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redclawsystems
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//! Icosahedral mesh encoder for weather prediction.
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//!
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//! This module implements the mesh structure and encoding/decoding
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//! for converting between regular grid data and icosahedral mesh
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//! representation used in GraphCast-style weather models.
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use weathercast_shared::{AtmosphericState, MeshConfig};
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// ============================================================================
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// Icosahedral Mesh Structure
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// ============================================================================
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/// Icosahedral mesh for global weather modeling.
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#[derive(Debug, Clone)]
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pub struct IcosahedralMesh {
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/// Mesh vertices as (x, y, z) on unit sphere.
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pub vertices: Vec<(f32, f32, f32)>,
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/// Mesh edges as vertex index pairs.
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pub edges: Vec<(usize, usize)>,
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/// Mesh faces as vertex index triplets.
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pub faces: Vec<(usize, usize, usize)>,
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/// Refinement level.
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pub refinement_level: usize,
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/// Average edge length in km.
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pub avg_edge_length: f32,
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}
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impl IcosahedralMesh {
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/// Create a new icosahedral mesh with given configuration.
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pub fn new(config: &MeshConfig) -> Self {
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let (vertices, edges, faces) = Self::generate_icosahedral_mesh(config.refinement_levels);
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Self {
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vertices,
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edges,
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faces,
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refinement_level: config.refinement_levels,
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avg_edge_length: config.avg_edge_length,
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}
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}
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/// Generate icosahedral mesh at given refinement level.
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fn generate_icosahedral_mesh(
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refinement: usize,
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) -> (
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Vec<(f32, f32, f32)>,
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Vec<(usize, usize)>,
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Vec<(usize, usize, usize)>,
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) {
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// Start with base icosahedron (12 vertices, 20 faces, 30 edges)
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let phi = f32::midpoint(1.0, 5.0_f32.sqrt()); // Golden ratio
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let mut vertices = vec![
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(-1.0, phi, 0.0),
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(1.0, phi, 0.0),
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(-1.0, -phi, 0.0),
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(1.0, -phi, 0.0),
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(0.0, -1.0, phi),
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(0.0, 1.0, phi),
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(0.0, -1.0, -phi),
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(0.0, 1.0, -phi),
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(phi, 0.0, -1.0),
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(phi, 0.0, 1.0),
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(-phi, 0.0, -1.0),
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(-phi, 0.0, 1.0),
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];
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// Normalize to unit sphere
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for v in &mut vertices {
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let len = (v.0 * v.0 + v.1 * v.1 + v.2 * v.2).sqrt();
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v.0 /= len;
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v.1 /= len;
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v.2 /= len;
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}
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// Base faces (20 triangular faces of icosahedron)
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let mut faces = vec![
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(0, 11, 5),
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(0, 5, 1),
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(0, 1, 7),
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(0, 7, 10),
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(0, 10, 11),
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(1, 5, 9),
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(5, 11, 4),
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(11, 10, 2),
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(10, 7, 6),
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(7, 1, 8),
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(3, 9, 4),
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(3, 4, 2),
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(3, 2, 6),
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(3, 6, 8),
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(3, 8, 9),
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(4, 9, 5),
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(2, 4, 11),
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(6, 2, 10),
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(8, 6, 7),
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(9, 8, 1),
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];
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// Refine mesh
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for _ in 0..refinement {
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let (new_vertices, new_faces) = Self::subdivide(&vertices, &faces);
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vertices = new_vertices;
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faces = new_faces;
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}
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// Generate edges from faces
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let mut edges = Vec::new();
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let mut edge_set = std::collections::HashSet::new();
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for &(a, b, c) in &faces {
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for (v1, v2) in [(a, b), (b, c), (c, a)] {
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let edge = if v1 < v2 { (v1, v2) } else { (v2, v1) };
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if edge_set.insert(edge) {
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edges.push(edge);
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}
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}
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}
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(vertices, edges, faces)
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}
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/// Subdivide mesh faces (each triangle becomes 4 triangles).
