Initial release

engine/plugins/solvers/aflops2.lua

@@ -0,0 +1,65 @@
+-- aflops2.lua: A-FloPS Midpoint (2 NFE, stateless)
+-- Midpoint-corrected exponential integrator.
+
+solver = {
+    name        = "aflops2",
+    display     = "A-FloPS Midpoint (2 NFE)",
+    description = "Midpoint-corrected exponential integrator",
+    nfe         = 2,
+    order       = 2,
+    needs_model = true,
+    stateful    = false,
+    stochastic  = false,
+}
+
+local function clamp_alpha(t)
+    local a = 1 - t
+    return math.max(1e-6, math.min(a, 1 - 1e-6))
+end
+
+function step(xt, vt, t_curr, t_prev, n, model_fn, vt_buf)
+    local dt = t_curr - t_prev
+
+    if t_curr < 1e-8 then
+        for i = 0, n-1 do xt[i] = xt[i] - vt[i] * dt end
+        return
+    end
+
+    local alpha_curr = clamp_alpha(t_curr)
+    local alpha_prev = clamp_alpha(t_prev)
+
+    -- Save v_curr
+    local v_curr = {}
+    for i = 0, n-1 do v_curr[i] = vt[i] end
+
+    -- Euler half-step to midpoint
+    local half_dt = dt * 0.5
+    local t_mid = t_curr - half_dt
+    local alpha_mid = clamp_alpha(t_mid)
+
+    local x_mid = {}
+    for i = 0, n-1 do x_mid[i] = xt[i] - v_curr[i] * half_dt end
+
+    -- Evaluate at midpoint
+    model_fn(xt, t_mid) -- xt used as scratch, but we need x_mid...
+    -- Actually we need to pass x_mid to model_fn. Fix:
+    -- Store xt, use x_mid for model_fn
+    local xt_save = {}
+    for i = 0, n-1 do xt_save[i] = xt[i]; xt[i] = x_mid[i] end
+    model_fn(xt, t_mid)
+
+    -- Compute w_mid from midpoint
+    local inv_alpha_mid = 1 / alpha_mid
+    local w_mid = {}
+    for i = 0, n-1 do
+        w_mid[i] = vt_buf[i] + x_mid[i] * inv_alpha_mid
+    end
+
+    -- Full step using midpoint residual
+    local alpha_ratio = alpha_prev / alpha_curr
+    local log_ratio = math.log(alpha_ratio)
+
+    for i = 0, n-1 do
+        xt[i] = alpha_ratio * xt_save[i] - alpha_prev * w_mid[i] * log_ratio
+    end
+end