# Unveiling the Reactivity of Oxygen and Ozone on C2N Monolayer: A First-
Principles Study

Soumendra Kumar Das  School of Physical Sciences, National Institute of
Science Education and Research (NISER) Bhubaneswar, HBNI, Jatni-752050,
Odisha, India  Lokanath Patra  Department of Mechanical Engineering,
University of California Santa Barbara, CA, 93106, USA.  Prasanjit Samal
School of Physical Sciences, National Institute of Science Education and
Research (NISER) Bhubaneswar, HBNI, Jatni-752050, Odisha, India  Pratap K.
Sahoo<EMAIL_ADDRESS><EMAIL_ADDRESS>School of Physical
Sciences, National Institute of Science Education and Research (NISER)
Bhubaneswar, HBNI, Jatni-752050, Odisha, India  Centre for Interdisciplinary
Sciences (CIS), NISER Bhubaneswar, HBNI, Jatni-752050, Odisha, India

(August 28, 2024)

###### Abstract

The process of environmental oxidation is pivotal in determining the physical
and chemical properties of two-dimensional (2D) materials. Its impact holds
great significance for the practical application of these materials in
nanoscale devices functioning under ambient conditions. This study delves into
the influence of O2 and O3 exposure on the structural and electronic
characteristics of the C2N monolayer, focusing on the kinetics of adsorption
and dissociation reactions. Employing first-principles density functional
theory calculations alongside climbing image nudged elastic band calculations,
we observe that the C2N monolayer exhibits resistance to oxidation and
ozonation, evidenced by energy barriers of 0.05 eV and 0.56 eV, respectively.
These processes are accompanied by the formation of epoxide (C–O–C) groups.
Furthermore, the dissociation mechanism involves charge transfers from the
monolayer to the molecules. Notably, the dissociated configurations
demonstrate higher bandgaps compared to the pristine C2N monolayer, attributed
to robust C-O hybridization. These findings suggest the robustness of C2N
monolayers against oxygen/ozone exposures, ensuring stability for devices
incorporating these materials.

##  I INTRODUCTION

The emergence of two-dimensional (2D) materials with interesting and improved
electronic, optical, plasmonic, thermoelectric, and mechanical properties
compared to their bulk counterparts has created enormous interest in the
research community in exploring novel physical phenomena for both fundamental
physics and technological applications [1, 2, 3, 4, 5]. The introduction of
quantum confinement due to reduced dimensionality in these systems has
unlocked a wide array of applications, benefiting both industries and
researchers [6, 7]. Among the large number of 2D materials studied so far
including graphene, hexagonal boron nitride (h-BN), transition metal
dichalcogenides, etc., nitrogenated holey graphene (C2N) monolayer is a
promising candidate having wide applications in optical devices [8, 9],
catalysis [10, 11], molecular membranes [12], photocatalysis [13],
photovoltaics [14], photocatalytic water splitting [15], hydrogen storage
[16], energy storage [17], gas separation [18] etc. The presence of a direct
band gap (1.96 eV), a porous structure with evenly distributed holes, high
specific surface area, and well-aligned band edge positions spanning the water
redox potential values makes the C2N monolayer highly attractive.

The synthesis of two-dimensional C2N structures through wet-chemical methods
is well-established [19], with often introducing impurities like functional
groups due to trapped small molecules (moisture, oxygen, etc.), leading to
unexpected physical, chemical, and mechanical properties in resulting
materials [20, 21]. Interestingly, the 2D C2N crystal exhibits semi-metallic
(graphene-like) behaviour before annealing, attributed to unintentional doping
effects caused by trapped impurities and/or adsorbed gases within the porous
crystal structure, suggesting tunable electronic properties [19].
Additionally, the comprehension of oxygen (O2) and ozone (O3) adsorption and
dissociation on new materials is also crucial from health and environmental
perspectives, along with their impact on diverse devices, considering their
extensive utilization in the semiconductor industry and various sectors such
as food, water treatment, textiles, pharmaceuticals, and medical fields [22,
23, 24, 25, 26, 27, 28, 29]. Furthermore, the catalytic activity of 2D
monolayers is significantly influenced by the adsorption and dissociation of
O2 molecules. Hence, understanding the influence of environmental conditions,
such as the interaction between various oxidizing species in the air and C2N,
holds both fundamental and technological significance.

In recent years, numerous research groups have extensively explored the
catalytic activity of metal-doped C2N in various gas reduction reactions, both
experimentally and theoretically [30, 31, 11, 32]. However, a comprehensive
understanding of the reaction mechanism between pristine C2N and O2/O3 remains
less investigated. In this study, we investigate the interaction between a C2N
monolayer and O2/O3 using a state-of-the-art theoretical approach that
integrates density functional theory with the climbing image nudged elastic
band (CINEB) method [33]. Our primary focus is on understanding the impacts of
O2 and O3 interaction on the geometrical and electronic structures of C2N by
examining chemical bonding, dissociation energy, and density of states [34,
35].

##  II Computational Methods

First-principles calculations based on density functional theory (DFT) were
performed using the Vienna Ab initio Simulation Package (VASP) [36, 37] with
the projector augmented-wave (PAW) method [38]. The exchange-correlation
functional was considered using the Perdew-Burke-Ernzerhof (PBE) [39]
parametrization-based generalized gradient approximation (GGA) level. The
DFT-D2 van der Waals corrections developed by Grimme [40] were implemented to
accurately describe the 2D layer system for the long-range interaction. A
vacuum layer of 20 Å was selected along the ‘Z’ direction from the surface to
avoid interaction between the periodic layers. The energy cut-off for the
plane wave basis was set at 520 eV. Brillouin zone sampling was performed
using a $\Gamma$-centred Monkhorst-Pack ($7\times 7\times 1$) k-mesh [41] for
the structural relaxation and ($9\times 9\times 1$) k-mesh for the electronic
structure calculation of the pristine and adsorbed C2N monolayer. However, a
denser ($18\times 18\times 1$) k-mesh was considered for the calculations of
the projected density of states using the tetrahedron method. The initial
separation between the C2N monolayer and the O2/O3 molecule was set at 4 Å.
The structural relaxation was performed for the pristine and adsorbed
monolayers until the total energy and the Helman-Feynman forces acting on each
atom were less than 10-6 eV and 0.01 eV/Å respectively. The O2 interaction was
studied using a single C2N monolayer with twelve carbon and six oxygen atoms.
In contrast, a larger ($2\times 2\times 1$) supercell was considered for the
ozonation process. The ionic relaxation was performed by placing the O2/O3
molecules at different locations on the C2N monolayer with both horizontal and
vertical orientation. The structure with minimum energy was considered for
further calculations. The CINEB method [33] was adopted to study molecular
interactions with the monolayer surface, describing the minimum energy path
between the initial and final configuration. Atomic charges at the adsorbed
molecules were calculated using Bader’s atoms-in-molecules approach [42]. The
molecule-C2N interaction binding energies ($E_{B}$) have been computed as:

