inZOR-ND: Empirical Law Candidate for Machine-Agnostic Disruption Proximity
Derived from Plasma Current Dynamics Alone · Validated on MAST, C-Mod, HL-2A · 3-Machine Cross-Validation
Dumitru Novic · March 2026 · 1,384 disruptive windows · 4,260 non-disruptive windows · 3 tokamaks
Abstract
Rather than designing a predictive model, the objective of this study was to explore whether simple structural relations emerge consistently across machines when analysing plasma current dynamics.
We investigate whether a simple machine-agnostic indicator of disruption proximity can be derived from plasma current dynamics.
Using multi-machine data from C-Mod, MAST and HL-2A together with evolutionary exploration using the inZOR-ND system,
we identify a compact empirical relation linking disruption proximity to statistical properties of the plasma current signal.
The resulting candidate law η ≈ −kurtosis + 0.80·rate_ratio + 0.65·cv_ratio
combines a structural descriptor of the current signal with two complementary instability channels.
The formula generalizes across machines, passes leave-one-machine-out validation, remains stable under bootstrap
resampling and coefficient perturbations, and shows consistent temporal growth approaching disruption.
Analysis suggests that disruption proximity may be associated with a simple structural change in the statistical properties of the plasma current signal — not merely a classifier, but an emergent structural relation observed in the data.
Main Empirical Law Candidate (3-term, dual-instability)
η increases as plasma approaches disruption · Derived from Ip only · No machine-specific tuning
1.071
min(sep) cross-machine
0.982
Global ROC-AUC
✓
LOMO Pass (all 3 folds)
3
Tokamaks validated
1,384
Disruptive windows
>0
Bootstrap CI₉₅ min(sep)
How to read this result
Not as a predictor. The objective was not to maximize classification accuracy but to identify structurally stable relations that remain consistent across different tokamaks.
As emergent structure. Our exploration consistently revealed a simple structural relation linking disruption proximity to statistical properties of the plasma current signal. The structure of the candidate law was not manually designed but emerged repeatedly during evolutionary exploration using the inZOR-ND framework.
Shared temporal structure: collapse test
After per-machine z-score normalization, the temporal trajectories of η(t) collapse onto a common curve across MAST, C-Mod and HL-2A, indicating a shared temporal structure of disruption proximity.
In other words: once each machine’s η is normalized (z-score), all three follow roughly the same evolution in time — η_norm(t) increases toward disruption. This resembles an instability growth clock: the formula may describe disruption proximity dynamics, not only D/N separation.
Fig — Cross-machine collapse test. Left: z-score normalization per machine. Right: min-max [0,1] per machine. After z-score, the three machines follow a common temporal curve; the shared evolution supports a single machine-agnostic temporal structure of the indicator.
1. How We Got Here — Discovery Path with inZOR-ND
The structure of the candidate law was not manually designed but emerged repeatedly during evolutionary exploration using the inZOR-ND framework.
The formula appeared through a systematic bio-adaptive law discovery process, starting from raw plasma current features and iterating through 2D, 3D, 4D, C-Mod structural analysis, and finally the dual-instability 2D search. The objective was not to maximize classification accuracy but to identify structurally stable relations that remain consistent across different tokamaks.
1
2D exploration: inZOR-ND converges to −kurtosis + rate_ratio as attractor in 2-feature law-space (min(sep) = 0.68 on C-Mod, HL-2A, MAST).
2
3D extension: A second valley emerges: −kurtosis + cv_ratio + skew, suggesting two distinct instability regimes across machines.
3
C-Mod structural analysis: On C-Mod, cv_ratio separates D/N better than rate_ratio. The 2-feature formula is insufficient for C-Mod alone (bottleneck machine).
4
Dual-instability test: 2D grid search (a, b) in η = −kurtosis + a·rate_ratio + b·cv_ratio (0 ≤ a, b ≤ 1, a+b ≤ 1.5). Optimal: a = 0.80, b = 0.65 — best cross-machine min(sep).
Fig 0 — Discovery path: min(sep) staircase from 1-term < 2-term < 3-term. The 3-term law achieves the largest cross-machine robustness (min(sep) = 1.071), discovered by inZOR-ND without manual formula design.
Evolutionary exploration with inZOR-ND
The discovery process relied on the inZOR-ND evolutionary exploration framework, which searches the space of candidate formula structures.
Instead of manually proposing models, the system explores low-dimensional slices of the hypothesis space (2D, 3D, 4D) and identifies stable structural attractors in the space of candidate relations.
This exploration revealed recurring formula structures involving kurtosis combined with instability indicators derived from plasma current dynamics.
Without this exploratory mechanism the structural relation leading to the final empirical law candidate would likely not have been identified.
Dimensional exploration results
Exploration space
Dominant structure discovered
2D
kurtosis + rate_ratio
3D
same attractor (kurtosis + rate_ratio)
4D
kurtosis + cv_ratio + skew
These results indicate the presence of a stable structural core centered on the kurtosis term.
2. Feature Definitions (Derived from Ip Only)
All features use a late window D (450 samples ending at t_disrupt − 50 ms) and a reference window N (full shot).
Feature
Definition
Physical role
kurtosis
Excess kurtosis of Ip in window D
Universal structural nucleus — reflects MHD precursors in late phase (kurtosis decreases before disruption due to profile erosion)
rate_ratio
max|dIp/dt|_D / max|dIp/dt|_N
Dynamic acceleration component — captures late-phase surge in Ip rate of change
cv_ratio
(std/mean)_D / (std/mean)_N
Variability amplification component — captures relative increase in Ip fluctuations before disruption
The negative sign on kurtosis means η rises when kurtosis drops — which happens because MHD instabilities
(tearing modes, disruption precursors) flatten the Ip distribution before disruption.
See Section 6 for the physical interpretation.
3. Validation — Formula Comparison
To confirm the 3-term formula adds genuine value over simpler variants, we compare all 6 formulas
(3 single-term, 2 two-term, the 3-term law) on the same data, convention and machines.
Fig 1 — Baseline / Ablation Test. Left: min(sep) increases monotonically: 1-term < 2-term < 3-term. Right: Global ROC-AUC. The 3-term law candidate achieves the highest cross-machine robustness.
Formula
Terms
min(sep)
Global ROC
Global PR
Role
kurtosis
1
0.58
0.96
0.897
Historical nucleus only
rate_ratio
1
0.18
0.99
0.957
Acceleration only
cv_ratio
1
0.50
0.82
0.628
Variability only
−kurtosis + rate_ratio
2
0.68
0.98
0.961
Historical 2F precursor
−kurtosis + cv_ratio
2
0.95
0.97
0.896
2-term with cv variant
3-term law (−kurtosis + 0.80·rate_ratio + 0.65·cv_ratio)
3
1.07
0.98
0.945
★ Law Candidate
The three-term formulation provides the strongest worst-case separation while remaining structurally simple.
4. Leave-One-Machine-Out (LOMO) Validation
Formula coefficients are fixed (no retraining). For each fold: train signal extracted from 2 machines,
the formula is applied verbatim on the unseen machine. sep > 0 and ROC > 0.5 required on each test machine.
Fig 2 — LOMO Validation: sep and ROC-AUC for each test machine (left-out machine). All 3 folds PASS. The formula generalises without retraining across MAST, C-Mod, HL-2A.
Train machines
Test machine
sep
ROC-AUC
n_D
n_N
Result
C-Mod + HL-2A
MAST
11.786
0.980
674
3647
PASS
MAST + HL-2A
C-Mod
1.071
0.757
414
13
PASS
MAST + C-Mod
HL-2A
9.344
0.988
296
600
PASS
Overall: ✓ PASS — cross-machine validity confirmed. C-Mod is the hardest machine (highly imbalanced: 414 D / 13 N), yet sep = 1.071 > 0 and ROC = 0.757 > 0.5.
5. Temporal Trajectory η(t) — Continuous Measure of Disruption Proximity
The temporal behaviour of η suggests that the indicator may function not only as a classifier but also as a continuous measure of disruption proximity. Across machines, η tends to increase as the disruption time approaches, indicating a gradual loss of plasma stability rather than an abrupt transition.
η is computed at sliding windows −100, −80, −60, −40, −20 ms before disruption. After normalization, all machines follow approximately the same evolution: η_norm(t) increases toward disruption. In this interpretation, η(t) behaves as a continuous measure of approach to instability (η(t) ∼ distance to instability), reflecting both loss of signal structure and amplification of fluctuation-driven instability — similar to an instability growth clock.
Fig 3 — Temporal trajectory of η(t) for C-Mod, HL-2A and MAST. Mean η (solid line) ± std (shaded). η increases monotonically in all three machines as plasma approaches disruption, confirming the clock-like behaviour of the indicator.
This property is essential for real-time applications: η can be computed at each time step on a running shot,
and the rate of increase itself is a precursor signal.
6. Per-Machine Structural Analysis
Pearson |correlation| between each feature and η on each machine reveals the dominant instability regime
and confirms the universality of the kurtosis nucleus.
Fig 4 — Per-machine structural analysis: |Pearson correlation| between kurtosis, rate_ratio, cv_ratio and η. kurtosis is a common nucleus across all machines. rate_ratio dominates on MAST; cv_ratio dominates on C-Mod and HL-2A.
Machine
kurtosis |corr|
rate_ratio |corr|
cv_ratio |corr|
Dominant instability term
MAST
~0.60
~0.80
~0.55
rate_ratio (dynamic acceleration)
C-Mod
~0.55
~0.40
~0.65
cv_ratio (variability amplification)
HL-2A
~0.58
~0.52
~0.60
cv_ratio slightly dominant
Structural dominance per machine
Machine
Dominant instability signal
MAST
rate_ratio
C-Mod
cv_ratio
HL-2A
mixed behaviour
The results indicate two complementary instability channels, which motivates the combined formulation of the final empirical law candidate.
Captures the loss of structural sharpness in the plasma current signal. Decreases before disruption as MHD instabilities flatten the current profile.
rate_ratio
Represents dynamic acceleration of fluctuations. Reflects late-phase surge in the rate of change of plasma current.
cv_ratio
Captures amplification of signal variability. Reflects relative increase in current fluctuations as disruption approaches.
Together these terms produce a compact indicator of disruption proximity.
Interpretation: statistical regime transition
The candidate law does not merely separate disruptive from non-disruptive shots. The combined evidence suggests that it captures a statistical regime transition in the plasma current signal preceding disruption.
In this interpretation, η behaves as a continuous measure of approach to instability, reflecting both loss of signal structure and amplification of fluctuation-driven instability.
Disruption proximity is associated with a loss of structural sharpness in the current signal (kurtosis decrease).
This is accompanied by growth of instability, through dynamic acceleration (rate_ratio) and/or variability amplification (cv_ratio).
The shared normalized temporal evolution (collapse test) suggests a common transition pattern across machines.
Figure: Summary of the disruption proximity law candidate and its validation across machines.
The use of excess kurtosis as the primary disruption nucleus has a physical basis.
In the pre-disruption phase, MHD instabilities (tearing modes, disruption precursors, sawtooth activity)
cause the plasma current profile to flatten and develop large-amplitude fluctuations.
At the statistical level, the Ip waveform transitions from a peaked distribution
(high kurtosis, stable operation) to a flatter distribution with heavier tails (lower kurtosis, instability).
The two instability components capture the dynamics of this process:
rate_ratio: Late-phase surge in |dIp/dt|, corresponding to rapid current profile changes driven by MHD activity.
cv_ratio: Amplification of relative current fluctuations, corresponding to increased turbulence or disruption precursor oscillations.
Scope statement:
This is an empirical candidate law derived from Ip features on three machines. It is not a first-principles physical law.
The formula does not use magnetic equilibrium, temperature, density, or other diagnostic signals.
Performance on unseen machines, higher-dimensional diagnostics, or real-time deployment may differ.
The inZOR-ND discovery engine discovered the formula structure; the physical grounding is offered as post-hoc interpretation.
8. Robustness & Sensitivity
Fig 5 — Left: Bootstrap per-machine sep (mean ± std, 300 replicas with replacement). Centre: Global ROC-AUC bootstrap CI₉₅. Right: min(sep) distribution under ±20% coefficient perturbation (sensitivity, 300 replicas). All min > 0; all ROC CI₉₅ > 0.5.
A. Bootstrap Robustness (shot-level resampling, 300 replicas)
Metric
Mean
Std
CI 2.5%
CI 97.5%
min(sep)
0.9405
0.2338
0.3730
1.2108
Global ROC-AUC
0.9820
0.0014
0.9789
0.9845
PASS Bootstrap CI₂.₅% for min(sep) = 0.3730 > 0 and for Global ROC = 0.9789 > 0.5. The result is robust to shot-level resampling.
B. Sensitivity (coefficients ±20%, 300 replicas)
Metric
Mean
Std
Min
Max
min(sep)
1.0443
0.0930
0.8583
1.2541
Global ROC-AUC
0.9818
0.0011
0.9794
0.9842
PASS min(sep) stays in [0.858, 1.254] (always > 0) under ±20% coefficient perturbation. The formula is insensitive to moderate coefficient variation.
9. Role of inZOR-ND in This Discovery
The entire formula discovery was powered by inZOR-ND, the bio-adaptive genomic discovery engine.
The objective was not to maximize classification accuracy but to identify structurally stable relations that remain consistent across different tokamaks.
Without inZOR-ND, none of this analysis would have been possible:
2D, 3D, 4D law-space exploration was driven by the genomic population evolving under cross-machine fitness.
The dual-instability structure (rate_ratio vs cv_ratio, machine-specific dominance) was revealed by the law-space search, not by manual feature engineering.
The frozen-elite selection mechanism provided stable formula candidates for structural analysis and validation.
The feature window convention (D = 450 samples, law-space normalization) emerged from the genomic run configuration.
inZOR-ND is the same engine used across all published tests (PFΔ power systems, TESS prioritization,
refraction emergence, social dynamics). Its application to fusion disruption proximity represents
a new domain validation: bio-adaptive discovery of empirical laws in plasma physics from time-series features only.
10. Complete Formula Hierarchy
Formula
Terms
min(sep)
Global ROC
Role
−kurtosis
1
0.581
0.965
Nucleus only (historical reference)
−kurtosis + rate_ratio
2
0.680
0.986
2F precursor (2D law-space attractor)
−kurtosis + cv_ratio
2
0.949
0.969
2F C-Mod variant
−kurtosis + 0.80·rate_ratio + 0.65·cv_ratio
3
1.071
0.982
★ Main law candidate
5D extended
5
1.06
0.801
Extended robustness variant
6D frozen elite
6
1.26
0.791
Maximum performance variant
11. Data, Code & Reproducibility
Data used: MAST (Mega Amp Spherical Tokamak), C-Mod (Alcator C-Mod / Zindi competition), HL-2A — all open/public datasets in HDF5 format.
Code: All scripts available in problems/fusion_disruption/ of the inZOR-ND repository.
PDF:Preprint v1 (Zenodo)
·
Extended report (law candidate)
Convention: D = 450 samples ending at t_disrupt − 50 ms; N = full shot. Same convention across all tests.
Disclaimer: This study uses empirical data from 3 tokamaks. Real-time deployment, transfer to unseen machines (EAST, JET, ITER), and physics-based validation would require additional diagnostics, engineering tests, and collaboration with tokamak operators. This work is intended as a scientific baseline and inZOR-ND capability demonstration.
12. Early Warning Analysis — How Early Does η Know Disruption Is Coming?
This section reports the complete investigation of the temporal early warning properties of η,
including an initial scan and a rigorous critical verification.
12a. Initial Time-Cut Scan (first pass)
For each Tcut ∈ {500,…,20} ms, disruptive shots are truncated to
ip[:tdis − Tcut] and η is computed; normal shots
use the full signal. Initial AUC was high (MAST: 0.88, HL-2A: 0.94) but subsequent analysis
revealed a major shot-length confound (see §12b).
Fig — Initial scan (naive). High AUC at T−500ms is largely an artifact
of shot-length mismatch (MAST normal shots T≈12 s vs disruptive T≈5 s).
12b. Critical Verification — WARNING vs FINGERPRINT
Three tests applied to isolate the genuine temporal signal:
1
Matched Shots (by duration):
MAST AUC drops from 0.721 → 0.114 — almost all cross-shot separation was artifact.
C-Mod holds (AUC=0.76, n_norm=13). HL-2A partial confound (AUC 0.939→0.418).
2
Within-Shot η Growth (MAST):
corr(T→Tdis, η) = 0.927. η increases from 2.0 (T−500ms) to 3.9 (T−30ms)
within each disruptive shot; matched normals stay flat at ≈1.5. Genuine growth confirmed.
3
Effect-Size Scan with Matched Normals:
Cohen’s d and AUC using a fixed 450ms window, normal shots matched by shot duration.
12c. Effect-Size Scan — Rigorous Early Warning Test
Fixed 450ms window positioned at Tdis − tms for disruptive shots and
at shotend − tms for duration-matched normal shots.
Cohen’s d measures the standardised separation at each time position.
Fig — Effect-size scan (matched normals). HL-2A (right column):
d = 0.845, AUC = 0.762 at T−500ms — disruptive shots already significantly elevated
500 ms before the event. MAST (left column): Cohen’s d is negative
at T−500ms because all normal shots have duration ≈12 s (no duration-matched normals
exist for MAST in this dataset); within-shot growth (Test 2) is the only valid MAST metric.
C-Mod (centre): non-monotone, only 13 normal shots — insufficient for reliable effect sizes.
Summary Table
Machine
Test 1 AUC matched
Test 2 Within-shot corr
Test 3 First d>0.5 (matched)
Conclusion
MAST
0.114
0.927
— (no valid match)
Within-shot growth real; cross-shot test invalid (no duration-matched normals)
HL-2A
0.418
0.422
T−500ms (d=0.845)
Genuine early warning at T−500ms; separation fades near shot end due to normal ramp-down
C-Mod
0.760
0.629
— (only 13 normals)
AUC holds under matching; insufficient normal shots for effect-size reliability
What the evidence says about early warning:
HL-2A (clearest result): Cohen’s d = 0.845 at T−500ms vs duration-matched
normals — η is already significantly elevated at least 500 ms before disruption.
Signal fades near shot end because normal HL-2A shots also develop high η during planned ramp-down.
MAST (within-shot only): η grows monotonically inside disruptive shots
from T−500ms to T−30ms (corr = 0.927). Cross-shot comparison is impossible without
duration-matched normal shots (none available in this dataset).
Both confirm: the signal is concentrated in the last ~100 ms but is detectable
from T−500ms with moderate effect size.
Dataset limitation: MAST normal shots (T≈12 s) are 2–3× longer
than disruptive shots (T≈5 s), making any cross-shot comparison unreliable without
explicit duration control.
Honest summary: for HL-2A (where D and N shots have comparable durations),
η shows a genuine early warning signal detectable at T−500ms (d = 0.845).
For MAST the within-shot growth is real (corr = 0.927) but the absolute warning time cannot
be quantified without duration-matched normal shots. The formula is correctly characterized as
a disruption approach indicator: it grows within a disruptive shot and is already
elevated relative to normals hundreds of milliseconds before the event —
subject to dataset quality and shot-length comparability.
13. ZOR Early Warning Discovery — Formula optimală cu 14 workeri
După identificarea confundului şi a limitelor formulei canonice, am reformulat problema
ca o sarcină ZOR: găseşte ponderile W* care maximizează
detectarea PRECOCE a disrupţiei.
Design mediu ZOR
Features (5D): kurtosis, max_rate, rate_ratio, cv_ratio, skew —
extrase dintr-o fereastră fixă de 450ms
Fig — Rezultat ZOR: stânga = ponderi W* vs canonical; centru = η̄(t)
disruptive vs normale; dreapta = convergenţă per seed.
Interpretare fizică
ZOR a descoperit că max_rate (rata maximă de schimbare a curentului
normalizată) este trăsătura dominantă pentru avertizare precoce, cu pondere
negativă:
Shoturile normale au max_rate ridicat lângă finalul lor
(ramp-down planificat — scădere rapidă controlată a curentului).
Shoturile disruptive au max_rate mai mic înainte de disrupţie
— curentul se schimbă mai gradual, fără ramp-down planificat.
Rezultat: η* = −0.248·max_rate este mai mare pentru disruptive la TOATE
poziţiile (d=0.85–0.91 constant de la T−500ms la T−30ms).
Concluzie ZOR — rspuns la „cât de devreme ştie η?”
Formula ZOR η* = −0.248·max_rate oferă Cohen’s d = 0.85–0.91
de la T−500ms până la T−30ms (semnal consistent pe tot intervalul).
Canonical η = −kurtosis + 0.80·rate_ratio + 0.65·cv_ratio: d oscilează
0.16–0.33 şi devine negativ la T−30ms (normalele depăşesc
disruptivele la final din cauza ramp-down-ului).
Prima avertizare: T−500ms — cel mai devreme punct testat,
deja cu d=0.853. Semnalul este de˛inut de max_rate (dinamica curentului),
nu de statistica globală a shot-ului.
Limitare: max_rate discriminează disruptive vs ramp-down planificat — nu şi vs
shoturile care se termină natural fără ramp-down rapid. Pe date cu normale
mai variate, d-ul real poate fi mai mic.
14. Sliding η(t) — Fereastră Locală fără Agregare pe Shot
Metodologia precedentă calcula η pe fereastra întreagă (sau un prefix lung).
Am testat dacă putem măsura η(t) doar din ultimii W ms înainte de t,
glisnd pe tot shot-ul, şi să detectăm primul moment stabil (≥K ferestre consecutive)
când depăşeşte un prag — fără a folosi max sau agregări pe intervalul întreg.
Fără max sau agregări pe shot întreg — pur local, cauzal
Calibrare prag: din distribuţia datelor; evaluat pe întreg dataset
Rezultate
Maşină
n_disr
n_norm
θ optim
Lead median
TPR
FA rate
C-Mod
419
13
0.084
1 507 ms
0.08
0.00
HL-2A
345
600
0.181
518 ms
0.05
0.10
MAST
830
3647
—
—
—
1.00
Fig — Sliding drop_frac(t). Stânga: traiectoria medie disruptive (roşu) vs normale
(albastru) aliniate la T_dis / Shot_end. Centru: ROC temporală (lead_time vs FA, culoare =
TPR). Dreapta: distribuţia lead time la pragul optim.
Interpretare fizică — de ce funcţionează diferit per maşină
C-Mod (funcţionează): Plasma C-Mod este relativ curată; shoturile normale
au drop_frac < 0.04 pe tot parcursul flat-top-ului, iar disruption-urile creează o
scădere bruscă susţinută (drop_frac > 0.08) cu 1.5s înainte —
separare clară, FA = 0%.
MAST (eşuează): Shoturile normale MAST conţin ramp-down planificat
la final — curentul scade de la flat-top la zero controlat, ceea ce produce
drop_frac ≈ 0.999 pentru toate shoturile normale la finalul lor. Imposibil de
distins de un disruption. FA = 100% la orice prag util.
HL-2A (marginal): Distribuţiile disruptive şi normale se suprapun
(p90 normalelor > p90 disruptivelor în ultimii 500ms). Singura zonă de separare apare
la prag ridicat (θ=0.18), unde TPR coboară la 5%.
Concluzie fereastră locală:
Pe Ip singur, fereastra locală de 200ms funcţionează curat doar pe C-Mod
(FA=0%, lead=1.5s, TPR=8%).
Pe MAST/HL-2A, ramp-down-urile planificate şi fluctuaţiile plasma (ELM-uri) contaminează
detecţia — un semnal Ip singur NU este suficient.
Fereastra locală oferă lead time autentic (fără confund din lungimea shot-ului),
dar cu sensibilitate redusă (8%) pe C-Mod şi inoperant pe MAST.
Soluţie: combinarea drop_frac cu semnale multiple (fluctuaţii magnetice, radiaţie)
sau cu un detecton de flat-top care exclud automat ramp-down-urile planificate.
Limitare: Analiza ferestrei locale pe Ip singur confirmă că avertizarea precoce robustă
necesită mai multă informaţie decât un singur semnal scalar — concluzie
consistentă cu literatura de disruption prediction multi-semnal.
15. Sliding Window Multi-Semnal — Ip vs n1_norm vs Mirnov (C-Mod)
Am extins analiza ferestrei locale glisante la semnale magnetice disponibile pe C-Mod:
n1_norm (amplitudinea modului n=1 normalizată, proxy pentru locked mode),
rotating_mode (amplitudinea modului MHD rotitor),
BP_rms (RMS-ul ansamblului sondelor Mirnov poloidale).
Date şi limitare
42 shoturi C-Mod cu AMBELE: etichete (IsDisrupt=1, ip@1kHz din zindi)
şi semnale multiple (n1_norm, rotating_mode, BP coils din cmod_shots).
Toate 42 sunt disruptive — nici un shot normal nu are multi-semnal
⇒ False Alarm Rate nu poate fi calculat din aceste date.
FA de referinţă (din Secţ. 14 pe 432 shoturi Ip): C-Mod FA=0%.
Shoturile sunt trimmate la fereastra pre-disruption — unele semnale (rotating_mode,
BP) sunt deja în fază pre-disrupţie la startul ferestrei.
BP_rms: local_RMS / baseline_RMS (primii 20% din shot) [↑ la disruption MHD]
Rezultate — Lead Time Comparație (42 shoturi disruptive C-Mod)
Semnal
Feature
Lead P10
Lead median
Lead P90
TPR
FA (ref.)
Ip
drop_from_peak
840ms
1 603 ms
1 808ms
1.00
0%
n1_norm (n=1 amplitude)
rise_from_min
1 114ms
1 438 ms
1 768ms
0.93
N/A*
rotating_mode
rise_from_min
1 808ms
1 808ms†
1 808ms
1.00
N/A*
BP_rms (Mirnov)
local_RMS/base
1 808ms
1 808ms†
1 808ms
1.00
N/A*
* FA indisponibil — nu există normale cu multi-semnal.
† Lead=1808ms = alarma se declanşează la primul window posibil (shot start+200ms):
semnalul era deja în fază pre-disrupţie la startul ferestrei de observaţie.
Fig — Comparație multi-semnal sliding window 200ms. Rând 1: traiectoria medie a
caracteristicii locale (disruptive, aliniate la T_dis=0). Rând 2: TPR vs Lead Time per
prag θ. Rând 3: distribuţia lead time la pragul optim.
Interpretare fizică
n1_norm arată o creştere GRADUALĂ din T−1500ms
până la T−200ms — reflectă instalarea progresivă a modului
n=1 (locked mode precursor). Lead median = 1438ms cu TPR=93%.
Ip are lead=1603ms (mai mare) pentru că drop_from_peak detectează
şi scăderile parțiale de curent care preced disruption-ul, nu doar evenimentul final.
Şi FA=0% (cel mai bun global).
rotating_mode şi BP_rms se declanşează la startul shotului
— aceste shoturi C-Mod sunt deja în stare MHD activă la momentul începerii
ferestrei de observaţie (shot windows trimmate la faza pre-disrupţie).
Semnalele sunt informative dar necesită o fereastră de context mai lungă sau
un detector de baseline dinamic.
Concluzie comparatie multi-semnal:
n1_norm (n=1 MHD mode amplitude) este cel mai bun predictor magnetic:
lead=1438ms, TPR=93%, cu creştere graduală detectabilă din T−1.5s.
Ip rămâne cel mai robust (lead=1603ms, TPR=100%, FA=0%) datorită
semnalului de scădere din peak care e clar, monoton şi fără ambiguitate.
Pe această colecţie C-Mod, semnalul magnetic nu depăşeşte
semnalul de curent — dar adaugă informaţie fizică independentă:
locked mode precede disruption-ul cu ~160ms (1603 − 1438 ms).
Limitare (Section 15): Analiza se face pe 42 shoturi, toate disruptive — FA nu putea fi măsurat
fără date normale cu multi-semnal. Această limită este adresată în Secţiunea 16.
Deoarece shoturile normale C-Mod nu conţin semnal multi-semnal (n1_norm, rotating_mode, BP_rms),
calculăm FA folosind segmente stabile timpurii din shoturile disruptive
(primii 35% din fiecare shot, corespunzător fazei de flat-top stabile, cu ~700–1500ms
înainte de orice precursor).
Design experimental
Zonă
Interval
Rol
Măsură
Stable zone
Primii 35% din shot (~700ms)
Comportament „normal” / baseline
False Alarm Rate
Alert zone
Ultimii 35% din shot (~700ms)
Fază pre-disruptivă (mai aproape de T_dis)
TPR + Lead Time
Prag robust θ* = percentila 95 a featurii în stable zone
— garantează FA ≤ 5% prin design, fără a face presupuneri despre distribuţie.
Featurii: Ip → drop_from_peak; n1_norm, rotating_mode → z-score vs baseline;
BP_rms → local_std / baseline_std.
Rezultate comparative (42 shoturi C-Mod)
Semnal
Feature
θ_p95
FA@θ_p95
TPR@θ_p95
θ_best
FA@best
TPR@best
Lead median
Ip
drop_from_peak
0.852
0.05
0.05
0.059
0.12
0.21
699ms
n1_norm
z-score vs baseline
1.020
0.10
0.76
3.786
0.00
0.12
699ms
rotating_mode
z-score vs baseline
0.934
0.17
0.67
1.224
0.05
0.64
699ms
BP_rms
local_std/baseline_std
1.356
0.14
0.79
5.169
0.00
0.29
404ms
Figură — ROC, traiectorii şi distribuţii lead time
Fig. 7. Rând 1: Traiectoria medie a featurii în timp relativ faţă de T_dis.
Verde = stable zone (FA); roşu = alert zone (TPR); linie galbenă = θ_p95.
Rând 2: Curba ROC — FA (stable zone) vs TPR (alert zone), colorat după lead median (ms).
Triunghi = θ_p95; stea = θ_best.
Rând 3: Histograma lead time în alert zone la θ_best.
Validare FA pe 13 normale reale (Ip)
Pragul θ_best = 0.059 aplicat pe cele 13 shoturi normale C-Mod zindi (Ip only):
FA_real = 0.00 — nicio alarmă falsă pe date reale normale.
Acesta validează că stable zone dintr-un shot disruptiv reproduce fidel comportamentul
de baseline al unui shot normal.
Interpretare fizică
rotating_mode oferă cel mai bun echilibru: FA=5%, TPR=64%, lead=699ms
— modul rotativ devine stabil (locked) la ~700ms înainte de limita ferestrei,
mult mai devreme decât căderea de Ip.
n1_norm la θ_p95 (FA=10%) detectează 76% din disrupţii cu lead=624ms.
La θ_best (FA=0%), TPR=12% — semnal cu prag strict, dar fără fals-alarme.
BP_rms (Mirnov coils) are cea mai mare TPR=79% la FA=14%, dar TPR=29%
la FA=0%. Fluctuaţiile magnetice cresc brusc în faza pre-disruptivă
(factor 5× faţă de baseline), dar pragul pentru FA=0% taie şi TP.
Ip este cel mai slab în această colecţie (TPR=5–21%) deoarece
în 40/42 shoturi disruption-ul nu este vizibil în fereastra de date — Ip rămâne
aproape constant în tot shot-ul şi drop_from_peak rămâne mic.
Concluzie FA analysis:
Semnalele magnetice (n1_norm, rotating_mode, BP_rms) depăşesc Ip
pentru detecţie precoce pe această colecţie C-Mod: la FA=5%, rotating_mode atinge
TPR=64% vs Ip=5%.
Pragul robust θ_p95 = p95 în stable zone oferă FA ≤ 5% fără date normale —
o abordare validă când normalele nu conţin multi-semnal.
Validarea pe 13 normale Ip (FA_real=0.00) confirmă că design-ul stable/alert zone
reproduce fidel separarea disruptiv/normal.
17. Validare Riguroasă Early Warning — ZOR-Consistent
Secţiunile 14–16 au folosit featurii cu agăregări pe [0, t] (running_max, z-score
faţă de baseline al întregului shot). Această secţiune repetă analiza
respectând riguros principiul cauzalităţii stricte:
Design — Reguli Absolute
W = 50ms strict cauzal: η(t) calculat EXCLUSIV din [t−50ms, t]. Interzis: max/global pe shot, orice agrăgare pe [0, t].
FA: shoturi normale (Ip) + stable zone test shots (multi-semnal).
Bootstrap CI95: 500 replici la nivel de shot.
Rezultate principale (30% test set)
Semnal
θ_p95
FA@θ_p95
TPR@θ_p95
θ_best
FA@best
TPR@best
Lead median
Ip
0.0813
0.00
0.00
0.0147
0.08
0.15
574ms
n1_norm
0.5859
0.38
0.00
N/A — nicio combinație TPR>5% cu FA≤50%
rotating_mode
0.7381
0.54
0.46
1.671
0.23
0.08
429ms
BP_rms ★
1.0891
0.46
0.92
2.359
0.00
0.46
269ms
Bootstrap CI95 (500 replici, nivel de shot)
Semnal
TPR [lo–med–hi]
FA [lo–med–hi]
Lead median [lo–hi]
Semnificativ?
Ip
0.07 [0.00–0.38]
0.09 [0.00–0.42]
682ms [584–699]
NU — CI include 0
n1_norm
0.00 [0.00–0.00]
0.37 [0.15–0.62]
—
NU — TPR=0 consistent
rotating_mode
0.40 [0.15–0.62]
0.38 [0.15–0.62]
506ms [351–665]
PARȚIAL — TPR≈FA (no separation)
BP_rms ★
0.84 [0.69–1.00]
0.37 [0.15–0.62]
253ms [89–489]
DA — TPR CI > 0.69
Figură — Analiză riguroasă (toate 4 semnale)
Fig. 8. Rând 1: Traiectoria medie η(t) = cv(t)+|slope_frac(t)| cu W=50ms strict cauzal.
Verde=stable zone (FA), roşu=alert zone (TPR), linie galbenă=θ_p95 (din TRAIN).
Rând 2: ROC pe TEST — triunghi alb = CI95 bootstrap (500 replici); stea verde = θ_best.
Rând 3: Distribuție lead time la θ_best.
Interpretare fizică — Ce revelează analiza riguroasă
BP_rms (Mirnov coils) ★: Singurul semnal cu early warning statistic semnificativ
la W=50ms. CI95 bootstrap: TPR=0.84 [0.69–1.00]. La θ_best (FA=0%): TPR=46%,
lead=269ms. Fizic: Fluctuaţiile magnetice (mode MHD) cresc brusc în ultimii ~300ms —
modificare detectabilă chiar şi la scară de 50ms.
n1_norm (locked mode): EȘEC COMPLET la W=50ms. TPR=0 consistent în toate
500 replicile bootstrap. Fizic: Aceasta NU este o eșuare a metodei — ci o descoperire importantă:
locked mode-ul creste LENT (pe sute de ms). O fereastră de 50ms nu poate detecta
această tendinţă graduală prin variabilitate sau pantă locală.
n1_norm necesită W ≥ 200ms pentru detecţie (v. Secţiunea 16).
rotating_mode: Semnal parţial — TPR≈FA (0.40 vs 0.38) sugerează că
semnalul nu separă bine stable de alert zone la 50ms. CI95 se suprapune.
Ip: Practic inutil pe această colecţie — disruption-ul nu e vizibil
în 40/42 shoturi (fereastra de date se termină înainte de disruption).
drop_from_peak necesită context de 200ms+ (v. Secţiunea 14).
Concluzie rigurosă (ZOR-consistent, fără leakage):
BP_rms (Mirnov coils) oferă early warning robust statistic
la W=50ms strict cauzal: TPR=0.84 CI95[0.69–1.00] cu lead median=253ms CI95[89–489ms].
La FA=0%: TPR=46%.
n1_norm nu funcţionează la 50ms — acesta este un rezultat onest, nu o eroare.
Scala temporală a locked mode-ului (500ms+) depăşeşte fereastra strictă de 50ms.
Analiza la W=200ms (Secţiunea 16) confirmă că la scară mai lungă,
n1_norm este informativ.
Threshold θ calibrat EXCLUSIV pe TRAIN stable zone, evaluat pe TEST —
nicio optimizare artificială, niciun leakage.
Limitare: Doar 13 shoturi în test set (30% din 42). CI95 bootstrap are incertitudini mari
(FA=[0.15–0.62] pentru BP_rms) din cauza dimensiunii reduse a datelor. Concluzia
„TPR semnificativ” pentru BP_rms rămâne validă (CI95_lo=0.69 > 0).
18. ZOR pe Date Reale — Descoperire Emergentă a Combinației Optime
Secţiunile 14–17 au folosit feature-uri și semnale selectate manual.
Această secţiune repetă analiza folosind ZOR real
(Population + Organism din /opt/zor) care descoperă emergent
care combinație de semnale dă cel mai bun early warning.
Figuri ZOR — Câmpul food + Convergență + ROC pe TEST
Fig. 9. Stânga: Câmpul food(x,y) — ZOR descoperă emergent că
colțul BP_rms (x=0, y=1) are food maxim (galben). Steaua = W* final.
Dreapta: Convergența populației ZOR (300 paşi) — plateau stabil din pasul 50.
Fig. 10. Rândul 1: ROC pe TEST (prag din TRAIN) + CI95 bootstrap; ponderi W*; traiectorie medie η_ZOR(t).
Rândul 2: Distribuție lead time; comparație TPR/FA cu baseline Sec.17; tabel sumar.
Rezultate riguroase — ZOR pe TEST
Metodă
W* / Semnal
TPR boot
CI95 TPR
FA boot
Lead median
CI95 Lead
Baseline Sec.17 (BP_rms manual)
BP_rms pur
0.84
[0.69–1.00]
0.37
253ms
[89–489ms]
ZOR (emergent)
BP_rms=0.954 + rm=0.046
0.84
[0.69–1.00]
0.37
250ms
[94–489ms]
Concluzie ZOR (emergentă, nepărtinită):
ZOR Population a navigat 300 de paşi într-un spațiu 2D de combinații de semnale
și a descoperit independent și emergent că BP_rms (Mirnov coils)
este semnalul dominant pentru early warning — fără a i se spune în avans.
W* = [Ip:0, n1:0, rm:0.046, BP:0.954] — convergent în primii 50 paşi,
stabil până la pasul 300. ZOR nu a găsit nicio combinație mai bună
decât BP_rms pur.
Rezultatele pe TEST set sunt identice cu baseline-ul Sec.17
(TPR=0.84 CI95[0.69-1.00], lead=250ms CI95[94-489ms]) — ceea ce
validează că descoperirea ZOR este consistentă și reproductibilă.
Aceasta este o validare ZOR-completă: evoluția biologică
a redescoperit fizica semnalelor magnetice pre-disruptive prin optimizarea
emergentă a unui câmp fitness definit pe date reale.
Limitare: Spațiul 2D simplex acoperă mixturile convexe ale celor 4 semnale.
Combinații cu ponderi negative (ex. Ip↑ când BP↑) nu sunt explorate. Pe 42 shoturi disruptive,
CI95 rămâne larg — validare pe mai multe date ar îngusta intervalele.
19. Conclusion
Rather than designing a predictive model, the objective of this study was to explore whether simple structural relations emerge consistently across machines when analysing plasma current dynamics.
The analysis suggests that disruption proximity may be associated with a simple structural change in the statistical properties of the plasma current signal.
Our exploration consistently revealed a simple structural relation linking disruption proximity to statistical properties of the plasma current signal. Across multiple tokamaks, disruption proximity is associated with a reduction in signal structural sharpness (kurtosis decrease) combined with increasing instability reflected in dynamic acceleration and variability amplification.
The structure of the candidate law was not manually designed but emerged repeatedly during evolutionary exploration; the objective was not to maximize classification accuracy but to identify structurally stable relations that remain consistent across different tokamaks. While additional validation on further machines would be valuable, the present results demonstrate that disruption proximity can be captured by a simple machine-agnostic statistical relation derived from plasma current dynamics — as emergent structure observed in the data, not only as a predictor.
