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:191@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20260421T120000 DTEND;TZID=Asia/Kolkata:20260421T130000 DTSTAMP:20260421T052655Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-cds-april-21-2026-tr ansformer-neural-operators-for-learning-generalized-solutions-of-partial-d ifferential-equations-and-data-assimilation/ SUMMARY:Change in timings: Ph.D. Thesis Defense: CDS: April 21\, 2026 "Tran sformer Neural Operators for Learning Generalized Solutions of Partial Dif ferential Equations and Data Assimilation" DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Def ense\n\n\n\nSpeaker : Mr. Boya Sumanth Kumar\nS.R. Number : 06-18-01-10-12 -20-1-18435\nTitle : "Transformer Neural Operators for Learning Generalize d Solutions of Partial Differential Equations and Data Assimilation"\nRese arch Supervisor : Dr. Deepak Subramani\nThesis examiner : Prof. Anoop Kris hnan\, IIT Delhi\nDate &\; Time : April 21\, 2026 (Tuesday) at 12:00 No on\nVenue: The Thesis Defense will be held on HYBRID Mode\n# 303 CDS Class Room /MICROSOFT TEAMS.\n\nPlease click on the following link to join the Thesis Defense\nMS Teams link\n\n\n\nABSTRACT\nScientific machine learning is transforming the way we solve physical dynamics governed by partial di fferential equations (PDEs). Solving nonlinear PDEs across multiple initia l and boundary conditions requires re-running traditional numerical solver s\, and existing physics-informed neural networks require costly retrainin g for each new condition. Furthermore\, given the limited availability of observational data in meteorological and oceanic sciences\, data assimilat ion in forward simulations is crucial. The above challenges are addressed by proposing three neural operators with architectural innovations: (1) th e Physics-Informed Transformer Neural Operator (PINTO) for simulation-free PDE solving that is trained using only physics loss and generalizes to un seen initial and boundary conditions\, (2) the Physics-Guided Transformer Neural Operator (PGNTO) for finding generalizable PDE solutions from simul ation data in the absence of governing equations\, and (3) the Attention b ased Coordinate Operator (ACO) for the data assimilation task of reconstru cting continuous fields from limited observational data. Collectively\, th e above contributions push the boundaries of scientific machine learning i n solving PDEs and data assimilation.\n\nThe first part of this thesis int roduces a novel Physics-Informed Transformer Neural Operator (PINTO). Curr ent neural operator approaches\, though capable of learning functional map pings between infinite-dimensional spaces\, suffer from two critical limit ations: dependence on substantial simulation data and poor generalization to unseen conditions. PINTO addresses these fundamental challenges by intr oducing a novel physics-informed framework that achieves efficient general ization through simulation-free\, physics-only training. The core innovati on of PINTO lies in the development of iterative kernel-integral operator units that leverage cross-attention mechanisms to transform domain points into initial- and boundary-condition-aware representation vectors. This at tention-based architecture enables context-aware learning that fundamental ly differs from existing neural operators\, allowing PINTO to learn mappin gs from input functions (initial/boundary conditions) to complete PDE solu tion spaces through a single forward pass. The architecture comprises thre e key stages: lifting layers that project the solution's domain coordinate s into a higher-dimensional representation space\, iterative kernel integr ation layers for context-aware representation learning\, and projection la yers that map the learned representation to the solution space. We demonst rate PINTO's superior performance across critical fluid mechanics and engi neering applications\, including linear advection\, the nonlinear Burgers equation\, and the steady and unsteady Navier-Stokes equations\, spanning multiple flow scenarios. Under challenging unseen conditions\, PINTO achie ves relative errors of merely 20 to 33\\% of those obtained by state-of-th e-art physics-informed neural operator methods when compared with analytic al and numerical solutions. Critically\, PINTO exhibits temporal extrapola tion capabilities absent in competing approaches\, accurately solving the advection and Burgers equations in time steps not present during training. \n\nIn the second part of the thesis\, we extend our framework to physics- guided transformer neural operators (PGNTO)\, trained on simulation data r ather than a physics loss\, to address scenarios where governing PDEs are unavailable and to eliminate the training instabilities that arise from ph ysics loss in high-dimensional PDEs. Our PGNTO successfully solves standar d PDE benchmarks\, including the nonlinear Burgers and airfoil problem\, a nd also scales to complex 3D turbulent flows\, specifically predicting wak e dynamics behind wind turbines under varying inlet velocities. Across all test cases\, PGNTO maintains superior accuracy\, with relative errors tha t are only one-third of those of competing neural operators.\n\nFinally\, in the third part of the thesis\, we introduce the Attention-based coordin ate operator (ACO) for neural data assimilation\, enabling the continuous reconstruction of fields from sparse observational data. By applying Gabor filters for coordinate lifting and Fourier filters for value representati on\, ACO outperforms existing implicit neural representation networks on r econstruction tasks. Notably\, a single ACO model generalizes across varyi ng sparsity levels\, eliminating the need for separate models tailored to different data availabilities. The performance of ACO is demonstrated usin g four challenging datasets: (i)sea surface height (SSH)\, (ii) chlorophyl l concentration (CHL)\, (iii) Global surface temperature (GST)\, and (iv) sea surface temperature (SST). The ACO model is compared with other leadin g deep neural models for physical field reconstruction.\n\nOverall\, this thesis demonstrates that transformer-based neural operators can effectivel y address both physics-informed PDE solving and neural data assimilation\, achieving unprecedented generalization\, computational efficiency\, and a ccuracy while requiring minimal training data. Our suite of transformer ne ural operators opens new avenues for real-time prediction and data assimil ation 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:20250421T120000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR