LaSIPDE: Latent-Space Identification of Partial Differential Equations from indirect, high-dimensional measurements

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dc.authorid0000-0002-5429-7669
dc.authorid0000-0003-2308-4043
dc.authorid0000-0003-0298-0690
dc.contributor.authorKoulali, Imaneen_US
dc.contributor.authorTuran, Erhanen_US
dc.contributor.authorEskil, Mustafa Taneren_US
dc.date.accessioned2026-05-04T11:51:03Z
dc.date.available2026-05-04T11:51:03Z
dc.date.issued2026-04-14
dc.departmentIşık Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering and Natural Sciences, Department of Computer Engineeringen_US
dc.descriptionThe author(s) declared that financial support was received for this work and/or its publication. This research was part of project number 118C122 supported by the Industrial Ph.D. Program (2244) of the Scientific and Technological Research Council of Turkey (TUBITAK).en_US
dc.description.abstractDiscovering governing equations from data is a central challenge in scientific machine learning, particularly when observations are high-dimensional and the underlying state variables are not directly accessible. In this work, we introduce a framework for data-driven discovery of partial differential equations (PDEs) from indirect high-dimensional observations. The proposed approach combines nonlinear representation learning through an autoencoder with sparse identification of governing equations in the latent space, enabling simultaneous model reduction and PDE discovery while preserving spatial structure. Unlike existing methods that either operate on observable variables or discover latent ordinary differential equations, our framework identifies PDEs directly in the learned latent coordinates. We validate the approach on high-dimensional observations generated from Burgers and Korteweg-de Vries (KdV) systems, where the true state variables are intentionally hidden. In both cases, the method successfully recovers the correct dynamical operators, including diffusion, nonlinear advection, and dispersive terms. Although the recovered coefficients differ due to latent coordinate transformations, we show both theoretically and empirically that the discovered equations are dynamically equivalent to the ground-truth systems up to an affine transformation. These results demonstrate that governing PDEs can be recovered from indirect, high-dimensional data without access to the physical state variables, providing a foundation for interpretable model discovery in realistic measurement settings.en_US
dc.description.sponsorshipTÜBİTAKen_US
dc.description.versionPublisher's Version
dc.identifier.citationKoulali, I., Turan, E. & Eskil, M. T. (2026). LaSIPDE: Latent-Space Identification of Partial Differential Equations from indirect, high-dimensional measurements. Frontiers in Applied Mathematics and Statistics, 14, 1-14. doi:https://doi.org/10.3389/fams.2026.1807939en_US
dc.identifier.endpage14
dc.identifier.issn2297-4687
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/11729/7371
dc.identifier.urihttps://doi.org/10.3389/fams.2026.1807939
dc.identifier.volume14
dc.identifier.wosWOS:001750852200001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakEmerging Sources Citation Index (ESCI)en_US
dc.institutionauthorKoulali, Imaneen_US
dc.institutionauthorEskil, Mustafa Taneren_US
dc.institutionauthorid0000-0002-5429-7669
dc.institutionauthorid0000-0003-0298-0690
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublished
dc.publisherFrontiers Media SAen_US
dc.relation.ispartofFrontiers in Applied Mathematics and Statisticsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAutoencoderen_US
dc.subjectEquation discoveryen_US
dc.subjectLatent-space identificationen_US
dc.subjectPartial differential equationsen_US
dc.subjectPhysics-informed algorithmen_US
dc.subjectReduced-order modelingen_US
dc.subjectSparse regressionen_US
dc.subjectSystem identificationen_US
dc.titleLaSIPDE: Latent-Space Identification of Partial Differential Equations from indirect, high-dimensional measurementsen_US
dc.typeArticleen_US
dspace.entity.typePublicationen_US

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