Preparing infrastructure for surprise: fusing synthetic network, interdependency, and cascading failure models

Faced with destabilizing conditions in the Anthropocene, infrastructure resilience modeling remains challenged to confront increasingly complex conditions toward quickly and meaningfully advancing adaptation. Data gaps, increasingly interconnected systems, and accurate behavior estimation (across scales and as both gradual and cascading failure) remain challenges for infrastructure modelers. Yet novel approaches are emerging—largely independently—that, if brought together, offer significant opportunities for rapidly advancing how we understand vulnerabilities and surgically invest in resilience. Of particular promise are interdependency modeling, cascading failure modeling, and synthetic network generation. We describe a framework for integrating these three domains toward an integrated modeling framework to estimate infrastructure networks where no data exist, connect infrastructure to establish interdependencies, assess the vulnerabilities of these interconnected infrastructure to hazards, and simulate how failures may propagate across systems. We draw from the literature as an evidence base, provide a conceptual structure for implementation, and conclude by discussing the significance of such a framework and the critical tools it may provide to infrastructure researchers and managers.


Introduction
There is a pressing need to understand fine-scale infrastructure dynamics of disturbances. Infrastructure managers often lack insight into how interdependent networks interact and affect each other when failures are triggered (Leavitt and Kiefer 2006, Vespignani 2010, FERC and NERC 2012, Chester and Allenby 2019, Mitsova 2021. Limited vision into how failures occur is accentuated by rapidly changing conditions in local and global environments (i.e. the Anthropocene, as defined by Lewis andMaslin 2015, Steffen et al 2015) which are increasingly subjecting infrastructure to hazards that exceed design conditions Chester 2018, Markolf et al 2021). The accretion of new technologies, climate change, and increasing interdependencies within and across infrastructure introduce novel cascading failure scenarios (Vespignani 2010, Arbesman 2016. Increasingly, small, localized outages initiate large cascading failure events (Ganin et al 2016, Zorn et al 2020. They are usually preceded by the confluence of unlikely factors leading to an extreme outcome (i.e. perfect storms) or are high-impact events that were unforeseen or unimagined (i.e. black swans) (Taleb 2007, Paté-Cornell 2012. These high-impact events are particularly challenging for modelers and infrastructure managers because risks are either unknown or not given necessary attention due to perceptions of low probability (Paté-Cornell 2012). In response to this increasing complexity, infrastructure managers require new models and methods to systematically search for weak signals that probe for new destabilizing conditions (i.e. horizon scanning) (Chester and Allenby 2022).
Horizon scanning requires continued investment toward understanding system dynamics and novel disruptors (  infrastructure's engineering design, construction, and dynamics are well understood. But there is a limited understanding of how infrastructure dynamically interacts with other systems (Chester and Allenby 2019). Infrastructure risk analysis models have historically failed to fill this gap (Buldyrev et al 2010, Hasan andFoliente 2015). Thus, researchers have developed bodies of literature to study infrastructure interdependency (Ouyang 2014, Mahabadi et al 2021 and cascading failure , Valdez et al 2020. These fields generally seek to identify trending behavior and propose changes to repel and resist disturbances and failures (i.e. resilience).
Unfortunately, data availability and low stakeholder participation remain persistent barriers to improving interdependency and cascading failure models (Ouyang 2014, Cantelmi et al 2021. In place data to build models of real networks (figure 1), cascading failure and interdependency models are forced to use benchmark networks like IEEE networks (Mohammadi and Saleh 2021) or virtual city networks like Micropolis (Balakrishnan and Cassottana 2022). However, these theoretical networks (figure 1) lack the realistic detail needed for new design algorithms and risk analysis of future scenarios like extreme climate events (Paté-Cornell 2012, Marcos et al 2017, Bachmann et al 2020. Novel models are needed to aid resilience efforts. In response to the need for detailed data, infrastructure sectors are beginning to develop Synthetic Networks (figure 1): fictional but realistic network models that imitate real-world networks' appearance and behavior (Marcos et al 2017). These networks can serve as platforms for diverse and enhanced urban infrastructure analysis. Realistic synthetic networks generally need to have three properties: the representativeness of existing networks, the confidentiality of real-world data, and the use of real engineering properties (Mohammadi and Saleh 2021). Methodologies and validation of these models are developing, and no established framework or vision is identified in the literature for how synthetic networks should be deployed for resilience research.