$E_{B}=E(molecule+C_{2}N)-E(molecule)-E(C_{2}N)$ (1)

where $E(molecule+C_{2}N)$, $E(molecule)$ and $E(C_{2}N)$ are the total
energies of the molecule adsorbed C2N configuration, the interacting molecule,
and the pristine C2N monolayer, respectively. The binding energies for the
physisorbed configurations are denoted as physisorbed energy
($E_{\text{phys}}$). The difference in energies between the non-interacting
configurations and the dissociated configurations is designated as
dissociation energy ($E_{\text{diss}}$).

##  III RESULTS AND DISCUSSION:

###  III.1 Structural properties

Structural relaxations were conducted for both C2N monolayers and O2 and O3
molecules using the PBE-DFT level of theory. The optimized lattice constant
for the pristine C2N monolayer was determined to be 8.33 Å, which aligns with
prior experimental [19] and theoretical investigations [16, 43, 15]. The
calculated bond lengths for C–C and C–N bonds are approximately 1.43 (1.47) Å
and 1.34 Å, respectively. Meanwhile, the optimized bond lengths for O2 and O3
molecules are 1.23 Å and 1.28 Å, respectively, and the bond angle of the O3
molecule is 118.23°, consistent with previous findings [44, 45, 46, 34].

The initial separation between the C2N monolayer and the molecules is set to 4
Å at various possible positions across the monolayer (refer to Table S1 for
details in the Supporting Information (SI)). Initially, these configurations
can be considered as non-interacting, given the small binding energies
observed, i.e. 0.03 eV and 0.07 eV for O2 and O3, respectively. Subsequently,
these configurations are allowed to fully relax to attain the physisorbed
configurations. The total energy values indicate that O2 and O3 molecules
oriented horizontally tend to remain positioned above the pyrazine ring (see
Fig. 1(a, c)) and the hollow region (see Fig. 1(e, h)) of the monolayer,
respectively. These lowest energy configurations are then selected for further
investigations. The optimized distances for the lowest energy configurations
are determined to be 2.79 Å (Fig. 1(a, c)) and 2.15 Å (Fig. 1(e, h)) for the
O2 and O3 adsorbed systems, respectively.

Figure 1: Structural configurations of O2/O3 interacting with C2N: Top view of
the relaxed configuration of (a) O2 molecule (b) atomic oxygen on C2N
monolayer surface. The bottom panel indicates the side view of the
corresponding structure.

Figures 1(b) and (d) illustrate the O2 dissociated systems, where the
individual O atoms are bonded to carbon atoms on the surfaces, forming epoxy
(C-O-C) groups, resembling the configuration observed in graphene and C3N
monolayer [34, 47]. Unlike O2, the dissociation of O3 involves two steps.
Initially, O3 decomposes into a molecular O2 and an atomic O. The O atom then
bonds to C-C bonds, creating a C-O-C group, while the O2 molecule remains
floating over the surface at a distance of 2.74 Å (see Fig. 1(f,i)),
resembling the O2-pristine C2N physisorbed configuration. In the final step,
the O2 molecule further dissociates into two O atoms, with each attached to
C-C bonds, resulting in the formation of two additional C-O-C groups as
observed in graphene [34] (see Fig. 1(g,j)). The creation of epoxy groups
involves charge transfers from the monolayer to the atoms, as discussed in the
following sections. The detailed information on the geometrical optimization
for the adsorption of O2/O3 on C2N monolayer are given in Fig. S1-S6 in the
SI.

Figure 2: Reaction pathway for O2 with C2N: Adsorption and dissociation
process of O2 on the C2N monolayer surface, including structural
configurations at intermediate stages. The colour scheme for atoms corresponds
to that utilized in Fig. 1.

###  III.2 Oxygen reactivity

Figure 2 illustrates the transition path depicting the chemical reactivity of
O2 on the pristine C2N monolayer. Initially, we positioned the O2 molecule on
the top of a 1 × 1 × 1 unit cell of the C2N monolayer, maintaining a vertical
distance of 4 Å from the surface. Given the negligibly small calculated
binding energy, this configuration serves as a non-interacting state, with
energy values for subsequent configurations calculated relative to this state.
Following complete ionic relaxation, we observed the distance between the C2N
surface and the O2 molecule is reduced to 2.79 Å (see Fig. 1(c)).
Additionally, the O-O bond length was found to be 1.24 Å, consistent with the
bond length of a free O2 molecule in the triplet state (see Table S2 in the
SI). Calculation of the binding energy yielded -0.16 eV, indicating weak
physisorption of O2 on pristine C2N surfaces. The molecular adsorption process
is further analyzed using Bader charge and charge density difference plot
analyses. Our findings reveal that physisorption involves a minor charge
transfer ( $\sim 0.12e$) from the C2N monolayer to the O2 molecule. This is
supported by the negligible charge accumulation observed at the O2 site in the
charge density difference plot (see Fig. 3(a)). Chakrabarty et al. [48] also
reported similar weak physisorption of O2 on the C2N monolayer.

Following physisorption, O2 encounters a small energy barrier of 0.05 eV as it
proceeds through several intermediate steps, ultimately dissociating the O2
molecule into two O atoms. These dissociated O atoms subsequently attach to
the C-C bonds, forming epoxide (C-O-C) groups on the surface, with a C-O bond
length of $\sim 1.4$ Å as depicted in Fig. 1(b, d) (see Table 1 for details).
Bader’s charge analysis indicates a charge transfer of approximately $1e$ from
C2N to the chemisorbed oxygen atoms. This is further supported by the
significant accumulation of charges at the O sites, as observed in the charge
difference plots provided in Fig. 3(b). The dissociation of O2 molecules into
two O atoms by accepting charges from the C2N monolayer can be attributed to
the antibonding nature of its lowest unoccupied molecular orbital (LUMO) [21].

Figure 3: Charge density difference of O2 on C2N: (a) physisorbed (O2) and (b)
dissociated (O + O) configurations. The iso-surface value was set at 0.03
e/Å3. The yellow and cyan colours represent charge accumulation and depletion,
respectively. The colour scheme for atoms corresponds to that utilized in Fig.
1.

###  III.3 Ozone reactivity

Similar to O2, we investigated the reactivity of O3 by placing it 4 Å above
the C2N monolayer. Following full relaxation, the O3 molecule relaxed to a
distance of 2.15 Å above the hollow region, as illustrated in Figure 1(e, h).
The relaxed configuration exhibited a weak binding energy of -0.31 eV,
indicating the presence of physical adsorption. Bader charge analysis suggests
that physisorption is facilitated by a minimal charge transfer of
approximately $\sim 0.08e$, which is confirmed by the negligible accumulation
of charges on the O3 molecule (Fig. 5(a)). The dissociation of ozone molecules
occurs in two steps: O${}_{3}\rightarrow$ O2 \+ O followed by O + O + O.
Interestingly, this process is similar to the ozone dissociation observed in
graphene monolayer [34].

It is well-established that O3 possesses longer and substantially weaker bonds
compared to O2 due to the coupling of a pair of electrons in orbitals on each
of the terminal atoms, representing a weak $\pi$ interaction within the
molecule [49]. Consequently, when O3 interacts with C2N monolayers, it
initiates bond breaking in the molecule, yielding O and O2, before further
dissociating into atomic oxygens. The complete transition path for O3
adsorption and dissociation is depicted in Fig. 4. Notably, the O3 molecule
must traverse three energy barriers during the dissociation process. Following
relaxation on the surface, O3 begins moving towards the border of the hollow
area from the centre, resulting in a higher energy metastable state. This
state, higher in energy than its previous intermediate state, leads to the
first energy barrier of 0.56 eV.

Figure 4: Reaction pathway for O3 with C2N: Adsorption and dissociation
process of O3 on the C2N monolayer surface, including structural
configurations at intermediate stages. The cyan arrow indicates the trajectory
of the O atom as it transitions between C-C bonds. The colour scheme for atoms
corresponds to that utilized in Fig. 1.

Subsequently, O3 breaks into O + O2, and the O2 molecule remains at a height
of 2.74 Å, indicating a physisorbed state. This height, slightly less than
that in the O2 physisorbed pristine C2N case (2.79 Å), can be attributed to
the attached O atom to the C2N monolayer suggesting a stronger interaction.
The Bader charge analysis and the charge density difference plots (Fig. 5(b))
reveal a charge accumulation of approximately $\sim 1e$ at the O site. The
dissociated O atom then relaxes from the C-C bond of the hollow site to the
C-C bond of the pyrazine ring (indicated by a cyan arrow in Fig. 4) to find a
position of minimum energy. This jump leads to the second energy barrier of
0.53 eV. Subsequently, the dissociated O and O2 on the C2N monolayer undergo
complete relaxation, marking the completion of the first step of the
dissociation process.

Figure 5: Charge density difference of O3 on C2N: (a) physisorbed (O3), (b) intermediate (O2 \+ O), and (c) dissociated (O + O + O) configurations. The iso-surface value for the O3 calculation was set at 0.09 e/Å3. The yellow and cyan colours represent charge accumulation and depletion, respectively. The colour scheme for atoms corresponds to that utilized in Fig. 1. Table 1: Calculated physisorption energy (Ephys), dissociation energy (Ediss), C-O bond lengths (RC-O), Bader charges at O sites (Q0/O), and energy barrier values (Ebarrier) of the initial, intermediate, and final configurations describing O2/O3 interaction with the C2N monolayer | O2 | O3
---|---|---
Process | Physisorption | Dissociation | Physisorption | intermediate | Dissociation
| (O2) | (O + O) | (O3) | (O + O2) | (O + O + O)
Ephys, eV | -0.16 | — | -0.31 | — | —
Ediss, eV | — | -0.94 | — | -0.95 | -3.29
RC-O, Å | 2.79 | 1.39 | 2.15 | 1.39, 2.74 | 1.38
Q0/O atom, $e$ | 0.05 | 1.04 | 0.03 | 1.08, 0.05 | 1.07
Ebarrier, eV | — | 0.05 | — | 0.56, 0.53, 0.43 | —

In the next step, the O2 molecule moves into the pyrazine ring by crossing the
third energy barrier of 0.43 eV. Interestingly, unlike in the pristine case,
the O2 molecule then breaks into two oxygen atoms instantaneously without
encountering any energy barrier. This observation suggests that the oxidized
C2N monolayer is more reactive to O2 exposure. Following this, the dissociated
O atoms attach to the two C-C bonds of the pyrazine ring. However, the O atoms
undergo relaxation and repel each other away, driven by the Coulomb
interaction between their p orbitals, eventually attaching to the benzene
rings (Fig. 4). A similar repulsion phenomenon is observed among chemisorbed
oxygen atoms on the phosphorene surface [50]. The average C-O bond lengths are
approximately $\sim 1.4$ Å for the epoxide (C-O-C) groups in the final relaxed
state. Table 1 provides a summary of the physisorption (Ephys), dissociation
energy (Ediss), C-O bond lengths (RC-O), Bader charges at O sites (Q0/O), and
energy barrier values (Ebarrier) associated with the reactivity of O2 and O3
with the C2N monolayer

###  III.4 Electronic Structure Analysis

Using the PBE-DFT level of theory, a direct band gap of 1.66 eV is estimated
for the pristine C2N monolayer (refer to Fig. 6(a)), consistent with previous
reports [19, 43]. The projected density of states (PDOS) for the pristine C2N
monolayer Fig. 6(a) show that the C and N ‘p’ orbitals majorly contribute to
the valence bands around the Fermi level (EF). Physisorption of O2 on the C2N
monolayer does not significantly alter the band dispersions; instead, it forms
localized molecular states around the EF (Fig. 6(b)). In contrast, the
dissociated configuration exhibits hybridized oxygen-C2N bands dispersed deep
inside the valence band region, nearly 2 eV below the EF. This dissociated
configuration shows an increased direct band gap of 2.09 eV, which is ascribed
to robust C-O hybridization within the epoxy (C-O-C) group on the surface
(Fig. 6(c)).

Figure 6: Projected density of states for O2/O3 interaction with C2N: Top
panel: (a) pristine C2N, (b) physisorbed (O2), and (c) dissociated (O + O)
oxygen configurations. Bottom panel: (a) physisorbed (O3) (b) intermediate (O2
\+ O), and (c) dissociated ( O + O + O) ozone configurations.

In the O3 physisorbed configuration, localized states are observed, indicating
minimal interaction between the molecule and the monolayer (Fig. 6(d)). Upon
dissociation of the O3 molecule into O2 \+ O, the resulting separated O atoms
hybridize with C atoms within the C2N monolayer, forming hybridized bands
situated below 3 eV from the EF. In contrast, the weakly absorbed O2 molecule
yields sharp peaks at the EF (Fig. 6(e)). Following the final step,
dissociated O atoms establish stronger bonds with C atoms on the C2N surface,
generating hybridized bands extending deep below the EF (Fig. 6(f)). This
dissociated configuration demonstrates an increased band gap (1.76 eV) as
compared to the pristine case (1.66 eV). These observations are further
evidenced from the electronic band structure calculations given in Fig. S7, in
the SI. Our findings indicate that the adsorption of O2 and O3 can
significantly modify the electronic structure of the C2N monolayer, primarily
due to the formation of epoxy groups on the C2N surface.

##  IV  CONCLUSION:

We conducted a systematic investigation into the interactions between O2 and
O3 molecules and C2N monolayers, employing DFT along with the CINEB approach.
Our findings reveal that C2N exhibits stability under exposure to O2 and O3,
with energy barriers of 0.05 eV and 0.56 eV, respectively. Upon interaction
with O2, dissociation occurs, leading to the formation of epoxy groups (C-O-C)
on the surface through the bonding of two O atoms. Conversely, ozonation
proceeds in two stages: firstly, O3 dissociates into an atomic O and molecular
O2, followed by further dissociation of O2 into two O atoms, resulting in the
creation of three epoxy groups on the C2N surface. Analyses based on charge
density difference and Bader charge suggest that the dissociation process
involves significant charge transfers from the surface to the molecules.
Examination of the electronic structure reveals higher bandgaps in the
dissociated configurations, attributed to C-O hybridizations. Overall, our
study indicates that C2N monolayers can undergo oxidation by O2/O3, overcoming
energy barriers, and resulting in enhanced bandgaps. Overall, the electronic
properties of C2N can be tailored by adjusting the level of O2/O3 exposure,
offering potential avenues for the design of electronic devices based on C2N
and facilitating advancements in various technological domains.

###### Acknowledgements.

The authors would like to thank the National Institute of Science Education
and Research (NISER), Department of Atomic Energy, Government of India, for
funding the research work through project number RIN-4001. The authors
acknowledge the high-performance computing facility at NISER.

