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data-assimilation

4D-Var / ensemble Kalman data assimilation

ECMWF 4D-Var, JEDI

SystemTechniques · 9Primitives · 48 data-assimilation DAG workflow executiondistributed · medium: Run a graph of dependent tasks by releasing each one when its inputs are done, longest chain first, and skip any task whose input hashes are unchanged.›Halo exchangedistributed · medium: Each rank stores its block plus a border copy of its neighbours' edge cells, refreshed by small messages every step; communication scales with block surface, not volume.›Parallel file system stripingdistributed · medium: Striping files across object storage targets (Lustre, GPFS); collective I/O and metadata serversData assimilation 4dvarnumerics · medium: Fit model initial state to observations by minimizing a cost over a time window with adjoint gradientsEnsemble kalman filternumerics · medium: Kalman update with covariance estimated from an ensemble; localization and inflation for huge statesSequential monte carlonumerics · medium: Particle filters and SMC samplers with resampling for sequential Bayesian inferenceSpherical harmonic transformnumerics · medium: Fast spherical harmonic transforms via FFT in longitude and Legendre in latitudeReverse-mode automatic differentiat…ml-training · low: Record the forward computation on a tape, then sweep it backwards once to get the gradient of a scalar loss for all inputs.›Conjugate gradientnumerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.›L-BFGSnumerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.›Kalman filterrobotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.›Spherical gridsnumerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issuesk-d treegeometry · low: A binary tree that splits k-dimensional points by one coordinate per level, giving fast nearest-neighbour and box queries on static low-dimensional data.›Linear and logistic regressionmachine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.›Collective communicationml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.›Spline interpolationnumerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tablesExtended Kalman filterrobotics · low: Kalman filter for nonlinear motion and measurement models: linearize f and h with Jacobians at the current estimate each step. The default estimator in robot navigation.›Robust statisticsstatistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.›Topological sortgraphs · low: Order the vertices of a DAG so every edge points forward; the core of build systems, schedulers and dependency resolution, with cycle detection for free.›Content-addressed storagestorage · low: Store each blob under the hash of its bytes: immutable, deduplicated by construction, self-verifying on every read, and composable into Merkle trees.›Exponential backoff with jittersystems · low: Retry after delays that grow geometrically and are randomized, so failed clients spread out instead of hammering a recovering service in synchronized waves.›Eager rendezvous protocoldistributed · low: MPI point-to-point: eager sends for small messages, rendezvous handshake for large onesRdmanetworking · low: RDMA verbs over InfiniBand/RoCE: queue pairs, memory registration, one-sided ops+ 2 more techniques+ 32 more primitives

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