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fn subdivide(
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vertices: &[(f32, f32, f32)],
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faces: &[(usize, usize, usize)],
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) -> (Vec<(f32, f32, f32)>, Vec<(usize, usize, usize)>) {
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let mut new_vertices = vertices.to_vec();
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let mut new_faces = Vec::new();
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let mut midpoint_cache: std::collections::HashMap<(usize, usize), usize> =
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std::collections::HashMap::new();
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let get_midpoint = |v1: usize,
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v2: usize,
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vertices: &[(f32, f32, f32)],
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new_vertices: &mut Vec<(f32, f32, f32)>,
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cache: &mut std::collections::HashMap<(usize, usize), usize>|
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-> usize {
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let key = if v1 < v2 { (v1, v2) } else { (v2, v1) };
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if let Some(&idx) = cache.get(&key) {
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return idx;
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}
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let p1 = vertices[v1];
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let p2 = vertices[v2];
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// Calculate midpoint and project to sphere
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let mut mid = (
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f32::midpoint(p1.0, p2.0),
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f32::midpoint(p1.1, p2.1),
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f32::midpoint(p1.2, p2.2),
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);
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let len = (mid.0 * mid.0 + mid.1 * mid.1 + mid.2 * mid.2).sqrt();
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mid.0 /= len;
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mid.1 /= len;
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mid.2 /= len;
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let idx = new_vertices.len();
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new_vertices.push(mid);
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cache.insert(key, idx);
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idx
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};
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for &(a, b, c) in faces {
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let ab = get_midpoint(a, b, vertices, &mut new_vertices, &mut midpoint_cache);
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let bc = get_midpoint(b, c, vertices, &mut new_vertices, &mut midpoint_cache);
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let ca = get_midpoint(c, a, vertices, &mut new_vertices, &mut midpoint_cache);
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new_faces.push((a, ab, ca));
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new_faces.push((b, bc, ab));
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new_faces.push((c, ca, bc));
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new_faces.push((ab, bc, ca));
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}
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(new_vertices, new_faces)
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}
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/// Get vertex latitude/longitude.
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pub fn vertex_latlon(&self, idx: usize) -> Option<(f32, f32)> {
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self.vertices.get(idx).map(|&(x, y, z)| {
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let lat = y.asin().to_degrees();
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let lon = x.atan2(z).to_degrees();
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(lat, lon)
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})
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}
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/// Find nearest vertex to given lat/lon.
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pub fn nearest_vertex(&self, lat: f32, lon: f32) -> usize {
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let lat_rad = lat.to_radians();
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let lon_rad = lon.to_radians();
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// Convert to Cartesian
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let x = lat_rad.cos() * lon_rad.sin();
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let y = lat_rad.sin();
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let z = lat_rad.cos() * lon_rad.cos();
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// Find nearest vertex
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self.vertices
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.iter()
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.enumerate()
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.min_by(|(_, v1), (_, v2)| {
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let d1 = (v1.0 - x).powi(2) + (v1.1 - y).powi(2) + (v1.2 - z).powi(2);
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let d2 = (v2.0 - x).powi(2) + (v2.1 - y).powi(2) + (v2.2 - z).powi(2);
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d1.partial_cmp(&d2).unwrap_or(std::cmp::Ordering::Equal)
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})
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.map_or(0, |(i, _)| i)
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}
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/// Get neighbors of a vertex.
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pub fn vertex_neighbors(&self, idx: usize) -> Vec<usize> {
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self.edges
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.iter()
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.filter_map(|&(a, b)| {
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if a == idx {
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Some(b)
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} else if b == idx {
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Some(a)
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} else {
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None
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}
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})
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.collect()
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}
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}
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// ============================================================================
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// Mesh Encoder
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// ============================================================================
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/// Encoder for converting between grid and mesh representations.
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#[derive(Debug)]
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pub struct MeshEncoder {
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/// Number of mesh nodes.
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#[allow(dead_code)]
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num_nodes: usize,
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/// Hidden dimension.
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hidden_dim: usize,
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/// Encoder weights.
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encoder_weights: Vec<f32>,
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/// Decoder weights.
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decoder_weights: Vec<f32>,
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/// RNG state.