This paper seeks to advance the vision for infrastructure resilience and risk analysis modeling. We propose that unique and critical insights exist at the intersection of the three modeling domains of Synthetic Networks, Interdependency Modeling, and Cascading Failure models (figure 1). We refer to this intersection as Synthetic, Interdependent, Cascading Failure Models (SICFMs). Because detailed data continues to challenge interdependency and cascading failure research (Ouyang 2014, Valdez et al 2020, SICFMs may provide the fine-scale analysis necessary to elucidate novel scenarios like black swans or aid in unearthing new solutions for wicked complex problems. Parenthetically, synthetic, and interdependent network models certainly provide research purposes beyond cascading failures (Wang et al 2022b). However, this paper is inspired by the lack of insight that infrastructure managers have toward extreme events and, thus, focuses on cascades. Thus, this paper will explore modeling possibilities for SICFMs. We aim to identify practical uses for fine-scale synthetic models combined with interdependency and cascading failures.
Toward identifying a framework of SICFMs, a state of practice will be conducted for the three research domains. It is necessary to understand procedures, methodologies, capabilities, and limitations for each domain. This state of practice will be focused on literature that uses at least one of the domains. As this study is concerned with modeling and resilience analysis for urban physical infrastructure, the literature search will focus on studies that use geospatial analysis in the model. The literature analysis will focus on physical infrastructure (e.g. power, water, road transportation), referred to as 'civil infrastructure' throughout the text. Reviews already exist for the individual domains, and we will utilize this knowledge base (Banerjee et al 2014, Ouyang 2014, Guo et al 2017, Marcos et al 2017, Wei et al 2019, Bachmann et al 2020, Valdez et al 2020, Mahabadi et al 2021, Mohammadi and Saleh 2021. Following the state of practice, a framework for SICFMs will be developed, and the capabilities from each domain will be synthetized to propose how future SICFMs can be deployed.

State of practice
The three domains in this study are at different stages of research maturity. Synthetic network research is younger than interdependency and cascading failure. However, synthetic studies have recently increased in publication. Interdependency research is rooted in physics and mathematical relationships between theoretical networks but is now applied to study real networks. Similarly, cascading failure research began in the physical sciences using theoretical models but increasingly uses engineering models to simulate failures. Interdependency and cascading failure models often lack detailed information about their networks. This gap appears to be a primary motivation for realistic synthetic network development. Academic search databases, Google Scholar, Web of Science, Scopus, and ASCE libraries were used. Keyword searches included combinations of the terms 'infrastructure,' 'cascading,' 'failure,' 'interdependent,' 'network,' and 'synthetic.' Seventy-six peer-reviewed research publications were identified and analyzed. In addition to the research publications, 18 academic review papers from 2010 to 2022 were included. The state of practice will present general observations about infrastructure network modeling and current practices for synthetic networks, interdependencies, and cascading failure.

General infrastructure network modeling state of practice
Three archetypical network structures were identified in the literature: theoretical, real, and synthetic, as already introduced in figure 1. The archetypes frame the models for infrastructure interdependencies and cascading failures. Theoretical networks generally do not mimic a real infrastructure network topology or operation. Rather, they are specifically designed to experiment with interdependencies between multiple networks or to test topology robustness considering cascading failure to inform future real network design , Wu et al 2021. Real networks use actual network data-often redacted-to study specific components or attributes of infrastructure to identify component criticality, resilience, or vulnerabilities. These models can give prescriptive recommendations to practitioners for maintenance, asset management, or hardening requirements (Abdel-Mottaleb et al 2019, Wang et al 2020, Zorn et al 2020). In contrast, synthetic network models are realistic but fictional networks. Often used for power infrastructure, synthetic networks are being developed to provide realistic test cases for future network optimization and emerging technologies such as microgrids and decentralized renewable generation (Marcos et al 2017, Meyur et al 2022. Theoretical and real networks were primarily used for interdependency studies and cascading failure simulations, whereas most literature on synthetic networks still focuses on model development (Marcos et al 2017).