## References

  * Novoselov  _et al._ [2016] K. Novoselov, A. Mishchenko, A. Carvalho, and A. Castro Neto, 2D materials and van der Waals heterostructures, Science 353, aac9439 (2016).
  * Gupta  _et al._ [2015] A. Gupta, T. Sakthivel, and S. Seal, Recent development in 2D materials beyond graphene, Progress in Materials Science 73, 44 (2015).
  * Schaibley  _et al._ [2016] J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nature Reviews Materials 1, 1 (2016).
  * Mannix  _et al._ [2017] A. J. Mannix, B. Kiraly, M. C. Hersam, and N. P. Guisinger, Synthesis and chemistry of elemental 2D materials, Nature Reviews Chemistry 1, 0014 (2017).
  * Glavin  _et al._ [2020] N. R. Glavin, R. Rao, V. Varshney, E. Bianco, A. Apte, A. Roy, E. Ringe, and P. M. Ajayan, Emerging applications of elemental 2D materials, Adv. Mater. 32, 1904302 (2020).
  * Liu and Hersam [2019] X. Liu and M. C. Hersam, 2d materials for quantum information science, Nature Reviews Materials 4, 669 (2019).
  * Turunen  _et al._ [2022] M. Turunen, M. Brotons-Gisbert, Y. Dai, Y. Wang, E. Scerri, C. Bonato, K. D. Jöns, Z. Sun, and B. D. Gerardot, Quantum photonics with layered 2D materials, Nature Reviews Physics 4, 219 (2022).
  * Guan  _et al._ [2015] S. Guan, Y. Cheng, C. Liu, J. Han, Y. Lu, S. A. Yang, and Y. Yao, Effects of strain on electronic and optic properties of holey two-dimensional C2N crystals, Appl. Phys. Lett. 107 (2015).
  * Sun  _et al._ [2016] J. Sun, R. Zhang, X. Li, and J. Yang, A many-body GW+BSE investigation of electronic and optical properties of C2N, Appl. Phys. Lett. 109 (2016).
  * Li  _et al._ [2016] X. Li, W. Zhong, P. Cui, J. Li, and J. Jiang, Design of efficient catalysts with double transition metal atoms on C2N layer, J. Phys. Chem. Lett. 7, 1750 (2016).
  * Ma  _et al._ [2016] D. Ma, Q. Wang, X. Yan, X. Zhang, C. He, D. Zhou, Y. Tang, Z. Lu, and Z. Yang, 3d transition metal embedded C2N monolayers as promising single-atom catalysts: a first-principles study, Carbon 105, 463 (2016).
  * Zhu  _et al._ [2015] L. Zhu, Q. Xue, X. Li, T. Wu, Y. Jin, and W. Xing, C2N: an excellent two-dimensional monolayer membrane for He separation, J. Mater. Chem. A 3, 21351 (2015).
  * Mahmood  _et al._ [2017] J. Mahmood, F. Li, S.-M. Jung, M. S. Okyay, I. Ahmad, S.-J. Kim, N. Park, H. Y. Jeong, and J.-B. Baek, An efficient and ph-universal ruthenium-based catalyst for the hydrogen evolution reaction, Nat. Nanotechnol. 12, 441 (2017).
  * Guan  _et al._ [2017] Z. Guan, C.-S. Lian, S. Hu, S. Ni, J. Li, and W. Duan, Tunable structural, electronic, and optical properties of layered two-dimensional C2N and MoS2 van der Waals heterostructure as photovoltaic material, J. Phys. Chem. C 121, 3654 (2017).
  * Das  _et al._ [2024] S. K. Das, L. Patra, P. Samal, and P. K. Sahoo, Strain-Induced Enhanced Performance in 2D C2N/MoS2 Heterostructures for Photocatalytic Water Splitting: A Meta-GGA Study, ACS Appl. Electron. Mater. 6, 1415 (2024).
  * Varunaa and Ravindran [2019] R. Varunaa and P. Ravindran, Potential hydrogen storage materials from metal decorated 2D-C2N: an ab initio study, Phys. Chem. Chem. Phys. 21, 25311 (2019).
  * Xu  _et al._ [2017] J. Xu, J. Mahmood, Y. Dou, S. Dou, F. Li, L. Dai, and J.-B. Baek, 2D frameworks of C2N and C3N as new anode materials for lithium-ion batteries, Adv. Mater. 29, 1702007 (2017).
  * Yong  _et al._ [2019] Y. Yong, H. Cui, Q. Zhou, X. Su, Y. Kuang, and X. Li, C2N monolayer as NH3 and NO sensors: A DFT study, Appl. Surf. Sci. 487, 488 (2019).
  * Mahmood  _et al._ [2015] J. Mahmood, E. K. Lee, M. Jung, D. Shin, I.-Y. Jeon, S.-M. Jung, H.-J. Choi, J.-M. Seo, S.-Y. Bae, S.-D. Sohn, _et al._ , Nitrogenated holey two-dimensional structures, Nat. Commun. 6, 6486 (2015).
  * Wang  _et al._ [2019] H. Wang, E. J. Sandoz-Rosado, S. H. Tsang, J. Lin, M. Zhu, G. Mallick, Z. Liu, and E. H. T. Teo, Elastic properties of 2D ultrathin tungsten nitride crystals grown by chemical vapor deposition, Adv. Funct. Mater. 29, 1902663 (2019).
  * Patra  _et al._ [2022] L. Patra, G. Mallick, R. Pandey, and S. P. Karna, Surface stability of WN ultrathin films under O2 and H2O exposure: A first-principles study, Appl. Surf. Sci. 588, 152940 (2022).
  * McDonnell and Wallace [2019] S. J. McDonnell and R. M. Wallace, UV-ozone functionalization of 2D materials, Jom 71, 224 (2019).
  * Wang  _et al._ [2017] G. Wang, R. Pandey, and S. P. Karna, Physics and chemistry of oxidation of two-dimensional nanomaterials by molecular oxygen, Wiley Interdiscip. Rev. Comput. Mol. Sci. 7, e1280 (2017).
  * Vig and LeBus [1976] J. Vig and J. LeBus, UV/Ozone cleaning of surfaces, IEEE Trans. Parts, Hybrids, Packag. 12, 365 (1976).
  * Vig [1985] J. R. Vig, UV/ozone cleaning of surfaces, J. Vac. Sci. Technol. A: Vac. Surf. Films 3, 1027 (1985).
  * Jourshabani  _et al._ [2022] M. Jourshabani, M. R. Asrami, and B.-K. Lee, An efficient and unique route for the fabrication of highly condensed oxygen-doped carbon nitride for the photodegradation of synchronous pollutants and H2O2 production under ambient conditions, Appl. Catal. B: Environ. 302, 120839 (2022).
  * De Smedt  _et al._ [2000] F. De Smedt, C. Vinckier, I. Cornelissen, S. De Gendt, and M. Heyns, A detailed study on the growth of thin oxide layers on silicon using ozonated solutions, J. Electrochem. Soc. 147, 1124 (2000).
  * Sankaranarayanan and Ramanathan [2010] S. K. Sankaranarayanan and S. Ramanathan, Electric field control of surface oxygen dynamics and its effect on the atomic scale structure and morphology of a growing ultrathin oxide film, J. Phys. Chem. C 114, 6631 (2010).
  * Perry and Yousef [2011] J. J. Perry and A. E. Yousef, Decontamination of raw foods using ozone-based sanitization techniques, Annu. Rev. Food Sci. 2, 281 (2011).
  * He  _et al._ [2016] B. He, J. Shen, and Z. Tian, Iron-embedded C2N monolayer: a promising low-cost and high-activity single-atom catalyst for CO oxidation, Phys. Chem. Chem. Phys. 18, 24261 (2016).
  * Cui  _et al._ [2018] X. Cui, W. An, X. Liu, H. Wang, Y. Men, and J. Wang, C2N-graphene supported single-atom catalysts for CO2 electrochemical reduction reaction: Mechanistic insight and catalyst screening, Nanoscale 10, 15262 (2018).
  * Mushtaq and Tit [2021] M. Mushtaq and N. Tit, Magnetic single atom catalyst in C2N to induce adsorption selectivity toward oxidizing gases, Sci. Rep. 11, 15848 (2021).
  * Henkelman and Jónsson [2000] G. Henkelman and H. Jónsson, Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points, J. Chem. Phys. 113, 9978 (2000).
  * Patra  _et al._ [2021] L. Patra, G. Sachdeva, R. Pandey, and S. P. Karna, Ozonation of group-IV elemental monolayers: A first-principles study, ACS Omega 6, 19546 (2021).
  * Rawat  _et al._ [2024] A. Rawat, L. Patra, R. Pandey, and S. P. Karna, First-principles study of the oxidation susceptibility of WS2, WSe2, and WTe2 monolayers, Nanoscale 10.1039/D3NR06089F (2024).
  * Kresse and Furthmüller [1996a] G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996a).
  * Kresse and Furthmüller [1996b] G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996b).
  * Blöchl [1994] P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  * Perdew  _et al._ [1996] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  * Grimme [2006] S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem. 27, 1787 (2006).
  * Monkhorst and Pack [1976] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  * Bader [1990] R. Bader,  _Atoms in Molecules: A Quantum Theory_ , International series of monographs on chemistry (Clarendon Press, 1990).
  * Ashwin Kishore and Ravindran [2017] M. Ashwin Kishore and P. Ravindran, Tailoring the electronic band gap and band edge positions in the C2N monolayer by P and As substitution for photocatalytic water splitting, J. Phys. Chem. C 121, 22216 (2017).
  * Moffitt [1951] W. Moffitt, The electronic structure of the oxygen molecule, Proc. R. soc. Lond. Ser. A-Contain. Pap. Math. Phys. Sci. 210, 224 (1951).
  * Mainali  _et al._ [2011] L. Mainali, D. R. Mishra, and M. M. Aryal, First principles calculations to study the equilibrium configuration of ozone molecule, arXiv preprint arXiv:1102.1051 (2011).
  * Kalemos and Mavridis [2008] A. Kalemos and A. Mavridis, Electronic structure and bonding of ozone, J. Chem. Phys. 129 (2008).
  * Zhao  _et al._ [2023] L. Zhao, W. Luo, Z. Huang, Z. Yan, H. Jia, W. Pei, and Y. Tu, Oxygen dissociation on the C3N monolayer: A first-principles study, Applied Surface Science 613, 155912 (2023).
  * Chakrabarty  _et al._ [2017] S. Chakrabarty, T. Das, P. Banerjee, R. Thapa, and G. Das, Electron doped C2N monolayer as efficient noble metal-free catalysts for CO oxidation, Appl. Surf. Sci. 418, 92 (2017).
  * Takeshita  _et al._ [2015] T. Y. Takeshita, B. A. Lindquist, and T. H. Dunning Jr, Insights into the electronic structure of ozone and sulfur dioxide from generalized valence bond theory: Bonding in O3 and SO2, J. Phys. Chem. A 119, 7683 (2015).
  * Ziletti  _et al._ [2015] A. Ziletti, A. Carvalho, D. K. Campbell, D. F. Coker, and A. C. Neto, Oxygen defects in phosphorene, Phys. Rev. Lett. 114, 046801 (2015).


