Physics Simulation & ML Integration Roadmap

Roadmap

For learners with calculus/linear-algebra basics who want a systematic physics-AI knowledge system. In recommended order, ~4-8 weeks.

Step 1: PDE basics & numerics (2-3 weeks)

• FDM, FVM (conservation, flux limiter), FEM (variational, element stiffness)
• Exercise: 1D heat FDM + 2D Laplace FVM in Python

Step 2: Classical CFD & OpenFOAM (1-2 weeks)

• blockMesh -> snappyHexMesh -> icoFoam/pisoFoam
• Cylinder RANS (Re=10^6), extract Cd/Cl

Step 3: Data-driven surrogate (1-2 weeks)

• Surrogate vs numerical: speed/accuracy/generalization trade-off
• FNO / DeepONet / CNN-U-Net on Burgers / Darcy / AirfRANS

Step 4: Physics-informed (1-2 weeks)

• PINN: autodiff encodes PDE residual
• Failure modes and fixes

Step 5: Multiphysics & frontier (1-2 weeks)

• Differentiable physics (JAX-Fluids / WarpX)
• Neural-operator pretraining (ClimateLearn, FourCastNet)
• Digital twin & real-time simulation

Who it's for

• Engineers (mech/civil/aero) moving into physics AI
• ML engineers entering scientific computing
• Researchers building a physics-AI system