PDE problems

Group PDEs by family and see which methods/baselines appear across papers.

How to use

Pick a PDE family → click View papers to jump into the Research table.

Browse by PDE problem

This page groups PDEs into common families. Each row links to the Research table with a PDE filter applied.

PDE tags for index-only papers are auto-extracted from titles and may be incomplete. Curated pages include better coverage.

Electromagnetics

PDE	# papers	Common method classes	Common baselines (curated pages)
Maxwell	4	Operator learning, Benchmark, PINN / physics-constrained	FNO, Transformer, ResNet, U-Net	View papers

Elliptic PDEs

PDE	# papers	Common method classes	Common baselines (curated pages)
Darcy flow	14	Operator learning, Diffusion, Benchmark	FNO, DeepONet, U-Net, PINO, U-NO	View papers
Helmholtz	4	Diffusion, PINN / physics-constrained	DiffusionPDE, PINO, FNO, DeepONet, PINN	View papers
Helmholtz equation	1	Diffusion	FNO, PINO, U-NO, U-WNO, Diffusion inpainting baseline	View papers
Poisson	12	PINN / physics-constrained, Operator learning, Diffusion	FNO, PINN, DeepONet, DiffusionPDE, PINO	View papers
Poisson equation	1	Diffusion	FNO, PINO, U-NO, U-WNO, Diffusion inpainting baseline	View papers

Fluid dynamics

PDE	# papers	Common method classes	Common baselines (curated pages)
Compressible Navier–Stokes	1	Benchmark	FNO, U-Net, ResNet, DeepONet, PINN	View papers
Fluid dynamics	7	SciML, Operator learning, PINN / physics-constrained	U-Net, TF-Net, ResNet, GCN, FCN	View papers
Kolmogorov flow	4	Diffusion, SciML, Operator learning	FNO, DeepONet, U-Net, DiffusionPDE, PINO	View papers
Navier–Stokes	24	Operator learning, Diffusion, PINN / physics-constrained	FNO, DeepONet, U-Net, PINO, DiffusionPDE	View papers
Navier–Stokes (2D/3D variants)	1	Operator learning	FNO, DeepONet, U-Net	View papers

Geophysical flows

PDE	# papers	Common method classes	Common baselines (curated pages)
Atmospheric dynamics (primitive equations)	11	Operator learning, SciML, Graph / mesh	Numerical solver, GraphCast, Pangu-Weather, FourCastNet, ECMWF IFS	View papers
Shallow water	4	Operator learning, Benchmark	FNO, Transformer, U-Net, ResNet, DeepONet	View papers

Hyperbolic PDEs

PDE	# papers	Common method classes	Common baselines (curated pages)
Wave	3	Operator learning, Diffusion	—	View papers
Wave equation	6	Operator learning, PINN / physics-constrained, Diffusion	FNO, DeepONet, WNO, U-NO, U-Net	View papers

Other

PDE	# papers	Common method classes	Common baselines (curated pages)
(baseline architecture; not PDE-specific)	1	CNN / U-Net	FCN / plain encoder–decoder CNNs	View papers
Advection	1	Benchmark	FNO, U-Net, ResNet, DeepONet, PINN	View papers
Biharmonic	1	PINN / physics-constrained	—	View papers
Black–Scholes	2	PINN / physics-constrained	Numerical solver, DeepBSDE, DGM	View papers
Burgers	18	PINN / physics-constrained, Operator learning, SciML	PINN, FNO, DeepONet, U-Net, PDE-FIND	View papers
Burgers equation	2	Diffusion, Operator learning	FNO, PINO, U-NO, U-WNO, Diffusion inpainting baseline	View papers
Compressible Euler	2	Operator learning, PINN / physics-constrained	FNO, U-NO, WNO, U-Net, PINN	View papers
Compressible flow	1	Graph / mesh	U-Net, Numerical solver	View papers
Continuum mechanics	1	Graph / mesh	Numerical solver	View papers
Inverse interface coefficient problem	1	Transformers	FNO, DeepONet, U-Net	View papers
Korteweg–De Vries	1	SciML	SINDy	View papers
Kuramoto–Sivashinsky	3	SciML, Diffusion	U-Net, FNO, PDE-Refiner, ResNet, SINDy	View papers
Schrödinger	2	PINN / physics-constrained	PINN, Numerical solver, DGM, Deep Ritz	View papers
Solid mechanics	2	PINN / physics-constrained	—	View papers
Stochastic PDEs	1	Operator learning	FNN, ResNet	View papers
Transport	3	Operator learning	FNO, WNO, U-NO, U-Net, CNO	View papers

Parabolic PDEs

PDE	# papers	Common method classes	Common baselines (curated pages)
Advection(-diffusion)	4	PINN / physics-constrained, SciML, Diffusion	—	View papers
Diffusion–reaction	1	Benchmark	FNO, U-Net, ResNet, DeepONet, PINN	View papers
Diffusion–reaction system	1	Operator learning	FNN, ResNet	View papers
Diffusion–sorption	1	Benchmark	FNO, U-Net, ResNet, DeepONet, PINN	View papers
Heat	1	PINN / physics-constrained	—	View papers
High-dimensional parabolic PDEs	1	PINN / physics-constrained	Numerical solver, DeepBSDE	View papers
Reaction–diffusion	2	SciML	PDE-FIND, SINDy	View papers

Reaction–diffusion / phase field

PDE	# papers	Common method classes	Common baselines (curated pages)
Allen–Cahn	4	Operator learning, PINN / physics-constrained	FNO, WNO, U-NO, U-Net, CNO	View papers