# Curiosity-driven Intuitive Physics Learning

Tejas Gaikwad  Dept. of Computer Science and Engineering
Indian Institute of Technology Jodhpur
Rajasthan, India
<EMAIL_ADDRESS>Romi Banerjee  Dept. of Computer Science and Engineering
Indian Institute of Technology Jodhpur
Rajasthan, India
<EMAIL_ADDRESS>
###### Abstract

Biological infants are naturally curious and try to comprehend their physical
surroundings by interacting, in myriad multisensory ways, with different
objects - primarily macroscopic solid objects - around them. Through their
various interactions, they build hypotheses and predictions, and eventually
learn, infer and understand the nature of the physical characteristics and
behavior of these objects. Inspired thus, we propose a model for curiosity-
driven learning and inference for real-world AI agents. This model is based on
the arousal of curiosity, deriving from observations along discontinuities in
the fundamental macroscopic solid-body physics parameters, i.e., shape
constancy, spatial-temporal continuity, and object permanence. We use the term
’body-budget’ to represent the perceived fundamental properties of solid
objects. The model aims to support the emulation of learning from scratch
followed by substantiation through experience, irrespective of domain, in
real-world AI agents.

###### Index Terms:

Intuitive Physics, Curiosity-driven Learning, Z-numbers, Visual Perception,
Knowledge Base, Knowledge Inference

##  I Introduction

How do we learn? How do we choose what to learn? How do we continually store
and update knowledge? When do we understand that we have understood?… It’s
been centuries that philosophers and scientists have been mulling over such
questions, and these have- and continue to- influence research across
disciplines; the fields of Artificial Intelligence and Machine Learning [1]
being at the pinnacle of such endeavours. Despite present-day machine learning
advancements, it is difficult for a machine to execute a task that a human
naturally performs. There is yet a huge gap between a machine’s ability to
observe, encode experiences and formulate reasons.
Here we present an approach that can potentially be used to design machines
that can ’understand’ the physical world around them. Our model draws
inspiration from the way infants learn [2]. It begins with parsing the
surroundings by sensing all that is in the physical space around them,
interacting with the objects to understand the dynamics, experimenting with
them, and deriving hypotheses and predictions, and eventually reasoning on the
body budget parameters (shape constancy, spatial-temporal continuity, object
permanence). Sensing refers to touch, smell, hearing, smell, and taste.
Physical space is the materialistic world around infant.These basic senses
help humans identify components in their physical space and their behavior,
followed by updating knowledge gathered on the objects through reasoning.
Whenever an unexpected event happens, curiosity gets triggered, which
contributes to the urge to ’know or learn more’ about such an event, further
supported with valid reasons (with as much confidence as is possible).
The way reinforcement learning works is broadly aligned with the biological
infants learning about the physical space. They perceive, they act, develop
the knowledge about the physical space, build the parameters about it,
interlink the knowledge with the parameters to have a virtual simulation of
the physical space around them. The infants learn a lot by observing the
actions, states, results and then try to imitate similar actions.
In our work, we have focused on the visual sense to demonstrate the proposed
method for curiosity-driven learning. We have considered three fundamental
solid body physics properties, essential for the comprehension of object-
dynamics, i.e., Spatial-temporal continuity, Object Permanence, and Shape
constancy, as discussed in the paper [3].

##  II Related Work

By focusing on learning as a function of inferences on fundamental properties
of solid objects, the designed mechanism is envisioned to serve as a substrate
for generalized learning and transfer learning. Some design inspirations are:

  * •

Nguyen et al. 2020[3] discuss the state-of-the-art method to learn intuitive
physics with the help of measuring the element of surprise and explaining it.
Surprises are explained by a function of motion-based surprise and appearance-
based surprise parameters. The evaluation metrics used were Absolute Error
Rate and Relative Error Rate for parameters of Object Permanence, Shape
Constancy, and Spatial-temporal Continuity.

  * •

Pathak et al. (2017)[4] used curiosity to explain the need to explore the
environment and discover novel states. Curiosity is considered an intrinsic
reward that enables the agent to explore the environment more. The method
empowers an agent to learn generalizable skills even in the absence of an
explicit goal.

  * •

Zhou et al. (2020) [5] present ’meta-imitation learning’ as a mechanism of
learning from few demonstrations and trying to imitate them through trial-n-
error.

  * •

Pal et al.(2013) [6] describe a way of representing a knowledge using Zadeh’s
Z-numbers [11]. A Z-number is of the form $<X,A,B>$, where ’X’ is the subject,
’A’ being predicate, a value from a set of possible values for X, and B is the
confidence in ’X’=’A’. The concept can be visually envisaged as the building
blocks of a knowledge graph where ’X’, ’A’ represent the graph nodes, and B
represents the edge weights. The edge weights are the function of
reinforcement. ’X’ and ’A’ are the function of an experience.

  * •

Chitnis et at. (2019)[8] describes a technique where an agent learns to pick
and operate on objects of different shapes and sizes. They trained the agent
in a multitask setting to learn different distribution of object shape and
sizes. Tanwani et al.(2020) [10] describes a semi-supervised approach, named
Motion2vec, towards acquiring manipulation skills shown in surgical videos for
surgical suturing. The main idea behind this approach is learning invariant
representations from surgical videos for tasks of action segmentation and pose
intimation.

  * •

Meier et al. (2017) [9] proposed an approach for learning to learn while
learning. Obtained results have proven fastening initial learning and faster
convergence on subsequent tasks.

