Skills Map¶
working
Ten competency pillars for a computational physicist working across aerospace, meteorology and astrophysics. Every note page on this site declares the pillar it serves, so this page doubles as the site's table of contents and as an honest account of where the gaps are.
The pillars are ordered roughly from physics to practice. Nobody is uniformly strong across all ten, and the useful question is not "do I know this" but "how fast can I get back to working competence."
The pillars¶
1. Physical modeling and domain theory¶
Deriving governing equations from conservation laws; nondimensionalization and scaling; identifying which regime you are in and which terms you are entitled to drop; closure choices and what they cost.
Foundation: classical mechanics, thermodynamics, fluid dynamics, electromagnetism and plasma physics, and quantum mechanics where it bites. Then per domain:
| Domain | Core theory |
|---|---|
| Aerospace | Aerodynamics, boundary layers, turbulence modelling (RANS/LES), propulsion, flight mechanics |
| Meteorology | Atmospheric dynamics and thermodynamics, radiative transfer, cloud physics, turbulence parameterization |
| Astrophysics | N-body and gravitational dynamics, MHD, radiative transfer |
→ Fluids · Aerospace · Meteorology · Astrophysics
2. Mathematical methods¶
PDE classification — hyperbolic, parabolic, elliptic — and what each implies about numerical treatment, boundary conditions and domains of dependence. Analytical solutions worth keeping in memory as sanity checks. Linear algebra and spectral theory. Tensors and curvilinear coordinates. Asymptotics and perturbation methods.
→ Foundations › Mathematical methods
3. Discretization and numerical analysis¶
Finite difference, finite volume, finite element and spectral methods, and the trade each makes. Consistency, stability and convergence. Conservation and well-balancing. Shock capturing, limiters, monotonicity. Dispersion and dissipation error — knowing what your scheme does to a wave before you run it. Grid generation and adaptive mesh refinement.
→ Foundations › Numerical methods
4. Solvers, time integration and adjoints¶
Direct versus Krylov methods; preconditioning; multigrid. Stiffness, and the explicit/implicit/IMEX decision. Operator splitting. CFL and the other step-size constraints that actually bind. Adjoint methods and sensitivity analysis for design optimization and for telling you which inputs your answer depends on.
→ Foundations › Linear solvers · Optimization and adjoints
5. Programming and software engineering¶
C++ for performance-critical code, Fortran for the numerical tradition and the large body of working legacy, Python for analysis and ML and prototyping, Bash for everything that glues them. Modular architecture and API design. Git, regression testing, code review. Generated documentation. Profiling, memory management, SIMD.
→ Computing › C++ and Fortran · Python performance
6. HPC and parallelism¶
MPI, OpenMP, CUDA. Supercomputer architecture and the memory hierarchy that drives every optimization decision. Schedulers — SLURM, PBS. Parallel file systems. Scaling analysis and benchmarking, strong and weak. CPU/GPU hybrid and exascale paradigms.
→ Computing › HPC · GPU and CUDA
7. Domain codes and toolchains¶
The software you are expected to arrive already knowing, rather than to learn on the job. This pillar is easy to underrate — it is not intellectually deep, but not knowing it is immediately visible.
| Area | Tools |
|---|---|
| CFD | OpenFOAM, ANSYS FLUENT, AMReX |
| Meshing | Pointwise, Gmsh |
| Weather and climate | WRF, ERF, MPAS, GFDL models; RRTM, libRadtran |
| Astrophysics | FLASH, Athena, Gadget; SPH and N-body codes |
| Visualization | ParaView, VisIt, Tecplot, yt |
| Geospatial | GDAL, Xarray, GeoPandas, QGIS |
| CAD | Parasolid, CATIA |
8. Data management, statistics and UQ¶
Terabyte-to-petabyte I/O and storage. Parallel I/O. NetCDF, GRIB, HDF5 — their layouts, their chunking behaviour, and the performance cliffs hiding in both. Automated post-processing pipelines. Statistical analysis, uncertainty quantification and statistical emulation. Data version control.
→ Computing › Data I/O · Foundations › UQ · Toolchains › Data formats
9. Scientific machine learning¶
Surrogates and reduced-order models — POD, DMD, autoencoders. Physics-informed neural networks. Operator learning: DeepONet, Fourier neural operators. Graph networks on unstructured meshes. Feature engineering and dimensionality reduction. Computer vision on scientific imagery. ML downscaling for weather and climate. Hybrid physics-ML coupling — and the judgement to recognise when ML is the wrong tool.
→ Scientific ML · Machine Learning · Deep Learning · Computer Vision
10. V&V, research craft and communication¶
Method of manufactured solutions, grid convergence studies, benchmark problems. Physics insight: knowing when and why a model breaks, which is a skill and not a by-product of knowing the equations. Literature review and hypothesis testing. Publication writing. Presenting to mixed audiences. Working across multidisciplinary teams.
→ Foundations › V&V · Research craft
Cross-cutting: operations¶
Cloud (AWS, GCP, Azure), containers (Docker, and Singularity/Apptainer for HPC), CI/CD for scientific codes, open-source contribution. Not a pillar of its own — it is the substrate the other ten now run on.
Self-assessment¶
solid — working competence, recap only. working — usable, actively being deepened.
growing — deliberate expansion area.
| # | Pillar | Standing | Why |
|---|---|---|---|
| 1 | Physical modeling | solid (aero/fluids), growing (meteorology) | Long training in aerospace and fluids; meteorology is a deliberate expansion |
| 2 | Mathematical methods | solid | Recap surface only |
| 3 | Discretization | solid | Recap surface only |
| 4 | Solvers and adjoints | solid | Adjoints worth a deeper pass |
| 5 | Programming | solid | C++/Fortran/Python all in active use |
| 6 | HPC | working | GPU and CUDA being deepened |
| 7 | Toolchains | working | Breadth varies sharply by tool |
| 8 | Data and UQ | working | Formats solid; UQ worth deepening |
| 9 | Scientific ML | growing | ML, DL, CV and SciML are the main growth areas |
| 10 | V&V and craft | solid | Recap surface only |
These standings are inferred, not self-reported
They come from the planning documents rather than from you, and the value of this page depends on them being honest — correct anything that reads wrong.
Note that a standing describes you, not the site. Every pillar now has written
pages; a pillar marked growing means the learning is ongoing, not that the section
is thin.