Open-source tools built for performance

Author

GridapROMs.jl

A Julia package for reduced-order modelling of parameterised PDEs. It covers a wide range of equations, ranging from electromagnetics to nonlinear fluid dynamics, steady or transient, from problems defined on moving geometries to ones partitioned across multiple processors in HPC-friendly environments. Its reduced-order algorithms have achieved speedups several thousand times over full-order simulations.

• POD, Tucker, tensor-train, interpolation, and localised subspace strategies, all behind the same high-level, readable interface.
• Distributed-memory (MPI) snapshot generation for the offline stage; newer than the rest of the library and still maturing.
• Lazy evaluation keeps the cost of generating training data under control, which matters most for large-scale problems, whether they're solved serially or in parallel.

Author

Opal.jl

A Julia package for data assimilation and inverse modelling, bringing sequential filters and variational estimators together behind a unified interface.

• Kalman -- including extended/unscented/ensemble versions -- and particle filters, plus 3D-/4D-Var, all sharing the same execution and diagnostics.
• Things like covariance localisation/inflation, adaptive noise estimation, and bias-aware correction are wrappers around a common filter interface, so you compose what you need instead of picking a monolithic implementation off a shelf.
• A reservoir-computing (echo state network) module I wrote from scratch for the bias correction, which turned out more accurate and cheaper to train than ReservoirComputing.jl on the benchmarks I ran.
• Natively integrated with SciML for ODEs and with Gridap/GridapROMs for full- and reduced-order PDE models, so a reduced-order surrogate can drop in for a full-order solver without touching the assimilation code.

Author · Work in progress

NonlinearROMs.jl

A Julia package for nonlinear, deep-learning-based reduced-order models, currently under active development. The focus is neural operators: Fourier neural operators (FNOs) and NOMADs are already implemented, DeepONets are in too, and graph neural operators (GNOs) are next.