Algorithms & Methods

Mathematics in and of Planet Earth



Where a process of Nature is not completely understood or can only be partially measured with today's technology, then one approach within a larger mathematical model is to substitute a few variables in lieu of a true representation of the 'missing' process, and then to 'tune' these variables as best possible, based on the 'skill' of the larger model to achieve a measurable macro-level performance. This method of approximation within a model is commonly known as 'parameterization' - and is subject to continuous improvement as more knowledge of the 'missing processes' is gained. Read more...


Adaptive Mesh Refinement (AMR)

Performance benchmarking and profiling


Finite-Volume Methods

Spectral Nudging

Spectral Transforms


Computational Fluid Dynamics (non-turbulent)

Both compressible and incompressible fluids


Vorticity, Helicity & Turbulence

Non-fluid flows

Stochastic Physics

Wherever we have errors in a model (initialization errors, sub-grid parameterization errors, or model structural errors), it may be possible to inject an element of noise and randomness, a 'stochastic' approach, and obtain additional outcomes and computational accuracy. For example, adding stochastic perturbations to a model may ensure it does not remain in one particular regime. Read more...

Uncertainty and Error Management

Errors can occur at all levels in the modelling and simulation paradigm. Models themselves can have structural errors, parameters within the model can have errors, and data used to initialiize or to update the simulation computations can have errors. In every case, the main issue is to estimate the magnitude of the error and to stop the error from growing with each iterative time-step of the computational process. Read more...


Linear equations



Ensemble Averaging

Slow Feature Analysis

Fracture Modelling

Data Mining

Predictive Analytics

Graph Analytics

Stochastic Gradient Descent

Bayesian Methods



Complex Network Analysis

Stretching Time

Sparse Matrices & Tensors

Sparse Fourier Transform

Quantum systems modelling

Machine Learning

Biological Methods