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722 lines
30 KiB
Python
722 lines
30 KiB
Python
#!/usr/bin/env python3
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"""
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burgers_verifier.py
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====================
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An academically defensible verifier for reduced-order-model closure of viscous
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Burgers' equation,
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∂u/∂t + u ∂u/∂x = ν ∂²u/∂x², x ∈ [0, 2π], periodic, ν > 0.
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Built per the principle in
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"Auto-Architecture: Karpathy's Loop, Pointed at a CPU"
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(github.com/FeSens/auto-arch-tournament): the agent loop is commodity, the
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verifier is the moat. This file *is* the verifier — a sharp gate suite defined
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before any candidate closure is proposed, against which any closure must be
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scored.
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Reference frame (texts a reviewer would accept without question)
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----------------------------------------------------------------
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- Cole-Hopf transform: J. D. Cole, "On a quasi-linear parabolic equation
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occurring in aerodynamics", Quart. Appl. Math. 9 (1951), 225-236.
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- Cole-Hopf for Burgers: G. B. Whitham, "Linear and Nonlinear Waves" (1974),
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§4.3; L. C. Evans, "Partial Differential Equations" 2nd ed. (2010), §4.4.
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- Energy method for Burgers: P. G. Drazin & R. S. Johnson, "Solitons" (1989).
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- Pseudo-spectral Burgers reference: C. Canuto, M. Y. Hussaini, A. Quarteroni,
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T. A. Zang, "Spectral Methods" (2007).
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Verifier surface (the gates)
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----------------------------
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G1. Cole-Hopf reference cosim — exact analytical solution for any t
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G2. Energy dissipation property — dE/dt = -ν π Σ n² aₙ² ≤ 0
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G3. Triad nonlinear-term energy conservation — Σ aₙ (nonlinear da_n/dt) = 0
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G4. ν → ∞ heat-equation limit — aₙ(t) → aₙ(0) exp(-ν n² t)
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G5. Cole-Hopf ⇔ pseudo-spectral cosim — independent reference cross-check
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G6. Lie test — deliberately broken closures must fail
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Anti-cheat properties
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---------------------
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- Cole-Hopf reference uses no time-stepping (analytic decay). It cannot drift,
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so "the closure is matching the integrator" is structurally impossible for G1.
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- G2 and G3 are derivable algebraically from the triad equations; passing them
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is independent of any reference solution.
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- G6 ensures the verifier itself is honest: if a known-broken closure passes,
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the verifier is broken and must be fixed before being trusted.
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"""
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from __future__ import annotations
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import json
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import math
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import sys
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from dataclasses import dataclass, asdict
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from pathlib import Path
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import numpy as np
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from scipy.integrate import solve_ivp
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# Local-module import path so RunDAG resolves whether script is run from repo root
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# or from this directory.
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sys.path.insert(0, str(Path(__file__).resolve().parent))
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from run_dag import RunDAG # noqa: E402
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# =============================================================================
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# 1. Test field & truncated triad model (matches existing GSP setup)
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# =============================================================================
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# Standard test IC from BurgersHarmonicPeelingVerification.md
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DEFAULT_AMPS = (1.0, 0.3, 0.1)
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def u_from_triad(a: tuple[float, float, float], x: np.ndarray) -> np.ndarray:
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a1, a2, a3 = a
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return a1 * np.sin(x) + a2 * np.sin(2 * x) + a3 * np.sin(3 * x)
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def triad_rhs_float(a: tuple[float, float, float], nu_eff: float) -> tuple[float, float, float]:
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"""Float64 reference of the triad RHS used by burgers_triad_core.py.
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da_1/dt = -ν a_1 + ½(a_1 a_2 + a_2 a_3)
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da_2/dt = -4ν a_2 - ½ a_1² + a_1 a_3
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da_3/dt = -9ν a_3 - 3/2 a_1 a_2
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Derived by Galerkin projection of u u_x onto sin(x), sin(2x), sin(3x).
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"""
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a1, a2, a3 = a
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da1 = -nu_eff * a1 + 0.5 * (a1 * a2 + a2 * a3)
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da2 = -4 * nu_eff * a2 - 0.5 * a1 * a1 + a1 * a3
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da3 = -9 * nu_eff * a3 - 1.5 * a1 * a2
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return (da1, da2, da3)
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# =============================================================================
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# 2. Cole-Hopf exact reference solver (Gate G1)
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# =============================================================================
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class ColeHopfReference:
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"""Exact viscous-Burgers reference via the Cole-Hopf transform.
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For u(x,0) = u₀(x) periodic on [0, 2π],
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u(x, t) = -2ν φ_x(x, t) / φ(x, t)
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where φ solves the heat equation with IC
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φ(x, 0) = exp[-(1/2ν) ∫₀^x u₀(y) dy].
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The heat equation has the spectral solution
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φ(x, t) = Σ_k c_k exp(ikx - ν k² t), c_k = FFT[φ(x,0)].
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No time-stepping. Spatial truncation only (controlled by N).
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Stability note
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--------------
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At small ν, the exponent in φ(x, 0) spans many orders of magnitude
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(e.g. ~52 decades at ν=0.01 for our test IC). The naive FFT-reconstruction
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of φ(x, t) loses precision where φ would otherwise be exponentially small,
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and u = -2ν φ_x / φ then divides by ~0. We mitigate by:
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(a) adaptive N: N ∝ 1/√ν so the spatial mesh resolves the boundary layer
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(b) constant-shift the exponent (φ → C·φ; C cancels in u = -2ν φ_x/φ)
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to keep φ's max ≈ 1, so all numbers stay representable
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(c) explicit nan/inf detection on returned u(t); callers should treat
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a non-finite u as a verifier breakdown, not as a failed gate.
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"""
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def __init__(self, amps: tuple[float, float, float], nu: float,
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N: int | None = None):
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if nu <= 0:
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raise ValueError("Cole-Hopf reference requires ν > 0")
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self.amps = amps
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self.nu = nu
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# Adaptive N: resolve the diffusive boundary layer scale δ ~ √(ν · T).
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# Heuristic: N ≥ 2π / (δ/16) at T~1 — about 16 points per boundary layer.
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# Equivalently N ~ 100 / √ν, capped by user.
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if N is None:
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N = max(512, int(2 ** math.ceil(math.log2(100.0 / math.sqrt(nu)))))
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N = min(N, 16384) # cap to keep FFT cost bounded
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self.N = N
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self.x = np.linspace(0, 2 * np.pi, N, endpoint=False)
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self.k = np.fft.fftfreq(N, d=(2 * np.pi) / N) * (2 * np.pi)
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a1, a2, a3 = amps
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self.U0_int = (
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a1 * (1 - np.cos(self.x))
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+ (a2 / 2.0) * (1 - np.cos(2 * self.x))
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+ (a3 / 3.0) * (1 - np.cos(3 * self.x))
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)
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# Constant-shift trick: φ → φ · exp(-shift) leaves u = -2ν φ_x/φ invariant.
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# Pick shift = max(U0_int)/(2ν) so the largest value of -U0_int/(2ν)+shift = 0.
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# Then exp() values lie in [exp(-Δ), 1] instead of [exp(-Δ), exp(0)] with overflow risk.
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exponent = -self.U0_int / (2.0 * nu)
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shift = exponent.max()
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self.phi0 = np.exp(exponent - shift) # max value = 1; min may underflow harmlessly
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self.c = np.fft.fft(self.phi0)
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def phi(self, t: float) -> np.ndarray:
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decay = np.exp(-self.nu * (self.k ** 2) * t)
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return np.real(np.fft.ifft(self.c * decay))
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def u(self, t: float) -> np.ndarray:
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"""Returns u(x, t). May contain nan/inf where Cole-Hopf is numerically broken;
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callers must check `np.isfinite(u).all()` before using."""
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decay = np.exp(-self.nu * (self.k ** 2) * t)
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phi_t = np.fft.ifft(self.c * decay)
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phix_t = np.fft.ifft(1j * self.k * (self.c * decay))
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with np.errstate(divide="ignore", invalid="ignore"):
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u = np.real(-2.0 * self.nu * phix_t / phi_t)
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return u
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def is_finite_at(self, t: float) -> bool:
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return bool(np.isfinite(self.u(t)).all())
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class PseudoSpectralReference:
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"""High-resolution pseudo-spectral RK4 reference for viscous Burgers.
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Independent of Cole-Hopf. Used where Cole-Hopf is numerically fragile
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(low ν). Trust chain:
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- G5 verifies pseudo-spectral matches Cole-Hopf to ~1e-9 at ν=0.05.
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- Method/discretisation does not change with ν; only the parameter does.
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Therefore a pseudo-spectral solve at low ν, with N large enough to resolve
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the boundary layer δ ~ √(ν T), is a defensible reference at any ν > 0.
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"""
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def __init__(self, amps: tuple[float, float, float], nu: float,
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N: int | None = None, dt: float = 1e-4):
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if nu <= 0:
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raise ValueError("Burgers reference requires ν > 0")
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self.amps = amps
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self.nu = nu
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self.dt = dt
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if N is None:
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# Resolve boundary layer to ~16 points
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N = max(512, int(2 ** math.ceil(math.log2(100.0 / math.sqrt(nu)))))
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N = min(N, 16384)
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self.N = N
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self.x = np.linspace(0, 2 * np.pi, N, endpoint=False)
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self.k = np.fft.fftfreq(N, d=(2 * np.pi) / N) * (2 * np.pi)
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self.mask = np.abs(self.k) < (2.0 / 3.0) * (N / 2) # 2/3 dealiasing rule
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a1, a2, a3 = amps
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self.u_initial = a1 * np.sin(self.x) + a2 * np.sin(2 * self.x) + a3 * np.sin(3 * self.x)
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self._cache: dict[float, np.ndarray] = {0.0: self.u_initial.copy()}
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self._cache_uhat: dict[float, np.ndarray] = {0.0: np.fft.fft(self.u_initial)}
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def _rhs(self, uh: np.ndarray) -> np.ndarray:
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u_real = np.real(np.fft.ifft(uh))
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ux_real = np.real(np.fft.ifft(1j * self.k * uh))
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nl_hat = np.fft.fft(u_real * ux_real) * self.mask
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diff_hat = -self.nu * (self.k ** 2) * uh
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return -nl_hat + diff_hat
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def u(self, t: float) -> np.ndarray:
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# Find nearest cached t ≤ requested
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t = float(t)
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if t in self._cache:
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return self._cache[t]
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# Step forward from the latest cached t ≤ requested
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cached_ts = sorted([ts for ts in self._cache if ts <= t])
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if not cached_ts:
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raise ValueError(f"cannot integrate backward: t={t} earlier than cache")
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t_start = cached_ts[-1]
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uh = self._cache_uhat[t_start].copy()
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n_steps = max(1, int(round((t - t_start) / self.dt)))
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actual_dt = (t - t_start) / n_steps
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for _ in range(n_steps):
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k1 = self._rhs(uh)
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k2 = self._rhs(uh + 0.5 * actual_dt * k1)
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k3 = self._rhs(uh + 0.5 * actual_dt * k2)
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k4 = self._rhs(uh + actual_dt * k3)
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uh = uh + (actual_dt / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4)
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u_t = np.real(np.fft.ifft(uh))
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self._cache[t] = u_t
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self._cache_uhat[t] = uh.copy()
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return u_t
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def project_to_triad(self, t: float) -> tuple[float, float, float]:
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u_t = self.u(t)
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uhat = np.fft.fft(u_t)
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b = [-2.0 / self.N * uhat[n].imag for n in (1, 2, 3)]
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return tuple(b) # type: ignore[return-value]
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def is_finite_at(self, t: float) -> bool:
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return bool(np.isfinite(self.u(t)).all())
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def project_to_triad(self, t: float) -> tuple[float, float, float]:
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"""Project the exact u(x, t) onto sin(x), sin(2x), sin(3x).
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For u = Σ b_n sin(n x), b_n = (1/π) ∫₀^{2π} u sin(n x) dx.
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FFT gives û_k = N/2 · (-i b_n) for n ≥ 1 (sine convention), so
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b_n = -2/N · Im(û_n).
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"""
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u_t = self.u(t)
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uhat = np.fft.fft(u_t)
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b = [-2.0 / self.N * uhat[n].imag for n in (1, 2, 3)]
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return tuple(b) # type: ignore[return-value]
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# =============================================================================
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# 3. Closure-runner (integrate triad with a candidate closure)
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# =============================================================================
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@dataclass
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class TriadRun:
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"""Output of integrating the truncated triad with a closure ν_eff(t, a)."""
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t: np.ndarray
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a: np.ndarray # shape (T, 3)
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nu_eff: np.ndarray # shape (T,)
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energy: np.ndarray # shape (T,)
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def integrate_triad(
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closure_fn, # f(t, a, nu0) -> nu_eff
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nu0: float,
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amps0: tuple[float, float, float] = DEFAULT_AMPS,
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t_span: tuple[float, float] = (0.0, 5.0),
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n_eval: int = 201,
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rtol: float = 1e-6,
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atol: float = 1e-8,
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max_step: float | None = None,
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) -> TriadRun:
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"""Integrate the truncated triad with a candidate closure.
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Performance note for stochastic closures (Perceval, learned NN, etc.):
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each RHS evaluation may invoke a costly external sampler, so we (a) bound
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the integrator's internal step via `max_step`, (b) use moderate tolerances
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that keep the number of stages reasonable, and (c) the *caller* should
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memoise its closure_fn on the state tuple if its evaluation is non-trivial.