The three domains have researched many different infrastructures but tend to focus on power, water, communications, transportation, and energy. Power was the most common and contained both transmission and distribution studies. Water primarily focused on network constructs, component criticality, and dependency on power infrastructure. Studies involving communications tended to focus on co-dependency with power and SCADA. Energy infrastructure (non-power), which refers primarily to fossil fuels (e.g. oil and natural gas), also focuses heavily on interdependencies with power. Finally, road and other transportation studies focused on interdependencies with communications networks, storm, water, sewer, and power.

Synthetic infrastructure networks
The development of realistic dynamic simulation methodologies for infrastructure has revealed a dearth of realistic networks to test these methodologies (Marcos et al 2017). Thus, synthetic networks are being developed and validated as realistic representations of their real infrastructure network counterparts. While some public data are often foundationally used, synthetic networks must function primarily without being informed by real network properties. They must also use engineering design for construction and operation (Mohammadi and Saleh 2021). Naturally, the unique functions of different infrastructure will have varying requirements to build a synthetic network. For example, transportation infrastructure has well-documented network topology with well-established models for traffic flow dynamics. This access to topology makes it easy to model the structure and simulate functions. In contrast, power infrastructure organizations do not generally release topology to the public; however, their operations are generally understood and can be engineered in models. So, unlike transportation, it is easy to model the operations of a power network but difficult to know how topology and design should imitate the real world. From 2015 to 2022, synthetic research has produced a small body of literature that has focused chiefly on methodologies for network development with some emphasis on operations. But their practical uses for interdependency or cascading failure simulations are beginning to emerge.
Synthetic power models are the most developed civil infrastructure. Mohammadi and Saleh (2021) completed the first systematic review of synthetic power models. Transmission models have advanced separately and faster than distribution models. Many transmission test networks, their datasets, and some open-source models are publicly available, but no convenient software platforms have been released. Additionally, studies have yet to automate the network creation process for transmission or distribution. Some expert design with manual input is still required.
Synthetic transmission power models commonly use population data to estimate large-scale loads (Gegner et al 2016) and contingency and sensitivity analysis to balance the model for realistic responses to demand fluctuations (Birchfield et al 2019, Birchfield and. Realistic topology is particularly challenging for synthetic transmission networks because the lines often cut across geographical features or do not follow other urban features such as roads. Thus, models often use economic and technical optimization to design transmission network topology (Espejo et al 2019). This topology construction is sometimes aided by Delaunay triangulation and 'minimum spanning tree,' a geometrical optimization method. Transmission line edges-covering more considerable distances-are mapped in a 'line of sight' direction from node to node (Mohammadi and Saleh 2021).
Synthetic power distribution models have kept pace with synthetic transmission models. Typically, distribution network edges are assumed to follow road topology from open-source street data (Mohammadi and Saleh 2021). Synthetic distribution feeders have been synthesized using generalized census data for small-grid test cases (Saha et al 2019), allowing for detailed, realistic grid monitoring in power flow simulators. Ali et al (2022) incorporated customer-level power data with demand for every facility in the distribution area. They used a validation methodology that included a review from industry experts at a local utility company. Notably, the researchers had access to detailed demand data-which deviates slightly from the tradition of synthetic models using public-only data. In partnership with NREL, Mateo et al (2020) created 'RNM-US,' a methodology to synthesize power distribution networks for large areas in the United States. Meyur et al (2022) created a synthetic distribution model using publicly available data in combination with engineering and economic optimization. The simultaneous emergence of various synthetic transmission and distribution models bodes well for the future of synthetic power research. Ideally, merging best practices will unify research efforts as methodologies are refined.
