe}};$$otherwise, the method returns the baseline. The certificate combines data, physics, boundary or initial-condition, and optimization residuals. Under a conditional stability estimate, these residuals yield an a posteriori reconstruction-error bound and a deterministic uncertainty radius. A high-probability certificate is also derived for physics residuals estimated from independent random collocation points. Numerical tests on Poisson source recovery, inverse heat reconstruction, limited-angle tomography, elliptic coefficient identification, and stochastic residual validation show that the selector accepts certified improvements, rejects shifted, hallucinated, or unfinished candidates, and becomes conservative in strongly ill-posed regimes. The framework is therefore a certification-and-selection layer, not another reconstruction architecture.
I need to clarify that a smaller certified upper bound does not necessarily imply a smaller actual reconstruction error. Strengthen the stability assumptions, calibration, and independent residual validation
Numerical Analysis (math.NA); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2606.07153 [math.NA]
(or arXiv:2606.07153v2 [math.NA] for this version)
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