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rng_state: u64,
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}
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impl MeshEncoder {
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/// Create a new mesh encoder.
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pub fn new(num_nodes: usize, hidden_dim: usize) -> Self {
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let mut encoder = Self {
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num_nodes,
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hidden_dim,
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encoder_weights: Vec::new(),
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decoder_weights: Vec::new(),
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rng_state: 42,
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};
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encoder.initialize_weights();
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encoder
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}
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/// Initialize encoder/decoder weights.
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fn initialize_weights(&mut self) {
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// Encoder: input_dim -> hidden_dim
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let input_dim = 8 * 5 + 5; // 8 pressure levels * 5 vars + 5 surface vars
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self.encoder_weights = (0..input_dim * self.hidden_dim)
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.map(|_| self.random() as f32 * 0.1 - 0.05)
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.collect();
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// Decoder: hidden_dim -> output_dim
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self.decoder_weights = (0..self.hidden_dim * input_dim)
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.map(|_| self.random() as f32 * 0.1 - 0.05)
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.collect();
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}
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/// Encode atmospheric state to mesh representation.
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pub fn encode_state(&mut self, state: &AtmosphericState, mesh: &IcosahedralMesh) -> Vec<f32> {
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let num_nodes = mesh.vertices.len();
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let mut mesh_state = vec![0.0f32; num_nodes * self.hidden_dim];
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// Flatten state to feature vector
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let features = self.state_to_features(state);
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// Apply encoder at each mesh node
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for node in 0..num_nodes {
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let (lat, lon) = mesh.vertex_latlon(node).unwrap_or((0.0, 0.0));
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// Modulate features by position
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let lat_factor = lat.to_radians().cos();
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let lon_factor = (lon.to_radians() * 2.0).sin() * 0.1;
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for h in 0..self.hidden_dim {
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let mut val = 0.0f32;
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// Linear projection with positional modulation
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for (f_idx, &f) in features.iter().enumerate() {
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let w_idx = f_idx * self.hidden_dim + h;
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let weight = self.encoder_weights.get(w_idx).copied().unwrap_or(0.01);
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val += f * weight;
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}
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// Add positional encoding
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val += (lat_factor * (h as f32 * 0.1)).sin() * 0.5;
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val += lon_factor * (h as f32 * 0.1).cos() * 0.3;
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// Apply non-linearity
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mesh_state[node * self.hidden_dim + h] = self.gelu(val);
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}
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}
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mesh_state
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}
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/// Decode mesh representation back to atmospheric state.
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pub fn decode_state(
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&mut self,
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mesh_state: &[f32],
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mesh: &IcosahedralMesh,
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timestamp: f32,
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) -> AtmosphericState {
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let num_nodes = mesh.vertices.len();
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// Average over all nodes (simplified global mean)
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let mut avg_hidden = vec![0.0f32; self.hidden_dim];
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for node in 0..num_nodes {
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for h in 0..self.hidden_dim {
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let idx = node * self.hidden_dim + h;
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avg_hidden[h] += mesh_state.get(idx).copied().unwrap_or(0.0) / num_nodes as f32;
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}
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}
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// Decode to output features
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let output_dim = 8 * 5 + 5;
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let mut output = vec![0.0f32; output_dim];
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for o in 0..output_dim {
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for h in 0..self.hidden_dim {
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let w_idx = h * output_dim + o;
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let weight = self.decoder_weights.get(w_idx).copied().unwrap_or(0.01);
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output[o] += avg_hidden[h] * weight;
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}
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}
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// Reconstruct atmospheric state with physical constraints
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self.features_to_state(&output, timestamp)
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}
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/// Convert atmospheric state to feature vector.
