Seminar syllabus
1 Overview
AI/ML Surrogate Models for Hydrodynamics: From Physics-Informed Neural Networks to Neural Operators
- Date: Wednesday, 18 November 2026
- Time: 09:00–10:30 IST
- Duration: 90 minutes
- Audience: Mixed background (students, researchers and faculty)
- Format: Short lectures, demonstrations and guided computational work
2 Learning objectives
After the seminar, participants should be able to:
- Describe the depth-averaged assumptions and conservation form of the two-dimensional shallow-water equations.
- Formulate a PINN loss from the PDE residual (how far a candidate solution is from satisfying the partial differential equations), the initial conditions and the boundary conditions.
- Explain operator learning as learning a mapping from input functions or fields to solution fields.
- Describe the basic ideas behind DeepONet, FNO and PINO.
- Train or run a neural-operator model for a shallow-water scenario and evaluate its predictions against a numerical reference.
- Identify limitations associated with generalization to new scenarios, walls and other non-periodic boundaries, conservation, and moving shorelines (wetting and drying).
3 Schedule
| Time | Topic | Duration |
|---|---|---|
| 09:00–09:08 | Motivation: why hydrodynamic surrogates? | 8 min |
| 09:08–09:20 | Inundation and the 2D shallow-water equations | 12 min |
| 09:20–09:33 | PINNs: solution networks and physics losses | 13 min |
| 09:33–09:48 | Operator learning: DeepONet and FNO | 15 min |
| 09:48–10:00 | PINO: physics-informed operator learning | 12 min |
| 10:00–10:25 | Hands-on: FNO/PINO shallow-water experiment | 25 min |
| 10:25–10:30 | Results, limitations and discussion | 5 min |
4 Computational problem
The common problem throughout the seminar is two-dimensional depth-averaged flow governed by the shallow-water equations. A custom finite-volume solver provides reference simulations. The benchmark uses smooth, fully wet scenarios in a walled basin over four terrain families; friction and wetting/drying are discussed as extensions but not modelled.
The learning exercises are deliberately complementary:
| Exercise | Model | Main question |
|---|---|---|
| 1 | Finite-volume solver | What is the reference hydrodynamic solution? |
| 2 | PINN (a plain fully connected network) | Can a network approximate one solution while satisfying the equations? |
| 3 | FNO | Can a network learn a mapping across multiple scenarios? |
| 4 | PINO | What changes when the PDE residual is added to operator training? |
DeepONet is introduced conceptually; the operator implementation uses an FNO. The central experimental comparison is data-trained FNO versus physics-informed FNO/PINO.
5 Prerequisites
Participants will benefit from familiarity with:
- Basic calculus, partial differential equations and vector notation.
- Introductory fluid mechanics.
- Basic Python and NumPy.
- Basic neural-network concepts.
Prior experience with PyTorch, automatic differentiation or Fourier neural operators is not required. The material will introduce the necessary ideas, but the hands-on exercises will move more quickly for participants already comfortable with Python.
6 Software and execution
The hands-on exercises are Jupyter notebooks that run in a ready-made Docker container. Participants need only Docker Desktop (Windows/macOS) or Docker Engine (Linux) and the hands-on folder; a host Python installation, Conda environment or package installation is not required. The setup guide covers both.
The container includes the shallow-water solver, dataset tools and the PINN, FNO and PINO training stack (CPU-only PyTorch).
7 What the seminar will and will not claim
A neural surrogate can make repeated predictions much faster after training, but speed alone does not establish physical reliability. Evaluation will distinguish training from inference cost and will examine held-out scenarios, prediction error, mass conservation and PDE residuals.
The introductory benchmark is not a complete operational flood model. In particular, standard smooth-field PINNs and Fourier-based operators do not automatically solve the numerical and physical challenges of discontinuities, moving wet/dry fronts, complex coastlines or arbitrary boundary conditions.