AI/ML Surrogate Models for Hydrodynamics
From Physics-Informed Neural Networks to Neural Operators
Seminar
Wednesday, 18 November 2026 · 09:00–10:30 IST
MAV Laboratory
1 The question
Can we replace repeated, computationally expensive hydrodynamic simulations with a learned model that predicts inundation for new scenarios while retaining the physical structure of the governing equations?
This seminar approaches that question through the two-dimensional shallow-water equations, the standard model for floods, tides and other wide, shallow flows. We move from the equations themselves to three families of learned models: physics-informed neural networks (PINNs), neural operators, and physics-informed neural operators (PINO). We finish with a hands-on exercise: an emulator, a learned model that stands in for the simulator and predicts inundation for scenarios it has not seen.
2 Learning pathway
2.1 1. Hydrodynamics and inundation
Understand depth-averaged flow, conservation of mass and momentum, topography, and the initial- and boundary-value problem.
2.2 2. Physics-informed neural networks
Represent one solution of the equations by a neural network, and train it so that it satisfies the equations themselves, not only data.
2.3 3. Neural operator learning
Instead of one solution, learn the whole map from a scenario (bed shape, initial water) to its solution, so that a new scenario needs no new training. Meet DeepONet and the Fourier Neural Operator (FNO).
2.4 4. Physics-informed neural operators
Train a neural operator on simulation data and on how well its predictions satisfy the equations.
2.5 5. Fast inundation emulation
Train and evaluate a learned model on a family of shallow-water scenarios. Examine accuracy, generalization, conservation and inference cost.
3 What you should take away
By the end of the seminar, you should be able to:
- Explain the assumptions and conservation laws behind the 2D shallow-water equations.
- Tell apart a network that represents one solution of a partial differential equation (PDE) from one that learns the map from any scenario to its solution (an operator).
- Explain how PINN and PINO training uses the governing equations.
- Train and evaluate a neural operator on scenarios not used during training.
- Critically assess whether a fast prediction is also physically credible.
4 How to use this site
Each chapter opens with learning objectives and closes with a summary and a few questions to check your understanding. Chapter 1 assumes no background in hydraulics; Chapter 2 introduces the neural-network ideas the rest of the seminar needs. Equations are numbered, and every figure and number comes from the seminar’s own runs. The hands-on notebooks let you rerun the key comparisons yourself.
Start with the setup guide before the seminar, and the syllabus for the schedule.
Scope of the first benchmark
The computational examples use smooth, fully wet water in a closed 10 m basin, over 0.5 s and, in a final test, 2.5 s. This keeps the numerical and learning ideas accessible. Moving shorelines (wetting and drying), sudden jumps in the water surface, friction and realistic flood boundaries are important extensions, not things the models here have been shown to handle.