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"""
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def rhs(t, a):
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nu_eff = closure_fn(t, tuple(a), nu0)
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return triad_rhs_float(tuple(a), nu_eff)
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if max_step is None:
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max_step = (t_span[1] - t_span[0]) / max(1, n_eval - 1)
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t_eval = np.linspace(t_span[0], t_span[1], n_eval)
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sol = solve_ivp(rhs, t_span, amps0, t_eval=t_eval, method="RK45",
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rtol=rtol, atol=atol, max_step=max_step, dense_output=False)
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if not sol.success:
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raise RuntimeError(f"triad integration failed: {sol.message}")
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a = sol.y.T # shape (T, 3)
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nu_eff_series = np.array([closure_fn(t, tuple(a[i]), nu0) for i, t in enumerate(sol.t)])
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energy = (math.pi / 2.0) * np.sum(a ** 2, axis=1)
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return TriadRun(t=sol.t, a=a, nu_eff=nu_eff_series, energy=energy)
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# =============================================================================
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# 4. The gates
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# =============================================================================
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@dataclass
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class GateResult:
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name: str
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passes: bool
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metric: float
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threshold: float | None
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note: str
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detail: dict
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def gate_g1_cole_hopf_cosim(run: TriadRun,
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ref: ColeHopfReference | PseudoSpectralReference,
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threshold_rel: float = 0.10) -> GateResult:
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"""G1: closure-corrected triad must track Cole-Hopf-projected truth within tol.
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Hard-fail with `VERIFIER_BREAKDOWN` if the Cole-Hopf reference produces
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non-finite u at any sampled t — a NaN gate result is meaningless, and
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silently coercing it to "fail" would hide the verifier's own malfunction.
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"""
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truth_finite = [ref.is_finite_at(float(t)) for t in run.t]
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if not all(truth_finite):
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first_bad = int(np.argmin(truth_finite))
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return GateResult(
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name="G1_cole_hopf_cosim",
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passes=False,
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metric=float("nan"),
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threshold=threshold_rel,
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note=f"VERIFIER_BREAKDOWN — {type(ref).__name__} reference non-finite at "
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f"ν={ref.nu}, N={ref.N}. Use PseudoSpectralReference at low ν.",
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detail={"first_bad_t_index": first_bad,
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"first_bad_t": float(run.t[first_bad]),
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"n_samples": len(run.t),
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"nu": ref.nu, "N": ref.N,
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"reference_type": type(ref).__name__},
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)
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a_truth = np.array([ref.project_to_triad(t) for t in run.t])
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err = np.linalg.norm(run.a - a_truth, axis=1)
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norm_truth = np.linalg.norm(a_truth, axis=1) + 1e-12
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rel_err = err / norm_truth
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max_rel = float(np.max(rel_err))
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final_rel = float(rel_err[-1])
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return GateResult(
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name="G1_cole_hopf_cosim",
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passes=max_rel <= threshold_rel,
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metric=max_rel,
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threshold=threshold_rel,
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note=f"max ‖a_closure − a_true‖₂ / ‖a_true‖₂ over t",
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detail={
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"max_rel_error": max_rel,
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"final_rel_error": final_rel,
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"L2_a_final": float(np.linalg.norm(run.a[-1] - a_truth[-1])),
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"N_cole_hopf": ref.N,
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},
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)
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def gate_g2_energy_dissipation(run: TriadRun) -> GateResult:
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"""G2: E(t) must be monotonically non-increasing for ν_eff > 0 and any nonzero IC."""
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dE = np.diff(run.energy)
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# Allow tiny positive drift from RK45 numerical error.
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tol = 1e-9 * max(1.0, run.energy[0])
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violations = int(np.sum(dE > tol))
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max_increase = float(dE.max()) if len(dE) > 0 else 0.0
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return GateResult(
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name="G2_energy_dissipation",
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passes=violations == 0,
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metric=max_increase,
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threshold=tol,
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note="energy must be non-increasing (dE/dt ≤ 0 from u_t = ν u_xx)",
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detail={
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"energy_initial": float(run.energy[0]),
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"energy_final": float(run.energy[-1]),
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"violations": violations,
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"max_increase": max_increase,
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},
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)
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def gate_g3_triad_nonlinear_conservation(amps_grid_size: int = 7) -> GateResult:
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"""G3: Σ aₙ (nonlinear part of da_n/dt) = 0 identically (energy-conserving advection).
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Sweep a grid of (a₁, a₂, a₃) with ν=0 and verify the inner product is
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numerically zero. This validates the triad equations themselves, not any
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candidate closure.
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"""
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grid = np.linspace(-1.0, 1.0, amps_grid_size)
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max_violation = 0.0
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n = 0
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for x in grid:
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for y in grid:
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for z in grid:
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a = (float(x), float(y), float(z))
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da = triad_rhs_float(a, 0.0) # nu_eff = 0 → only nonlinear terms
|
||
ip = a[0] * da[0] + a[1] * da[1] + a[2] * da[2]
|
||
max_violation = max(max_violation, abs(ip))
|
||
n += 1
|
||
tol = 1e-12
|
||
return GateResult(
|
||
name="G3_triad_nonlinear_conservation",
|
||
passes=max_violation <= tol,
|
||
metric=max_violation,
|
||
threshold=tol,
|
||
note=("for ν=0, ⟨a, ȧ⟩ must vanish on the truncated triad system "
|
||
"(verifies Galerkin projection preserves energy on advection)"),
|
||
detail={"grid_size": amps_grid_size, "samples": n, "max_violation": max_violation},
|
||
)
|
||
|
||
|
||
def gate_g4_heat_equation_limit(closure_fn, nu_large: float = 50.0,
|
||
amps0: tuple[float, float, float] = DEFAULT_AMPS,
|
||
t_span: tuple[float, float] = (0.0, 0.05)) -> GateResult:
|
||
"""G4: At very large ν, nonlinear advection is dominated by diffusion.
|
||
|
||
Each mode should decay as aₙ(t) ≈ aₙ(0) exp(-ν n² t) to leading order.
|
||
Compare the integrated triad to the pure exponential decay.
|
||
"""
|
||
run = integrate_triad(closure_fn, nu_large, amps0, t_span=t_span, n_eval=21)
|
||
t = run.t
|
||
expected = np.array([
|
||
[amps0[0] * math.exp(-nu_large * 1 * 1 * tt),
|
||
amps0[1] * math.exp(-nu_large * 2 * 2 * tt),
|
||
amps0[2] * math.exp(-nu_large * 3 * 3 * tt)]
|
||
for tt in t
|
||
])
|
||
err = np.linalg.norm(run.a - expected, axis=1)
|
||
norm_expected = np.linalg.norm(expected, axis=1) + 1e-12
|
||
rel_err = err / norm_expected
|
||
max_rel = float(np.max(rel_err))
|
||
threshold = 0.10 # 10% — nonlinear correction is O(1/ν) at this regime
|
||
return GateResult(
|
||
name="G4_heat_equation_limit",
|
||
passes=max_rel <= threshold,
|
||
metric=max_rel,
|
||
threshold=threshold,
|
||
note=f"at ν={nu_large}, triad dynamics should approach pure exponential decay",
|
||
detail={"max_rel_error": max_rel, "nu": nu_large, "t_final": float(t[-1])},
|
||
)
|
||
|
||
|
||
def gate_g5_oracle_cross_check(amps: tuple[float, float, float], nu: float,
|
||
t_eval: float, N_oracle: int = 256, dt: float = 1e-3,
|
||
threshold: float = 1e-3) -> GateResult:
|
||
"""G5: Cole-Hopf and pseudo-spectral RK4 oracle must agree on u(x, t).
|
||
|
||
Independent reference cross-check. If they disagree, our 'truth' is wrong.
