Dual Agent Architecture: Order vs Chaos
Overview
Two opposing agents act on a viscous Burgers simulation: a chaos agent (injects perturbation \(\varepsilon\), probes fragility) and an order agent (adds artificial viscosity \(\nu_{\text{art}}\), enforces smoothness). Neither alone is sufficient — chaos alone causes blow-up, order alone causes stagnation. The optimal balance defines a learnable annealing schedule via the meta-gradient \(\partial T_{\text{blowup}} / \partial(\text{chaos} - \text{order})\).
Key Results
| Configuration | Blow-Up Time | Leverage vs Baseline |
|---|---|---|
| No agents (baseline) | \(T_0\) | 1.0× |
| Chaos only | \(0.3 \, T_0\) | — (accelerates blow-up) |
| Order only | \(3.5 \, T_0\) | 3.5× |
| Dual agent (optimal) | \(4.2 \, T_0\) | 4.2× |
Optimal Balance
| Parameter | Value | Meaning |
|---|---|---|
| Optimal \(\psi = \text{chaos} - \text{order}\) | \(-0.018\) | Slightly order-dominant |
| Temperature at optimum | \(\approx 0.49\) | Near-balanced, marginal order bias |
| Smoothness extension | 32.6% | Dual beats order-only by this margin |
Interpretation. The dual agent outperforms pure order by 32.6% because the chaos agent discovers fragile regions that the order agent then stabilises. The optimal balance \(\psi = -0.018\) is nearly symmetric — the system needs almost equal chaos and order, with a slight tilt toward stability. This is the self-learning annealing schedule: temperature \(= \text{chaos} / (\text{chaos} + \text{order})\) converges to \(\approx 0.49\).
Analysis
- Order leverage (3.5–4.2×). Artificial viscosity delays blow-up substantially, but cannot prevent it indefinitely. The dual agent squeezes an additional 20% by probing weaknesses first.
- Adaptive annealing. The meta-gradient \(\partial S / \partial \psi\) provides a learnable signal: the annealing schedule is not hand-tuned but emerges from the dynamics.
- Neither agent alone suffices. Chaos alone accelerates blow-up by 70%. Order alone stagnates learning. The interplay is the key mechanism.
Reproducibility
../simplex/build/sxc exp_ns_dual_agent.sx -o build/exp_ns_dual_agent.ll
OPENSSL_PREFIX=$(brew --prefix openssl)
clang -O2 build/exp_ns_dual_agent.ll \
../simplex/runtime/standalone_runtime.c \
-o build/exp_ns_dual_agent \
-lm -lssl -lcrypto -L${OPENSSL_PREFIX}/lib
./build/exp_ns_dual_agentRelated
- Blow-Up Countdown — S as early warning for singularity
- 3D Galerkin NS — extends dual agent to 3D with vortex stretching
- Viscosity Spectrum — chaos/order balance maps to viscosity spectrum