##  III Methodology and System Design

We propose a method for curiosity-driven learning of intuitive physics through
interactions with everyday objects. We have considered object’s body-budget
parameters (shape constancy, spatial-temporal continuity, and object
permanence) to parse and understand the physical world around. As stated in
the article [3], these parameters come handy while parsing natural physical
objects-object interactions. All these parameters are represented in the form
of a linear plot w.r.t. time / frame-sequence. These plots demonstrate the
behavior of the object in a given event (from the data-set) as a line plot.
These plots are then examined to identify discontinuity in the object
responses if any, and further trigger the curiosity component if discontinuity
is observed.

###  III-A Dataset

Dataset used for learning and training of our agent is the Intuitive Physics
Dataset [12]. This dataset constitutes a set of possible and impossible events
presented through animations. Every event in the dataset has some objects,
which can be any or all of a cube, cone, and a sphere. These events may or may
not contain an occluder which is a wall in our case. These events can be
further classified as static or dynamic based on the object’s movement in the
event. The sample event of possible and impossible with occluder as a wall is
shown in Fig.1

Figure 1: Dataset Sample Event Representation. In above image, we have 2
object types, a sphere and a wall constituting 9 different scenarios as shown.
Diagram taken from Intuitive Physics Dataset Website

###  III-B System Architecture

The proposed solution is shown in Fig 2. The video input is given to YOLO-v4
model for object detection and localization[7]. The localized object
information is used to obtain linear plots for the body budget parameters.
These linear plots are then used to analyze discontinuities in the responses
as shown in Fig 4. These discontinuities are detected by comparing the
obtained responses for parameters of body budget with the predicted one. The
predictions for the body budget parameters are made using Kalman Filter. Such
discontinuities trigger the curiosity block in the agent’s mind. The curiosity
block makes the agent revisit the previous event and check if there is any
external factor affecting the expected responses of the body budget, factors
like the presence of an occluder. If occluder is detected for the same time
when discontinuities are observed, then the agent accepts this as the reason
for the object behavior, and matches the decision with the ground truth which
is already provided with the dataset. If the responses are matched, the agent
proceeds further for a new event, else it is labeled as an exceptional case.
This exception case is still stored in the knowledge base of the agent, which
further seeks similar responses to gain confidence about that event. If the
agent cannot find reasoning for the discontinuities, it is tagged as an
impossible event and further matched with the ground truth. If ground truth
matches with the labeling by the agent, then it proceeds further for a new
event else added as an exception. The exception added is further generalized
if the number of events gets the same responses for the same state and is also
labeled as a reasoning label, the same way we humans accept some facts which
we might not aware of the reasoning yet but accepts the existence of it.

Figure 2: System Architecture

###  III-C Knowledge Update and Inference

  * •

A generated score for each body budget parameter represents unique
characteristics about the object in the given environment.

  * •

We consider a hypothetical space that we term latent space. The latent space
is similar to plotting data points in a 2D plane and classifying these data
points using clustering. Latent space is divided into three spaces that
represents classes.

  * •

We plot the scores obtained for an unknown object in this latent space. The
closer the calculated data point, the more confident the agent will be to
classify the unknown object as a specific class. The score generated is a
function of parameters of body budget multiplied with constants
$(\alpha,\beta,\gamma)$ with values ranging from 0 to 1, determining the
priority of a particular concept. Priority is decided on the basis of the
presence of the occluder.

  * •

These scores then are represented in the form of a Z-number. A Z-number of the
form $<X,A,B>$ in which ‘X’ represents a class, ‘A’ represents the score
calculated as shown in equation (1), and ‘B’ represents confidence which is
calculated as shown in equation (4) and inference is shown in equation (5)

###  III-D Curiosity Driven Learning

  * •

With a discontinuity in the linear plot of the body budget, the curiosity
block gets activated.

  * •

On activation, the agent revisits the event and tries to find out the
reasoning for the discontinuity as shown in Fig. 2

  * •

If no reasoning found, it will add exceptional value to the reasoning and keep
the information as per ground truth.

  * •

With further past experience, this exception will be removed if multiple
similar experiences are observed.

Figure 3: Example Event. This is the actual dataset sample event whose body
budget concept’s Linear plot is shown in Fig. 4. This event has 2 different
objects, a sphere and a cone moving from one end to another. Sphere follows
the normal path and does not have any surprise factor whereas cone suddenly
appears in one time frame, follows a continuous path and then disappears which
give rise to curiosity Riochet et al.[12] Figure 4: Body Budget parameters
Linear Plot. The continuous line represent the actual path travelled and the
dotted represents the predicted path. Different colors are used for different
object class

###  III-E Equations

As discussed in Section III.B, Z-numbers constitutes of $<X,A,B>$. For an
unknown object, ’X’ will be null initially. ’A’ being the score of the object
w.r.t. the body budget parameters is shown in equation (1). Score generated
for object permanence is given in equation (2).

$A=\alpha*S_{op}+\beta*S_{sc}+\gamma*S_{stc}$ (1)

$S_{op}$ is Score for Object permanence, $S_{sc}$ is Score for Shape
Constancy, $S_{stc}$ is Score for Spatial Temporal Continuity.$S_{sc}$ is
obtained from YOLO-v4 object prediction scores.

$S_{op}=\frac{\sum_{n=1}^{N}P_{Yolo}(O(x_{t}))*ImpactValue}{1000}$ (2)

$P_{Yolo}(O(x_{t}))$ is the prediction score of the detected object. Impact
Value is the unique value specific to a class. For our consideration, we have
assigned constant value of 10 for sphere, value of 100 for cone and a value of
1000 for cube. As we are doing summation, we will be having these value in
terms of 100’s etc. giving unique score for a given class. ’N’ represents
total number of frames. The range for $S_{op}$ will be different for different
class having unique range for each class. $S_{sc}$ is normalised euclidean
distance between object’s images.

$S_{stc}=1-\frac{N-Count\ O(x_{t})}{N}$ (3)

Here, Count O($x_{t}$) is the count of frames in which the object was
detected.

