BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Asia/Kolkata X-WR-TIMEZONE:Asia/Kolkata BEGIN:VEVENT UID:189@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20260407T110000 DTEND;TZID=Asia/Kolkata:20260407T120000 DTSTAMP:20260404T141956Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-cds-april-07-2026-tr ansformer-neural-operators-for-learning-generalized-solutions-of-partial-d ifferential-equations-and-data-assimilation/ SUMMARY:Postpone: Ph.D. Thesis Defense: CDS: April 07\, 2026 "Transformer N eural Operators for Learning Generalized Solutions of Partial Differential Equations and Data Assimilation" DESCRIPTION:Please Note: Mr. Boya Sumanth kumar's Ph.D. thesis Defense whic h was originally scheduled on April 07 at 11:00 AM \, has been postponed. Regret for the inconvenience caused. We will broadcast the detailed timing s and venue shortly.\n\n\n\nDEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\ nPh.D. Thesis Defense\n\n\n\nSpeaker : Mr. Boya Sumanth Kumar\nS.R. Number : 06-18-01-10-12-20-1-18435\nTitle : "Transformer Neural Operators for Le arning Generalized Solutions of Partial Differential Equations and Data As similation"\nResearch Supervisor : Dr. Deepak Subramani\nThesis examiner : Prof. Anoop Krishnan\, IIT Delhi\nDate &\; Time : April 07\, 2026 (Tue sday) at 11:00 AM\nVenue : The Thesis Defense will be held on HYBRID Mode\ n# 303 CDS Class Room /MICROSOFT TEAMS.\n\nPlease click on the following l ink to join the Thesis Defense\nMS Teams link\n\nABSTRACT\nScientific mach ine learning is transforming the way we solve physical dynamics governed b y partial differential equations (PDEs). Solving nonlinear PDEs across mul tiple initial and boundary conditions requires re-running traditional nume rical solvers\, and existing physics-informed neural networks require cost ly retraining for each new condition. Furthermore\, given the limited avai lability of observational data in meteorological and oceanic sciences\, da ta assimilation in forward simulations is crucial. The above challenges ar e addressed by proposing three neural operators with architectural innovat ions: (1) the Physics-Informed Transformer Neural Operator (PINTO) for sim ulation-free PDE solving that is trained using only physics loss and gener alizes to unseen initial and boundary conditions\, (2) the Physics-Guided Transformer Neural Operator (PGNTO) for finding generalizable PDE solution s from simulation data in the absence of governing equations\, and (3) the Attention based Coordinate Operator (ACO) for the data assimilation task of reconstructing continuous fields from limited observational data. Colle ctively\, the above contributions push the boundaries of scientific machin e learning in solving PDEs and data assimilation.\n\nThe first part of thi s thesis introduces a novel Physics-Informed Transformer Neural Operator ( PINTO). Current neural operator approaches\, though capable of learning fu nctional mappings between infinite-dimensional spaces\, suffer from two cr itical limitations: dependence on substantial simulation data and poor gen eralization to unseen conditions. PINTO addresses these fundamental challe nges by introducing a novel physics-informed framework that achieves effic ient generalization through simulation-free\, physics-only training. The c ore innovation of PINTO lies in the development of iterative kernel-integr al operator units that leverage cross-attention mechanisms to transform do main points into initial- and boundary-condition-aware representation vect ors. This attention-based architecture enables context-aware learning that fundamentally differs from existing neural operators\, allowing PINTO to learn mappings from input functions (initial/boundary conditions) to compl ete PDE solution spaces through a single forward pass. The architecture co mprises three key stages: lifting layers that project the solution's domai n coordinates into a higher-dimensional representation space\, iterative k ernel integration layers for context-aware representation learning\, and p rojection layers that map the learned representation to the solution space . We demonstrate PINTO's superior performance across critical fluid mechan ics and engineering applications\, including linear advection\, the nonlin ear Burgers equation\, and the steady and unsteady Navier-Stokes equations \, spanning multiple flow scenarios. Under challenging unseen conditions\, PINTO achieves relative errors of merely 20 to 33\\% of those obtained by state-of-the-art physics-informed neural operator methods when compared w ith analytical and numerical solutions. Critically\, PINTO exhibits tempor al extrapolation capabilities absent in competing approaches\, accurately solving the advection and Burgers equations in time steps not present duri ng training.\n\nIn the second part of the thesis\, we extend our framework to physics-guided transformer neural operators (PGNTO)\, trained on simul ation data rather than a physics loss\, to address scenarios where governi ng PDEs are unavailable and to eliminate the training instabilities that a rise from physics loss in high-dimensional PDEs. Our PGNTO successfully so lves standard PDE benchmarks\, including the nonlinear Burgers and airfoil problem\, and also scales to complex 3D turbulent flows\, specifically pr edicting wake dynamics behind wind turbines under varying inlet velocities . Across all test cases\, PGNTO maintains superior accuracy\, with relativ e errors that are only one-third of those of competing neural operators.\n \nFinally\, in the third part of the thesis\, we introduce the Attention-b ased coordinate operator (ACO) for neural data assimilation\, enabling the continuous reconstruction of fields from sparse observational data. By ap plying Gabor filters for coordinate lifting and Fourier filters for value representation\, ACO outperforms existing implicit neural representation n etworks on reconstruction tasks. Notably\, a single ACO model generalizes across varying sparsity levels\, eliminating the need for separate models tailored to different data availabilities. The performance of ACO is demon strated using four challenging datasets: (i)sea surface height (SSH)\, (ii ) chlorophyll concentration (CHL)\, (iii) Global surface temperature (GST) \, and (iv) sea surface temperature (SST). The ACO model is compared with other leading deep neural models for physical field reconstruction.\n\nOve rall\, this thesis demonstrates that transformer-based neural operators ca n effectively address both physics-informed PDE solving and neural data as similation\, achieving unprecedented generalization\, computational effici ency\, and accuracy while requiring minimal training data. Our suite of tr ansformer neural operators opens new avenues for real-time prediction and data assimilation in physics and engineering applications.\n\n\n\nALL ARE WELCOME CATEGORIES:Events,Thesis Defense END:VEVENT BEGIN:VTIMEZONE TZID:Asia/Kolkata X-LIC-LOCATION:Asia/Kolkata BEGIN:STANDARD DTSTART:20250407T110000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR