Causal Structure is Invariant: How CDE Holds Where Neural Networks Collapse

CDE Industrial Case Studies — Breakthrough Results (v2)

The Problem

Every neural network in industrial monitoring makes the same hidden bet: the future looks like the past. Train an LSTM on a turbofan engine under one operating regime, and it works. Move to a different regime — different altitude, different throttle profile, different fault mode — and the predictions fall apart.

LSTM OOD Collapse

Dataset	Op. Conditions	Fault Modes	RMSE	MAE	Degradation
FD001	1	1	3.04	2.38	—
FD002	6	1	37.31	31.41	+1,127%
FD003	1	2	22.47	12.04	+639%
FD004	6	2	37	31.53	+1,117%

A properly trained LSTM baseline achieves RMSE 3.04 in-distribution. On FD002 (different operating conditions): +1,127% degradation. On FD003 (different fault modes): +639% degradation. On FD004 (both): +1,117% degradation.

CDE Structural Discovery (FD001 — 50 Engines)

Theory familycausal_dynamics_graph

Theory score0.72

Field typevector_field

Symmetrytime-translation (preserved)

Decomp. explained var.69.7%

Graph entropy91.346

Path fidelity0.643

Confidence0.726

SNR estimate3.9

Claims produced15

CDE identifies this as a causal dynamics graph with vector field structure on Euclidean topology. Time-translation symmetry is preserved. The conservative + dissipative decomposition explains 69.7% of dynamics — quantifying the split between reversible and irreversible degradation processes.

The Breakthrough: Structural Invariance Across Regimes

Dataset	Ops	Faults	Graph Entropy	Path Fidelity	Confidence	Entropy Δ
FD001	1	1	91.346	0.643	0.726	—
FD002	6	1	91.488	0.583	0.658	+0.16%
FD003	1	2	91.465	0.786	0.719	+0.13%
FD004	6	2	91.291	0.58	0.657	−0.06%

Key Finding

CDE graph entropy varies by less than 0.22% across all four regimes. The LSTM degrades by 1,127% on the same data. The causal structure is effectively invariant.

FD003 (different fault modes) achieves higher path fidelity (0.786) than FD001 (0.643). The two interacting degradation mechanisms create stronger causal signals, enabling CDE to recover more coherent structure.

Tennessee Eastman Process: Near-Perfect Path Recovery

Path fidelity0.997

Confidence0.833

Graph entropy263.01

Theory familycausal_dynamics_graph

CDE achieves 0.997 path fidelity — 99.7% consistency between learned dynamics and actual causal pathways. Confidence of 0.833 is the highest across all experiments.

What CDE Provides That Neural Networks Cannot

Causal Graph: Which sensors causally influence which — directional, not correlative

Identifiability: When data is insufficient to resolve ambiguity, CDE tells you what experiments to run next

Symmetry Detection: Time-translation symmetry preserved — degradation follows the same laws everywhere in the trajectory

Decomposition: 69.7% conservative + dissipative split — how much is reversible vs. irreversible

OOD Detection: Explicit flagging when operating outside validated scope, with severity and recommended actions

Reproducibility

All experiments used ARDA's public API. No embedded code. Data: NASA CMAPSS (4 subsets) + Tennessee Eastman Process. LSTM: a competitive baseline (RMSE 3.04 in-distribution). Hardware: CPU only. Script: experiments/cde_case_studies/run_breakthrough.py

Bottom line: When operating conditions change — and in industry they always change — neural networks become unreliable. CDE discovers the underlying causal structure, which remains invariant. Graph entropy varies by 0.22% where LSTM accuracy degrades by 1,127%. This is a different category of analysis.