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Simulation and scientific computing
wildfire-spread
wildfire spread simulation
FARSITE, WRF-Fire
System
Techniques · 6
Primitives · 28
wildfire-spread
Polygon clipping
geometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicates
Radiometric calibration
media · medium: Convert sensor counts to reflectance: radiometric and atmospheric correction
Ensemble kalman filter
numerics · medium: Kalman update with covariance estimated from an ensemble; localization and inflation for huge states
Level set methods
numerics · medium: Implicit surfaces as signed distance fields: advection, reinitialization, fast marching
Time-series anomaly detection
statistics · medium: Predict the expected value from a seasonal baseline, scale the residual by a robust spread (MAD), threshold at a chosen false-alarm rate, then merge flags into incidents.
›
Flux limiters upwinding
numerics · medium: Upwind schemes, TVD flux limiters, MUSCL and Riemann solvers for shock-capturing advection
Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
›
Geospatial cell index (geohash, S2,…
geometry · low: Map a lat/lon to a 64-bit cell id on a hierarchical grid, so "near" becomes an integer range scan in any ordinary sorted index.
›
Line simplification
geometry · low: Douglas-Peucker and Visvalingam polyline simplification
Map projections
geometry · low: Web Mercator, UTM and equal-area projections, datums and coordinate transforms
Vector tile encoding
geometry · low: Mapbox Vector Tile protobuf: zigzag-delta geometry commands, layers and feature attributes
Cellular automata
graphics · low: Grid cells updated by local rules (Life, cave generation, Nagel-Schreckenberg traffic)
Dijkstra's algorithm
graphs · low: Single-source shortest paths with non-negative edge weights by settling vertices in order of distance with a priority queue.
›
Common alerting protocol
networking · low: CAP alert message format: areas as polygons/circles, severity, urgency, multilingual info blocks
Conjugate gradient
numerics · 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.
›
Monte Carlo integration
numerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.
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d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
+ 12 more primitives
System
Techniques · 6
Primitives · 28
wildfire-spread
Polygon clipping
geometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicates
Radiometric calibration
media · medium: Convert sensor counts to reflectance: radiometric and atmospheric correction
Ensemble kalman filter
numerics · medium: Kalman update with covariance estimated from an ensemble; localization and inflation for huge states
Level set methods
numerics · medium: Implicit surfaces as signed distance fields: advection, reinitialization, fast marching
Time-series anomaly detection
statistics · medium: Predict the expected value from a seasonal baseline, scale the residual by a robust spread (MAD), threshold at a chosen false-alarm rate, then merge flags into incidents.
›
Flux limiters upwinding
numerics · medium: Upwind schemes, TVD flux limiters, MUSCL and Riemann solvers for shock-capturing advection
Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
›
Geospatial cell index (geohash, S2,…
geometry · low: Map a lat/lon to a 64-bit cell id on a hierarchical grid, so "near" becomes an integer range scan in any ordinary sorted index.
›
Line simplification
geometry · low: Douglas-Peucker and Visvalingam polyline simplification
Map projections
geometry · low: Web Mercator, UTM and equal-area projections, datums and coordinate transforms
Vector tile encoding
geometry · low: Mapbox Vector Tile protobuf: zigzag-delta geometry commands, layers and feature attributes
Cellular automata
graphics · low: Grid cells updated by local rules (Life, cave generation, Nagel-Schreckenberg traffic)
Dijkstra's algorithm
graphs · low: Single-source shortest paths with non-negative edge weights by settling vertices in order of distance with a priority queue.
›
Common alerting protocol
networking · low: CAP alert message format: areas as polygons/circles, severity, urgency, multilingual info blocks
Conjugate gradient
numerics · 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.
›
Monte Carlo integration
numerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Kalman filter
robotics · 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.
›
Covariance shrinkage
statistics · low: Ledoit-Wolf shrinkage for stable covariance matrices from few samples
Runge-Kutta 4
numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.
›
Isolation forest
machine-learning · low: Score each record by how few random axis-aligned splits it takes to isolate it in a small forest of random trees; anomalies are few and different, so they isolate fast.
›
Exponential smoothing (ETS, Holt-Wi…
statistics · low: Forecast by keeping a few running states (level, trend, seasonal) updated by a fraction of each forecast error; O(1) memory per series and a strong baseline.
›
STL decomposition (seasonal-trend w…
statistics · low: Split a series into trend, seasonal and remainder with iterated loess smoothing; the seasonal shape may drift and robust weights keep outliers out of it.
›
Quadtree octree
geometry · low: Adaptive spatial subdivision trees for queries and level of detail; loose and linear variants
Space filling curves
geometry · low: Z-order/Morton (geohash) and Hilbert curves mapping multi-dimensional points to sortable keys
Rejection sampling
ml-training · low: Best-of-n and filtered sampling: generate many candidates, keep those passing a verifier or reward threshold
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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