$B_{c}=\frac{\frac{\begin{vmatrix}A_{avg_{c}}-A_{u}\end{vmatrix}}{A_{avg_{c}}}}{\sum_{1}^{N}\
\frac{\begin{vmatrix}A_{avg_{c}}-A_{u}\end{vmatrix}}{A_{avg_{c}}}},B\epsilon\
[0,1],C\epsilon\begin{Bmatrix}Cube,Sphere,Cone\end{Bmatrix}$ (4)

Here, $A_{avg_{c}}$ is average ’A’ score for a particular class, $A_{u}$ is
’A’ value of unknown class. Based on this, ’Z’ will be calculated as in
equation (5)

$Z=C,for\ C\ with\ min\ (B_{c})$ (5)

##  IV Experiment

For the experiment described in Table 1, we considered the ground truth as
’sphere’ and obtained the following values: N = 90, $P_{yolo}(O(x(t))$ = 0.6
(for sphere) and 0.17(for cone). As this does not involve any occluder,
$\alpha=\beta=\gamma=0.33$, Count $O(x_{t})$ for sphere = 48, for cone = 0.

| Object
---
Ground
Truth
| Object
---
Assumed
$S_{op}$ | $S_{stc}$ | $S_{sc}$ | $A$ | $A_{avg}$ | $B$ |  | Inference
---
(Z)
Ground Truth | Sphere | 0.288 | 0.53 | 0.68 | 0.494 | 1.57 | 1.076 | Sphere
Object | 8.16 | 0 | 0.27 | 2.78 | 17.88 | 15.08

TABLE I: Experiment Results Algorithm 1 Algorithm

1:$\textrm{CD()}\ as\ \textrm{Curiosity\ Driven\ Function}$

2:$x_{t}\leftarrow\textrm{Frame\ at\ Time}\ t$

3:$x_{t-1}\leftarrow\textrm{Frame\ at\ Time}\ t-1$

4:$O(x_{t})\leftarrow\textrm{Objects\ located\ in}\ x_{t}\ \textrm{frame}$

5:$G(x_{t})\leftarrow\textrm{Ground\ truth\ of\ objects}$

6:$EoF\leftarrow\textrm{End\ of\ frame}$

7:$O(x_{t}),G(x_{t})\in\\{C_{1},C_{2},C_{3},C_{4}\\}$

8:$C_{1},\ C_{2},\ C_{3},\ C_{4}\ are\ classes$

9:while EoF != True do

10: if O$(x_{t})\in\\{C_{1},C_{2},C_{3}\\}$ then

11: if O($x_{t}$) == O$(x_{t-1})$ then

12: $FlagEvent\leftarrow\textrm{Possible}$

13: $count\ O(x_{t})+=1$

14: else

15: $FlagEvent=\textrm{CD()}$

16: end if

17: else if $O{x_{t-1}}\notin\\{C_{1},C_{2},C_{3}\\}$ then

18: $FlagEvent\leftarrow\textrm{CD()}$

19: end if

20:end while

21:procedure CD( )

22: while EoF != True do

23: if O$(x_{t})\in C_{4}$ then

24: $countwall$ += 1

25: end if

26: if $countwall$ in range $(0.7\times\textrm{count\ O}(x_{t})+\textrm{count\
O}(x_{t}),\textrm{count\ O}(x_{t})))$ then

27: $FlagEvent\leftarrow\textrm{Possible}$

28: else

29: $FlagEvent\leftarrow\textrm{Not Possible}$

30: end if

31: end while

32:return $FlagEvent$

33:end procedure

##  V Conclusion and Discussions

To the best of our knowledge, the proposed idea of curiosity-driven learning
mechanism is a novel technique. It shows promise in applications / areas that
require learning from scratch and learning from learning. Some directions for
future work are as follows,

  * •

Incorporation of a knowledge graph towards never-ending learning and Z-number
based in-policy reinforcement and transfer learning.

  * •

Knowledge-clustering and generation of concept-clouds and ’subjective’
experiences.

  * •

Robots learning from scratch, and eventually from experiences, in any domain.

## References

  * [1] A.M. Turing (1950). “I.—Computing Machinery and Intelligence”. In: Mind LIX.236, pp. 433–460. ISSN: 0026-4423. DOI: 10.1093/mind/LIX.236.433. eprint: https://academic.oup.com/mind/articlepdf/LIX/236/433/30123314/lix-236-433.pdf. URL: https://doi.org/ 10.1093/mind/LIX.236.433.
  * [2] Foti, Francesca et al. (2018). “Are young children able to learn exploratory strategies by observation?” eng. In: Psychological research 82.6. 28725993[pmid], pp. 1212–1223. ISSN: 1430-2772. DOI: 10.1007/s00426-017-0896-0. URL: https://pubmed.ncbi.nlm.nih.gov/28725993.
  * [3] Nguyen, H. et al. (2020). “Learning Intuitive Physics by Explaining Surprise”. In: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pp. 1539–1542. DOI: 10 . 1109 / CVPRW50498 . 2020 . 00195\.
  * [4] Pathak, Deepak et al. (2017). Curiosity-driven Exploration by Self-supervised Prediction. arXiv: 1705.05363 [cs.LG].
  * [5] Zhou, Allan et al. (2020). Watch, Try, Learn: Meta-Learning from Demonstrations and Reward. arXiv: 1906.03352 [cs.LG].
  * [6] Sankar Pal, Romi Banerjee, Soumitra Dutta, Samar Sen Sarma (2013). An insight into the Z-number approach to CWW. Fundamenta Informaticae. 124. 197-229. 10.3233/FI-2013-831.
  * [7] Alexey Bochkovskiy, Chien-Yao Wang, Hong-Yuan Mark Liao:YOLOv4: Optimal Speed and Accuracy of Object Detection. CoRR abs/2004.10934 (2020)
  * [8] R. Chitnis, L. P. Kaelbling, T. Lozano-Pérez, ”Learning Quickly to Plan Quickly Using Modular Meta-Learning,” 2019 International Conference on Robotics and Automation (ICRA), 2019, pp. 7865-7871, doi: 10.1109/ICRA.2019.8794342.
  * [9] Franziska Meier, Daniel Kappler, Stefan Schaal: Online Learning of a Memory for Learning Rates. CoRR abs/1709.06709 (2017)
  * [10] Ajay Kumar Tanwani, Pierre Sermanet, Andy Yan, Raghav Anand, Mariano Phielipp, Ken Goldberg: Motion2Vec: Semi-Supervised Representation Learning from Surgical Videos. CoRR abs/2006.00545 (2020)
  * [11] Lotfi Zadeh (2011). A Note on Z-numbers. Inf. Sci.. 181. 2923-2932. 10.1016/j.ins.2011.02.022.
  * [12] Ronan Riochet, Mario Ynocente Castro, Mathieu Bernard, Adam Lerer, Rob Fergus, Véronique Izard, Emmanuel Dupoux: IntPhys: A Framework and Benchmark for Visual Intuitive Physics Reasoning. CoRR abs/1803.07616 (2018) Link