The combining of synthetic transmission and distribution networks was only identified once in the literature. Li et al (2020) combined a synthetic power distribution grid model created by the RNM-US model  with existing synthetic transmission methodologies (Gegner et al 2016, Birchfield et al 2017 to develop a realistic and cross-scale synthetic power grid for the entire state of Texas. The methodology was validated using utility-provided metadata. Water distribution models have received some synthetic methodology development. DynaVIBe was one of the earliest attempts to synthesize water networks (Sitzenfrei et al 2010). The model used roads to create a realistic topology with simplified demand estimations. The authors later improved their loop methodology to reduce unnecessary redundancies (Mair et al 2014). Then, using an Integrated Urban Water Management Model by Sharvelle et al (2017) to estimate small-scale demand, Ahmad et al (2020) automated the hydrology design in EPAnet using the minimum spanning tree and looping algorithm inspired from Mair et al (2014), resulting in a model that realistically imitated the Phoenix Metro Region. More recently, a synthetic dynamic water flow framework was developed in a multi-infrastructure synthetic study by Wang et al (2022b). Instead of focusing on realistic network generation, they used existing synthetic networks to develop a methodology for dynamic flow throughout the water network and between the other networks. Momeni et al (2023) designed an iterative WDN synthetic network generator. They used standard design criteria to govern network creation and used resilience and cost constraints as optimization factors.
The remaining infrastructure types that included synthetic networks were road transportation, communications, energy, stormwater, and buildings. Synthetic development appears nascent for these sectors. Most research for transportation infrastructure focuses on road networks (Mohebbi et al 2020). Road topology is well documented with publicly accessible data, eliminating the need for synthesizing. Additionally, existing dynamic traffic flow models are abundant, but they have significant theoretical components because of the agent-based nature of traffic flow . As such, they are not 'synthetic' in the same ways as, for example, power or water. Thus, the characteristics of synthetic networks may vary across infrastructure domains. Despite these differences, other infrastructure models aim to recreate realistic behavior. For example, a synthetic road model was coupled with synthetic stormwater to analyze resilience during intense storms and floods. The geographic and physical interdependencies revealed more realistic responses for the two infrastructures that would have been latent in single-network analysis (Yang et al 2019). Moreover, in a later study, the same authors added variance to storm sewer component conditions for nuance and realistic behavior (Yang et al 2020b). Additionally, Wang et al (2022b) modeled dynamic exchanges of resources within and between natural gas, power, and water networks instead of static or binary interdependencies. Two studies created synthetic communication networks and paired them with synthetic power grids. In both cases, the communication network topology was based on the power topology. Additionally, network operation was calculated stochastically instead of realistic engineering parameters (Korkali et al 2017, Fu et al 2022. Some published research has mapped approximate connections of global internet infrastructure (Durairajan et al 2013). But, generally, models for other infrastructures do not seek to meet the same intent as current power and water synthetic models.
Validation methodologies for synthetic networks appear primarily for power and water. Most commonly, models use metadata from real-world infrastructure counterparts to validate topology (Sitzenfrei et al 2010, Espejo et al 2019. Some real-world test datasets may be compared to model topology and functionality. Ahmad et al (2020) followed this validation method for synthetic water models by testing topology and operation against a publicly available small-town water distribution network. Similarly, Meyur et al (2020) obtained a small subset of real-world data within their study region and compared topology and network performance to their model for validation. Synthetic power network operational validation is improved by analyzing voltage variability across time to test realistic behaviors (Idehen et al 2020). Additionally, the water and power research communities have provided open-source test sets that researchers may use to improve methodologies. But test cases have significant real-world limitations in their realism (Marcos et al 2017). So, while test cases may be helpful for development, the validation process still requires some real-world data (Sitzenfrei et al 2010, Mohammadi andSaleh 2021). One model for synthetic power distribution used industrial validation, sending the model and data output to the utility provider from the region of study. The utility provider analyzed and compared the model to the real-world network without compromising security and then provided feedback to the research team (Ali et al 2022). Using industrial experts seemed to be the most robust validation method, but stakeholder participation may be a barrier for different locations.