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fn state_to_features(&self, state: &AtmosphericState) -> Vec<f32> {
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let mut features = Vec::new();
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// Normalize and add pressure level variables
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for i in 0..8 {
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features.push(state.temperature.get(i).copied().unwrap_or(250.0) / 300.0);
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features.push(state.geopotential.get(i).copied().unwrap_or(5000.0) / 10000.0);
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features.push(state.humidity.get(i).copied().unwrap_or(0.005) * 100.0);
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features.push(state.wind_u.get(i).copied().unwrap_or(0.0) / 50.0);
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features.push(state.wind_v.get(i).copied().unwrap_or(0.0) / 50.0);
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}
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// Surface variables
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features.push(state.surface_pressure / 101325.0);
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features.push(state.temperature_2m / 300.0);
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features.push(state.wind_u_10m / 20.0);
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features.push(state.wind_v_10m / 20.0);
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features.push(state.precipitation / 10.0);
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features
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}
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/// Convert feature vector back to atmospheric state.
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fn features_to_state(&mut self, features: &[f32], timestamp: f32) -> AtmosphericState {
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let pressure_levels = vec![1000.0, 925.0, 850.0, 700.0, 500.0, 300.0, 200.0, 50.0];
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let mut temperature = Vec::new();
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let mut geopotential = Vec::new();
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let mut humidity = Vec::new();
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let mut wind_u = Vec::new();
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let mut wind_v = Vec::new();
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for i in 0..8 {
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let base = i * 5;
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// Clamp temperature to physically reasonable range (150K to 350K)
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let temp = (features.get(base).copied().unwrap_or(0.83) * 300.0).clamp(150.0, 350.0);
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temperature.push(temp);
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geopotential.push(features.get(base + 1).copied().unwrap_or(0.5) * 10000.0);
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humidity.push((features.get(base + 2).copied().unwrap_or(0.5) / 100.0).max(0.0));
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wind_u.push(features.get(base + 3).copied().unwrap_or(0.0) * 50.0);
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wind_v.push(features.get(base + 4).copied().unwrap_or(0.0) * 50.0);
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}
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// Add some stochastic variability (small enough to stay in range)
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for t in &mut temperature {
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*t += (self.random() as f32 - 0.5) * 2.0;
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*t = t.clamp(150.0, 350.0); // Ensure still in range after noise
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}
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AtmosphericState {
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temperature,
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geopotential,
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humidity,
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wind_u,
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wind_v,
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pressure_levels,
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surface_pressure: features.get(40).copied().unwrap_or(1.0) * 101325.0,
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temperature_2m: (features.get(41).copied().unwrap_or(0.96) * 300.0).clamp(150.0, 350.0),
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wind_u_10m: features.get(42).copied().unwrap_or(0.0) * 20.0,
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wind_v_10m: features.get(43).copied().unwrap_or(0.0) * 20.0,
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precipitation: (features.get(44).copied().unwrap_or(0.0) * 10.0).max(0.0),
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timestamp,
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}
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}
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/// GELU activation function.
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fn gelu(&self, x: f32) -> f32 {
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0.5 * x * (1.0 + ((2.0 / std::f32::consts::PI).sqrt() * (x + 0.044715 * x.powi(3))).tanh())
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}
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/// Random number generator.
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fn random(&mut self) -> f64 {