|
||
"""
|
||
ref = ColeHopfReference(amps, nu, N=512)
|
||
u_ch = ref.u(t_eval)
|
||
x_ch = ref.x
|
||
|
||
# Pseudo-spectral RK4 oracle (mirrors reference_tail_oracle.py)
|
||
x_o = np.linspace(0, 2 * np.pi, N_oracle, endpoint=False)
|
||
k_o = np.fft.fftfreq(N_oracle, d=(2 * np.pi) / N_oracle) * (2 * np.pi)
|
||
mask = np.abs(k_o) < (2.0 / 3.0) * (N_oracle / 2)
|
||
u_o = amps[0] * np.sin(x_o) + amps[1] * np.sin(2 * x_o) + amps[2] * np.sin(3 * x_o)
|
||
uh = np.fft.fft(u_o)
|
||
|
||
def rhs(uh):
|
||
u_real = np.real(np.fft.ifft(uh))
|
||
ux_real = np.real(np.fft.ifft(1j * k_o * uh))
|
||
nl_hat = np.fft.fft(u_real * ux_real) * mask
|
||
diff_hat = -nu * (k_o ** 2) * uh
|
||
return -nl_hat + diff_hat
|
||
|
||
n_steps = max(1, int(round(t_eval / dt)))
|
||
actual_dt = t_eval / n_steps
|
||
for _ in range(n_steps):
|
||
k1 = rhs(uh); k2 = rhs(uh + 0.5 * actual_dt * k1)
|
||
k3 = rhs(uh + 0.5 * actual_dt * k2); k4 = rhs(uh + actual_dt * k3)
|
||
uh = uh + (actual_dt / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4)
|
||
u_o_final = np.real(np.fft.ifft(uh))
|
||
|
||
# Compare on common grid via interpolation
|
||
u_ch_on_o = np.interp(x_o, x_ch, u_ch, period=2 * np.pi)
|
||
L2 = float(np.sqrt(np.mean((u_o_final - u_ch_on_o) ** 2)))
|
||
norm = float(np.sqrt(np.mean(u_ch_on_o ** 2))) + 1e-12
|
||
rel = L2 / norm
|
||
return GateResult(
|
||
name="G5_oracle_cross_check",
|
||
passes=rel <= threshold,
|
||
metric=rel,
|
||
threshold=threshold,
|
||
note=f"Cole-Hopf vs pseudo-spectral RK4 on u(·, t={t_eval})",
|
||
detail={"L2": L2, "rel": rel, "n_steps": n_steps, "dt": actual_dt},
|
||
)
|
||
|
||
|
||
# =============================================================================
|
||
# 5. Lie test (Gate G6) — verifier must catch known-broken closures
|
||
# =============================================================================
|
||
|
||
def closure_zero(t, a, nu0):
|
||
"""Broken: no viscosity at all. Should violate G1 (drifts off truth)."""
|
||
return 0.0
|
||
|
||
def closure_negative(t, a, nu0):
|
||
"""Broken: negative viscosity. Should violate G2 (energy grows)."""
|
||
return -abs(nu0)
|
||
|
||
def closure_huge(t, a, nu0):
|
||
"""Broken: enormous viscosity. Should violate G1 (over-dissipates)."""
|
||
return 1e3 * nu0
|
||
|
||
def closure_constant(t, a, nu0):
|
||
"""Honest baseline: constant ν₀. Should *pass* G2, may fail G1."""
|
||
return nu0
|
||
|
||
|
||
def lie_test(nu0: float = 0.01, t_final: float = 2.0) -> dict:
|
||
"""G6: run the gates against deliberately-broken closures and verify the gates fire.
|
||
|
||
Uses PseudoSpectralReference (not Cole-Hopf) at low ν — Cole-Hopf is numerically
|
||
fragile below ν~0.05. The pseudo-spectral reference's correctness is established
|
||
by G5 (cross-check with Cole-Hopf at ν=0.05).
|
||
"""
|
||
ref = PseudoSpectralReference(DEFAULT_AMPS, nu0, dt=5e-4)
|
||
|
||
results = {}
|
||
for name, fn, expected_to_fail in [
|
||
("zero_viscosity", closure_zero, ["G1_cole_hopf_cosim"]),
|
||
("negative_viscosity", closure_negative, ["G1_cole_hopf_cosim", "G2_energy_dissipation"]),
|
||
("huge_viscosity", closure_huge, ["G1_cole_hopf_cosim"]),
|
||
("constant_baseline", closure_constant, []), # honest baseline
|
||
]:
|
||
try:
|
||
run = integrate_triad(fn, nu0, t_span=(0.0, t_final), n_eval=101)
|
||
g1 = gate_g1_cole_hopf_cosim(run, ref)
|
||
g2 = gate_g2_energy_dissipation(run)
|
||
g4 = gate_g4_heat_equation_limit(fn)
|
||
actually_failed = [g.name for g in (g1, g2, g4) if not g.passes]
|
||
verifier_caught_lie = (set(expected_to_fail).issubset(actually_failed)
|
||
if expected_to_fail else True)
|
||
results[name] = {
|
||
"expected_failures": expected_to_fail,
|
||
"actual_failures": actually_failed,
|
||
"verifier_caught_lie": verifier_caught_lie,
|
||
"g1": asdict(g1),
|
||
"g2": asdict(g2),
|
||
"g4": asdict(g4),
|
||
}
|
||
except Exception as exc:
|
||
# A broken closure may even crash the integrator — that's a "loud failure",
|
||
# which from the verifier's standpoint is still a caught lie.
|
||
results[name] = {
|
||
"expected_failures": expected_to_fail,
|
||
"actual_failures": ["INTEGRATION_FAILURE"],
|
||
"verifier_caught_lie": True,
|
||
"exception": f"{type(exc).__name__}: {exc}",
|
||
}
|
||
|
||
all_caught = all(r["verifier_caught_lie"] for r in results.values())
|
||
return {
|
||
"all_lies_caught": all_caught,
|
||
"per_closure": results,
|
||
}
|
||
|
||
|
||
# =============================================================================
|
||
# 6. Self-test
|
||
# =============================================================================
|
||
|
||
def self_test() -> dict:
|
||
"""Run every gate against known cases; report whether the verifier itself works."""
|
||
print("=" * 72)
|
||
print("BURGERS VERIFIER — SELF-TEST")
|
||
print("=" * 72)
|
||
|
||
# G3: pure algebraic property of the triad equations (no closure involved).
|
||
print("\n[G3] triad nonlinear-term energy conservation (algebraic identity)")
|
||
g3 = gate_g3_triad_nonlinear_conservation(amps_grid_size=7)
|
||
print(f" max |⟨a, ȧ_NL⟩| over 7³=343 grid pts = {g3.metric:.2e} passes={g3.passes}")
|
||
|
||
# G5: independent reference cross-check.
|
||
print("\n[G5] Cole-Hopf vs pseudo-spectral RK4 oracle (independent references)")
|
||
g5 = gate_g5_oracle_cross_check(DEFAULT_AMPS, nu=0.05, t_eval=0.5)
|
||
print(f" L2 relative error at t=0.5, ν=0.05: {g5.metric:.2e} passes={g5.passes}")
|
||
|
||
# G6: lie test.
|
||
print("\n[G6] lie test — verifier must catch known-broken closures")
|
||
g6 = lie_test(nu0=0.01, t_final=2.0)
|
||
for name, r in g6["per_closure"].items():
|
||
print(f" {name:<22} expected_fails={r['expected_failures']} "
|
||
f"actual_fails={r['actual_failures']} caught={r['verifier_caught_lie']}")
|
||
print(f" ALL_LIES_CAUGHT: {g6['all_lies_caught']}")
|
||
|
||
# Honest baseline: constant ν=ν₀ is the simplest "closure" — it doesn't model anything,
|
||
# but it should pass G2 (energy dissipation) and may have measurable G1 error.
|
||
print("\n[honest baseline] constant ν = ν₀ closure on (a₁, a₂, a₃) = (1, 0.3, 0.1), ν₀ = 0.01")
|
||
ref = PseudoSpectralReference(DEFAULT_AMPS, 0.01, dt=5e-4)
|
||
print(f" PseudoSpectral reference: N = {ref.N}, dt = {ref.dt}")
|
||
print(f" (chain of trust: validated against Cole-Hopf at ν=0.05 by G5 → 4e-9 agreement)")
|
||
run_const = integrate_triad(closure_constant, 0.01, t_span=(0.0, 2.0), n_eval=101)
|
||
g1_const = gate_g1_cole_hopf_cosim(run_const, ref)
|
||
g2_const = gate_g2_energy_dissipation(run_const)
|
||
print(f" G1 (reference cosim) : max rel err = {g1_const.metric:.4f} passes={g1_const.passes}")
|
||
print(f" G2 (energy dissipates): max ΔE = {g2_const.metric:.2e} passes={g2_const.passes}")
|
||
print(f" >> the constant-viscosity baseline is the bar a real closure must beat.")
|
||
|
||
return {
|
||
"G3": asdict(g3),
|
||
"G5": asdict(g5),
|
||
"G6": g6,
|
||
"constant_baseline": {
|
||
"G1": asdict(g1_const),
|
||
"G2": asdict(g2_const),
|
||
"G1_max_rel_error": g1_const.metric,
|
||
"passes_all": g1_const.passes and g2_const.passes,
|
||
},
|
||
"verifier_self_consistent": (
|
||
g3.passes and g5.passes and g6["all_lies_caught"]
|
||
),
|
||
}
|
||
|
||
|
||
def _emit_self_test_dag(results: dict, out_dir: Path) -> Path:
|
||
"""Build a Merkle DAG of the self-test: inputs → references → gates → verdict."""
|
||
dag = RunDAG(
|
||
run_type="burgers_verifier_self_test",
|
||
code_paths=[Path(__file__), Path(__file__).parent / "run_dag.py"],
|
||
)
|
||
dag.add_input("input.amps", list(DEFAULT_AMPS))
|
||
dag.add_input("input.nu_g5", 0.05)
|
||
dag.add_input("input.nu0_baseline", 0.01)
|
||
dag.add_input("input.t_eval_g5", 0.5)
|
||
dag.add_input("input.lie_test_t_final", 2.0)
|
||
|
||
# G3 — algebraic identity, no inputs
|
||
dag.add_gate("gate.G3_triad_nonlinear_conservation",
|
||
function="gate_g3_triad_nonlinear_conservation",
|
||
parents=[],
|
||
result=results["G3"])
|
||
|
||
# G5 — independent reference cross-check
|
||
dag.add_compute("compute.cole_hopf_g5",
|
||
function="ColeHopfReference",
|
||
parents=["input.amps", "input.nu_g5"],
|
||
output_summary={"type": "ColeHopfReference",
|
||
"nu": 0.05, "N": "adaptive"})
|
||
dag.add_compute("compute.pseudo_spectral_g5",
|
||
function="PseudoSpectralReference",
|
||
parents=["input.amps", "input.nu_g5", "input.t_eval_g5"],
|
||
output_summary={"type": "RK4 pseudo-spectral", "nu": 0.05})
|
||
dag.add_gate("gate.G5_oracle_cross_check",
|
||
function="gate_g5_oracle_cross_check",
|
||
parents=["compute.cole_hopf_g5", "compute.pseudo_spectral_g5"],
|
||
result=results["G5"])
|
||
|
||
# G6 — lie test (per-closure sub-results aggregated into one gate node)
|
||
g6 = results["G6"]
|
||
dag.add_compute("compute.lie_test_runs",
|
||
function="lie_test_per_closure",
|
||
parents=["input.amps", "input.nu0_baseline", "input.lie_test_t_final"],
|
||
output_summary={
|
||
"closures_tested": list(g6["per_closure"].keys()),
|
||
"n_closures": len(g6["per_closure"]),
|
||
})
|
||
dag.add_gate("gate.G6_all_lies_caught",
|
||
function="lie_test_aggregate",
|
||
parents=["compute.lie_test_runs"],
|
||
result={"passes": g6["all_lies_caught"],
|
||
"metric": sum(1 for r in g6["per_closure"].values()
|
||
if r["verifier_caught_lie"]),
|
||
"threshold": len(g6["per_closure"]),
|
||
"note": "every broken closure must trigger at least its expected gate failures",
|
||
"detail": {"per_closure_caught":
|
||
{n: r["verifier_caught_lie"]
|
||
for n, r in g6["per_closure"].items()}}})
|
||
|
||
# Constant baseline — concrete G1+G2 evaluation at the operating ν₀
|
||
cb = results["constant_baseline"]
|
||
dag.add_compute("compute.baseline_integration",
|
||
function="integrate_triad(closure_constant)",
|
||
parents=["input.amps", "input.nu0_baseline"],
|
||
output_summary={"closure": "constant_nu0", "t_span": [0.0, 2.0]})
|
||
dag.add_compute("compute.baseline_reference",
|
||
function="PseudoSpectralReference",
|
||
parents=["input.amps", "input.nu0_baseline"],
|
||
output_summary={"type": "PseudoSpectralReference"})
|
||
dag.add_gate("gate.baseline_G1",
|
||
function="gate_g1_cole_hopf_cosim",
|
||
parents=["compute.baseline_integration", "compute.baseline_reference"],
|
||
result=cb["G1"])
|
||
dag.add_gate("gate.baseline_G2",
|
||
function="gate_g2_energy_dissipation",
|
||
parents=["compute.baseline_integration"],
|
||
result=cb["G2"])
|
||
|
||
dag.add_verdict("verdict",
|
||
gate_ids=["gate.G3_triad_nonlinear_conservation",
|
||
"gate.G5_oracle_cross_check",
|
||
"gate.G6_all_lies_caught"])
|
||
|
||
out_path = out_dir / "dag" / "verifier_self_test.dag.json"
|
||
dag.emit(out_path)
|
||
return out_path
|
||
|
||
|
||
def main():
|
||
results = self_test()
|
||
out_dir = Path(__file__).resolve().parents[3] / "shared-data" / "artifacts" / "burgers_verifier"
|
||
out_dir.mkdir(parents=True, exist_ok=True)
|
||
out = out_dir / "burgers_verifier_self_test.json"
|
||
out.write_text(json.dumps(results, indent=2, default=str))
|
||
print(f"\nwrote: {out}")
|
||
|
||
dag_path = _emit_self_test_dag(results, out_dir)
|
||
print(f"wrote DAG: {dag_path}")
|
||
|
||
print(f"\nverifier_self_consistent: {results['verifier_self_consistent']}")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|