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ICES
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OUTREACH
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FACILITY
Algorithms & Methods
Mathematics in and of Planet Earth
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Optimization
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Parameterization
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.
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Assimilation
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Adaptive Mesh Refinement (AMR)
Performance benchmarking and profiling
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Grids
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Finite-Volume Methods
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Spectral Nudging
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Spectral Transforms
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Solvers
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Computational Fluid Dynamics (non-turbulent)
Both compressible and incompressible fluids
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Convection
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Vorticity, Helicity & Turbulence
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Non-fluid flows
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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.
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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.
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Variability
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Linear equations
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Randomness
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Statistics
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Ensemble Averaging
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Slow Feature Analysis
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Fracture Modelling
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Data Mining
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Predictive Analytics
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Graph Analytics
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Stochastic Gradient Descent
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Bayesian Methods
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Parallelization
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Downscaling
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Complex Network Analysis
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Stretching Time
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Sparse Matrices & Tensors
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Sparse Fourier Transform
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Wavelets
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Quantum systems modelling
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Machine Learning
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Biological Methods
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The renormalization group
A powerful method that uses the tools of quantum field theory, has found a place in biophysics.
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Thermodynamics
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