MiNO: Cotangent-bundle propagator learning for PDEs

[2608.15187] MiNO: Cotangent-bundle propagator learning for PDEs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.15187 (cs) [Submitted on 15 Aug 2026] Title: MiNO: Cotangent-bundle propagator learning for PDEs Authors: Gnankan Landry Regis N'guessan , Bum Jun Kim View a PDF of the paper titled MiNO: Cotangent-bundle propagator learning for PDEs, by Gnankan Landry Regis N'guessan and 1 other authors View PDF HTML (experimental) Abstract: Scientific machine learning for partial differential equations commonly targets solution fields, as in physics-informed neural networks, or solution maps, as in neural operators. We study a third target: the propagator itself, a phase and amplitude in phase space. The motivation is a gap in regularity. A transported discontinuity is nonsmooth in space and time, yet the rule that moves it can be a polynomial phase carrying unit amplitude, so the object that generates an evolution can be far smoother than the field it generates. The microlocal neural operator (MiNO) learns that object, using the eikonal equation for the phase and the transport equation for the amplitude, and recovers the solution by an oscillatory integral. Sharp fronts and caustics then belong to propagation geometry rather than to a field fitted pointwise. Small residuals certify more than the reconstructed field. They place the learned canonical relation, the geometry that carries singularities, close to the exact one, and they separate trainable error from the frequency-truncation tail. On a matched-budget discontinuous-advection benchmark, MiNO stops improving within 10,000 steps at the accuracy limit of its finite reconstruction window, a limit predicted in closed form, whereas a physics-informed neural network with neural-tangent-kernel loss balancing stays near its initial error. On smooth advection, the mean error is $3.84\times10^{-3}$ for MiNO and $3.12\times10^{-2}$ for a supervised Fourier neural operator. Single-branch MiNO is the smallest model compared, and one trained generator serves five unseen initial conditions without retraining. Comments: 35 pages, 6 figures Subjects: Machine Learning (cs.LG) ; Computational Engineering, Finance, and Science (cs.CE); Numerical Analysis (math.NA) Cite as: arXiv:2608.15187 [cs.LG] (or arXiv:2608.15187v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.15187 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bum Jun Kim [ view email ] [v1] Sat, 15 Aug 2026 12:02:03 UTC (289 KB) Full-text links: Access Paper: View a PDF of the paper titled MiNO: Cotangent-bundle propagator learning for PDEs, by Gnankan Landry Regis N'guessan and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs cs.CE cs.NA math math.NA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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