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:20260421T110000 DTEND;TZID=Asia/Kolkata:20260421T120000 DTSTAMP:20260415T150736Z 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:Ph.D. Thesis Defense: CDS: April 21\, 2026 "Transformer Neural Oper ators for Learning Generalized Solutions of Partial Differential 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 11:00 AM \nVenue: The Thesis Defense will be held on HYBRID Mode\n# 303 CDS Class R oom /MICROSOFT TEAMS.\n\nPlease click on the following link to join the Th esis Defense\nMS Teams link\n\n\n\nABSTRACT\nScientific machine learning i s transforming the way we solve physical dynamics governed by partial diff erential equations (PDEs). Solving nonlinear PDEs across multiple initial and boundary conditions requires re-running traditional numerical solvers\ , and existing physics-informed neural networks require costly retraining for each new condition. Furthermore\, given the limited availability of ob servational data in meteorological and oceanic sciences\, data assimilatio n in forward simulations is crucial. The above challenges are addressed by proposing three neural operators with architectural innovations: (1) the Physics-Informed Transformer Neural Operator (PINTO) for simulation-free P DE solving that is trained using only physics loss and generalizes to unse en initial and boundary conditions\, (2) the Physics-Guided Transformer Ne ural Operator (PGNTO) for finding generalizable PDE solutions from simulat ion data in the absence of governing equations\, and (3) the Attention bas ed Coordinate Operator (ACO) for the data assimilation task of reconstruct ing continuous fields from limited observational data. Collectively\, the above contributions push the boundaries of scientific machine learning in solving PDEs and data assimilation.\n\nThe first part of this thesis intro duces a novel Physics-Informed Transformer Neural Operator (PINTO). Curren t neural operator approaches\, though capable of learning functional mappi ngs between infinite-dimensional spaces\, suffer from two critical limitat ions: dependence on substantial simulation data and poor generalization to unseen conditions. PINTO addresses these fundamental challenges by introd ucing a novel physics-informed framework that achieves efficient generaliz ation through simulation-free\, physics-only training. The core innovation of PINTO lies in the development of iterative kernel-integral operator un its that leverage cross-attention mechanisms to transform domain points in to initial- and boundary-condition-aware representation vectors. This atte ntion-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 complete PDE soluti on spaces through a single forward pass. The architecture comprises three key stages: lifting layers that project the solution's domain coordinates into a higher-dimensional representation space\, iterative kernel integrat ion layers for context-aware representation learning\, and projection laye rs that map the learned representation to the solution space. We demonstra te PINTO's superior performance across critical fluid mechanics and engine ering applications\, including linear advection\, the nonlinear Burgers eq uation\, and the steady and unsteady Navier-Stokes equations\, spanning mu ltiple flow scenarios. Under challenging unseen conditions\, PINTO achieve s relative errors of merely 20 to 33\\% of those obtained by state-of-the- art physics-informed neural operator methods when compared with analytical and numerical solutions. Critically\, PINTO exhibits temporal extrapolati on capabilities absent in competing approaches\, accurately solving the ad vection and Burgers equations in time steps not present during training.\n \nIn the second part of the thesis\, we extend our framework to physics-gu ided transformer neural operators (PGNTO)\, trained on simulation data rat her than a physics loss\, to address scenarios where governing PDEs are un available and to eliminate the training instabilities that arise from phys ics loss in high-dimensional PDEs. Our PGNTO successfully solves standard PDE benchmarks\, including the nonlinear Burgers and airfoil problem\, and also scales to complex 3D turbulent flows\, specifically predicting wake dynamics behind wind turbines under varying inlet velocities. Across all t est cases\, PGNTO maintains superior accuracy\, with relative 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-based coordinat e operator (ACO) for neural data assimilation\, enabling the continuous re construction of fields from sparse observational data. By applying Gabor f ilters for coordinate lifting and Fourier filters for value representation \, ACO outperforms existing implicit neural representation networks on rec onstruction tasks. Notably\, a single ACO model generalizes across varying sparsity levels\, eliminating the need for separate models tailored to di fferent data availabilities. The performance of ACO is demonstrated using four challenging datasets: (i)sea surface height (SSH)\, (ii) chlorophyll concentration (CHL)\, (iii) Global surface temperature (GST)\, and (iv) se a surface temperature (SST). The ACO model is compared with other leading deep neural models for physical field reconstruction.\n\nOverall\, this th esis demonstrates that transformer-based neural operators can effectively address both physics-informed PDE solving and neural data assimilation\, a chieving unprecedented generalization\, computational efficiency\, and acc uracy while requiring minimal training data. Our suite of transformer neur al operators opens new avenues for real-time prediction and data assimilat ion 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:20250421T110000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR