Examination of Deep Learning Algorithm for Nuclear Proliferation Risk Modeling

Figures & data

TABLE I Comparison of the Models Included in the Literature on Proliferation Determinants

	Variables
Authors	Domestic Environment	External Environment	Nonproliferation Norms	Technological Capacity
				Economic/Technical Capability	Nuclear Assistance	Nuclear Fuel Cycle	Tacit Knowledge
Singh and Way^[Citation4]	X	X		X
Jo and Gartzke^[Citation5]	X	X	X	X
Fuhrmann^[Citation6]	X	X	X	X	X
Kroenig^[Citation7]	X	X	X	X	X
Li et al.^[Citation8]	X	X	X	X		X
Brown and Kaplow^[Citation9]	X	X	X	X	X
Bell^[Citation10]	X	X	X	X	X
Baxter^[Citation17]	X	X		X			X

TABLE II Timeline of Nuclear Proliferation of a Country Coded by Bleek^[19]

Country	Explore	Pursue	Acquire
United States	1939–	1942–	1945–
Russia	1942–	1943–	1949–
United Kingdom	1940–	1941–	1952–
France	1945–	1954–	1960–
China	1952–	1955–	1964–
Israel	1949–	1955–	1967–
South Africa	1969–1991	1974–1991	1979–1991
Pakistan	1972–	1972–	1987–
India	1948–	1964–1966, 1972–1975, 1980–	1987–
Korea, North	1962–	1980–	2006–
Yugoslavia	1949–1962, 1974–1987	1953–1962, 1982–1987
South Korea	1969–1981	1970–1981
Libya	1970–2003	1970–2003
Brazil	1966–1990	1975–1990
Iraq	1975–1991	1975–1990
Iran	1974–1979, 1984–	1989–
Syria	2000–	2002–2007
Germany	1939–1945
Japan	1941–1945, 1967–1972
Switzerland	1945–1969
Sweden	1945–1970
Norway	1947–1962
Egypt	1955–1980
Italy	1955–1958
Australia	1956–1973
Germany, West	1957–1958
Indonesia	1964–1967
Taiwan	1967–1976, 1987–1988
Romania	1978–1989
Argentina	1978–1990
Algeria	1983–1991

TABLE III Description of the Label in the Time Series Data Set

Multiclass Label	Class Code	Description
No Interest	0	States without any interest in developing a nuclear weapons programs in a given year
Explore	1	Leaders of the state are opening the door to a potential nuclear weapons program in a given year
Pursue	2	Active programs are ongoing, authorized by leaders with the aim of acquiring nuclear weapons or the capacity to construct them on short notice in a given year.
Acquire	3	States obtaining at least rudimentary deliverable nuclear explosive devices in a given year

TABLE IV Model Features

Variable	Description	Source	Range
Economic/Technical Capability Category
Gross domestic product per capita	Purchasing power parity gross domestic product per capita	Ref. [4]	Numeric
Gross domestic product	Gross domestic product	Ref. [8]	Numeric
Industrial capacity	Binary indicator including the threshold value of domestic steel production, electricity generation capacity, and energy consumption of a country	Ref. [4]	0/1
Composite index of capabilities	The composite index of capabilities is a measure of a state’s power, including population, iron and steel production, energy consumption, military expenditure, and military personnel.	Ref. [20]	0 to 1
Nuclear Fuel Cycle Capability Category
Uranium ore production	Uranium ore processing capability (tonnes of uranium per year)	Ref. [8]	Normalized from 0 to 1 (All values are divided by the maximum value of each variable.)
Uranium conversion capability	Uranium conversion capability (tonnes of heavy metal per year)	Ref. [8]
Uranium enrichment capability	Uranium enrichment capability (tonnes of separative work unit per year)	Ref. [8]
Uranium oxide fuel fabrication capability	Uranium oxide fuel fabrication capability (tonnes heavy metal per year)	Ref. [8]
Mixed-oxide fuel fabrication capability	Mixed-oxide fuel fabrication capability (tonnes heavy metal per year)	Ref. [8]
Wet spent fuel storage facility	Away-from-reactor wet spent fuel storage (tonne heavy metal)	Ref. [8]
Dry spent fuel storage facility	Away-from-reactor dry spent fuel storage (tonnes of heavy metal)	Ref. [8]
Spent fuel reprocessing capability	Spent fuel reprocessing capability (tonnes of heavy metal per year)	Ref. [8]
Zirconium alloy processing capability	Zirconium alloy processing capability (tonnes per year)	Ref. [8]
Zircaloy tube fabrication capability	Zircaloy tubing fabrication capability (tonnes per year)	Ref. [8]
Heavy water production capability	Heavy water production capability (tonnes per year)	Ref. [8]
Power reactor capacity	Electricity generation from commercial nuclear reactors [MW(electric)]	Ref. [8]
Number of all reactors	Number of all kinds of reactors	Ref. [8]
Number of fast reactors	Number of fast research reactors	Ref. [8]
Number of heavy water research reactors	Number of heavy water research reactors	Ref. [8]
Number of graphite research reactors	Number of graphite research reactors	Ref. [8]
Number of light water research reactors	Number of light water research reactors	Ref. [8]
Number of other types of research reactors	Number of other types of research reactors	Ref. [8]
Latency level	Variable indicating whether a state had an enrichment or reprocessing plant in operation: 2 if a state had pilot-scale plants of enrichment/reprocessing plants (including weapon possession), 1 if a state had at least laboratory-scale plants of enrichment/reprocessing plants, and 0 if state did not have any of them.	Ref. [21]	0/1/2
Nuclear Assistance Category
Sensitive nuclear assistance	Binary variable whether the state had an experience in receiving sensitive nuclear technologies (i.e., plutonium reprocessing, uranium enrichment) up to that year	Ref. [22]	0/1
Civilian nuclear assistance	Binary variable whether the state had an experience in receiving civilian nuclear assistance up to that year	Ref. [12]	0/1
Cumulative total number of civilian nuclear assistance	Cumulative number of the civilian nuclear assistance that the state had received or transferred up to that year	Ref. [12]	Numeric
Security/Threat Environment Category
Disputes	5-year moving average of the number of militarized interstates per year in which a state is involved	Ref. [4]	Numeric
Rivalry	Binary indicator whether a state was involved in one or more enduring rivalries in a given year	Ref. [4]	0/1
Allies	Binary indicator whether a state has a security guarantee in the form of a defense pact from a nuclear-armed power states (United States, Soviet Union/Russia, China, France, United Kingdom)	Ref. [4]	0/1
Centdems	The percentage of states each year that receive a score of 7 or higher on the Polity IV measure	Ref. [4]	Numeric
Domestic Environment Category
Polity	Polity IV score ranging from −10 to 10 indicating the level of autocracy (−10) to democracy (10)	Ref. [4]	−10 to 10
Openness	Exports plus imports as a share of gross domestic product	Ref. [4]	Numeric
Liberalization	5-year change in Openness variable	Ref. [4]	Numeric
Nonproliferation Norms Category
IAEA membership	Binary indicator whether a state was a member of IAEA at that year	Ref. [23]	0/1
NPT membership	Binary indicator whether a state was a member of the NPT	Ref. [5]	0/1
Safeguard	Binary indicator whether a state ratified the traditional IAEA safeguards (i.e., comprehensive safeguards agreements)	Ref. [8]	0/1
Additional protocol	Binary indicator whether a state has ratified additional protocol	Ref. [24]	0/1
Tacit Knowledge Environment Category
Network size	Diameter reachable (the distance between the nodes farthest from each reachable node) of a social network related to nuclear fuel cycle research	Ref. [17]	Numeric
Network density	Ratio of the number of links versus maximum possible links for a nuclear fuel cycle research network	Ref. [17]	0 to 1
Network clustering	Clustering coefficient measured by social network related to a nuclear fuel cycle research	Ref. [17]	0 to 1
Network diffusion	Ratio of the distance between entities in a network related to nuclear fuel cycle research	Ref. [17]	0 to 1

Fig. 1. MLP used in this study.

TABLE V Specifications of the Data Set in This Study

Specification	Data Set
Batch	64
Epoch	300
Model	MLP
Layers	(41, 28, 20, 12, 8, 4)
Output layer function	Softmax
Loss function	Cross-entropy loss
Optimizer	ADAM
Total data points	4587
Training set	60%
Validation set	20%
Test set	20%

Fig. 2. Loss curve during model training and validation.

TABLE VI Results of the MLP Model

Result	MLP
Validation accuracy (%)	98.037
Validation loss score	12.512
Test accuracy (%)	97.821

TABLE VII Precision, Recall, and F-1 Score of the Test Set

	Level	Score
Precision	No Interest	0.991
	Explore	0.840
	Pursue	0.692
	Acquire	0
Recall	No Interest	0.992
	Explore	0.656
	Pursue	0.947
	Acquire	0
F-1 Score	No Interest	0.991
	Explore	0.737
	Pursue	0.800
	Acquire	0

Fig. 3. ROC curve of the test results.

TABLE VIII MLP Model Specification in the Five-Fold Cross-Validation Analysis

Specification	Model 1	Model 2	Model 3 (Original Model)	Model 4
Number of layers	2	4	6	8
Perceptrons for each layer	(41, 4)	(41, 20, 10, 4)	(41, 28, 20, 12, 8, 4)	(41, 36, 32, 24, 16, 12, 8, 4)

Fig. 4. Stratified five-fold cross-validation results of different MLP models.

TABLE IX Stratified Five-Fold Cross-Validation Results of Different Machine Learning Algorithms

Machine Learning Model	Average Accuracy (%)	Maximum Accuracy (%)	Minimum Accuracy (%)
MLP (six-layer)	95.534	96.841	94.009
Multinomial logistic regression	87.400	93.207	78.105
SVC	75.648	80.501	71.756
kNN	93.198	93.899	92.585
NB (Bernoulli)	78.769	85.605	58.824

Fig. 5. Projection of North Korea.

Fig. 6. Projection of Iran.

Fig. A.1. Confusion matrix of the test results.

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