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self.rng_state = self
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.rng_state
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.wrapping_mul(6364136223846793005)
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.wrapping_add(1442695040888963407);
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(self.rng_state >> 11) as f64 / (1u64 << 53) as f64
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}
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}
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// ============================================================================
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// Tests
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// ============================================================================
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_mesh_creation() {
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let config = MeshConfig::from_refinement(3);
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let mesh = IcosahedralMesh::new(&config);
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assert!(!mesh.vertices.is_empty());
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assert!(!mesh.edges.is_empty());
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assert!(!mesh.faces.is_empty());
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}
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#[test]
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fn test_mesh_refinement_levels() {
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// Test different refinement levels
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for level in 0..4 {
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let config = MeshConfig::from_refinement(level);
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let mesh = IcosahedralMesh::new(&config);
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// Icosahedral mesh: V = 10 * 4^n + 2
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let expected_vertices = 10 * 4_usize.pow(level as u32) + 2;
|
||||
assert_eq!(mesh.vertices.len(), expected_vertices);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_vertices_on_unit_sphere() {
|
||||
let config = MeshConfig::from_refinement(2);
|
||||
let mesh = IcosahedralMesh::new(&config);
|
||||
|
||||
for &(x, y, z) in &mesh.vertices {
|
||||
let len = (x * x + y * y + z * z).sqrt();
|
||||
assert!((len - 1.0).abs() < 0.001, "Vertex not on unit sphere");
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_vertex_latlon() {
|
||||
let config = MeshConfig::from_refinement(2);
|
||||
let mesh = IcosahedralMesh::new(&config);
|
||||
|
||||
for idx in 0..mesh.vertices.len() {
|
||||
let latlon = mesh.vertex_latlon(idx);
|
||||
assert!(latlon.is_some());
|
||||
|
||||
let (lat, lon) = latlon.unwrap();
|
||||
assert!(lat >= -90.0 && lat <= 90.0);
|
||||
assert!(lon >= -180.0 && lon <= 180.0);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_nearest_vertex() {
|
||||
let config = MeshConfig::from_refinement(3);
|
||||
let mesh = IcosahedralMesh::new(&config);
|
||||
|
||||
// Find vertex near New York City
|
||||
let nyc_vertex = mesh.nearest_vertex(40.7, -74.0);
|
||||
let (lat, _lon) = mesh.vertex_latlon(nyc_vertex).unwrap();
|
||||
|
||||
// Should be reasonably close
|
||||
assert!((lat - 40.7).abs() < 10.0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_vertex_neighbors() {
|
||||
let config = MeshConfig::from_refinement(2);
|
||||
let mesh = IcosahedralMesh::new(&config);
|
||||
|
||||
let neighbors = mesh.vertex_neighbors(0);
|
||||
|
||||
// Each vertex should have multiple neighbors (typically 5-6 for icosahedral mesh)
|
||||
assert!(!neighbors.is_empty());
|
||||
assert!(neighbors.len() >= 3);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_mesh_encoder_creation() {
|
||||
let encoder = MeshEncoder::new(100, 64);
|
||||
assert_eq!(encoder.num_nodes, 100);
|
||||
assert_eq!(encoder.hidden_dim, 64);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_encode_decode_roundtrip() {
|
||||
let config = MeshConfig::from_refinement(2);
|
||||
let mesh = IcosahedralMesh::new(&config);
|
||||
let mut encoder = MeshEncoder::new(mesh.vertices.len(), 64);
|
||||
|
||||
let original_state = weathercast_shared::sample_atmospheric_state();
|
||||
let encoded = encoder.encode_state(&original_state, &mesh);
|
||||
let decoded = encoder.decode_state(&encoded, &mesh, 0.0);
|
||||
|
||||
// Check that decoded state has same structure
|
||||
assert_eq!(decoded.temperature.len(), original_state.temperature.len());
|
||||
assert_eq!(
|
||||
decoded.pressure_levels.len(),
|
||||
original_state.pressure_levels.len()
|
||||
);
|
||||
|
||||
// Values should be in reasonable ranges
|
||||
for t in &decoded.temperature {
|
||||
assert!(*t > 100.0 && *t < 400.0, "Temperature out of range: {}", t);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_encoder_mesh_state_size() {
|
||||
let config = MeshConfig::from_refinement(2);
|
||||
let mesh = IcosahedralMesh::new(&config);
|
||||
let hidden_dim = 64;
|
||||
let mut encoder = MeshEncoder::new(mesh.vertices.len(), hidden_dim);
|
||||
|
||||
let state = weathercast_shared::sample_atmospheric_state();
|
||||
let encoded = encoder.encode_state(&state, &mesh);
|
||||
|
||||
assert_eq!(encoded.len(), mesh.vertices.len() * hidden_dim);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_gelu_activation() {
|
||||
let encoder = MeshEncoder::new(10, 32);
|
||||
|
||||
// GELU(0) should be approximately 0
|
||||
assert!(encoder.gelu(0.0).abs() < 0.01);
|
||||
|
||||
// GELU should be monotonically increasing for positive x
|
||||
assert!(encoder.gelu(1.0) > encoder.gelu(0.5));
|
||||
assert!(encoder.gelu(0.5) > encoder.gelu(0.0));
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user