As progress continues in developing realistic infrastructure models, researchers have begun to couple different infrastructure types together. Wang et al (2022b) combined synthetic power, water, and gas to investigate interdependent relationships during flow variations. As already mentioned, Yang et al (2019Yang et al ( , 2020b coupled stormwater and road transportation. But, thus far, these are the only two studies with coupled synthetic networks.
Synthetic network model development is still nascent for most infrastructure. The power research community has recognized the need to develop robust synthetic methodologies (Marcos et al 2017, Mohammadi and Saleh 2021). Some water models have been developed but are still emerging, and other infrastructure disciplines appear to be focused elsewhere. Synthetic network development for multiple infrastructure may aid interdependency modeling (Marcos et al 2017), and a few synthetic studies attempt to couple multiple infrastructure (Yang et al 2019, Yang et al 2020b, Wang et al 2022b. More work is needed to develop other infrastructure methodologies. The need for a greater understanding of interdependencies may accelerate synthetic development in other infrastructure disciplines.

Infrastructure interdependence
Interdependency research is the study of interactions between mutually reliant infrastructure. Usually, these studies involve reactions to disturbances . It is more mature than the synthetic infrastructure domain but still needs major progress for models to be useful in the real world (Banerjee et al 2014). The events of 9-11 accelerated awareness of the urgent need for increased infrastructure security and how infrastructure interacts and is accessed and affected via multiple mediums. Among the research efforts, significant work has been done by Sandia National Labs focusing on large-scale interdependencies and relationships with infrastructure resilience on large and small scales (Glass et al 2012). Thus, interdependency research seeks to inform the design and management of various infrastructure (Rinaldi et al 2001, Pederson et al 2006. For example, urban fires can cause power infrastructure failures, which cut power to water pumps, hampers firefighting capabilities, and simultaneously deprive power plants of cooling water, leading to more power outages (Bagchi et al 2010). Large urban disturbances often congest roads and lead to cascading feedback loops between transportation and communication (Barrett et al 2010). Terrorist attacks can disable coupled energy infrastructure like power and gas (Wu et al 2016). Earthquakes can simultaneously disable power and communication, adding confusion and complexity to response efforts (Cardoni et al 2020) and can cause further interdependent losses to critical infrastructure like water and gas (Cárdenas et al 2022). Also noteworthy, interdependencies between environmental and technological factors can quietly amplify social vulnerabilities and inequalities (Wakhungu et al 2021). To discuss the state of practice for interdependency research, this section will briefly overview the evolution of interdependent models. A generalized discussion of methodologies to study interdependencies will follow. This section concludes with ongoing challenges and paths forward.
The infrastructure community recognizes four general types of infrastructure interdependencies: (i) physical (a direct link between two networks where inputs and outputs directly affect each other), (ii) geographic (co-location such that a local event can create a mutual state change), (iii) cyber (relying on communications infrastructure and its dataflows for proper function), and (iv) logical (mutual reliance via a means that is not physical, geographic, or cyber-related, e.g. financial) (Rinaldi et al 2001). Many physical interdependency studies focused on the nexus of water and energy (Min et al 2007, Bagchi et al 2010, Holden et al 2013, Heracleous et al 2017, Kong et al 2019, Zorn et al 2020, Munikoti et al 2021, Balakrishnan and Cassottana 2022, Cárdenas et al 2022, Sharma and Gardoni 2022, Wang et al 2022a, Yin et al 2022. Geographic interdependencies were also common in real network analysis, likely because realistic geospatial data were available. Multiple studies examined the interdependencies between power and communications. Still, many of them recognize that the modeling logic used between the power-cyber nodes may be more representative of a physical interdependency than a cyber interdependency (Kalstad and Wolthusen 2007, Min et al 2007, Buldyrev et al 2010, Eusgeld et al 2011  . Some studies used logical interdependence to represent human factors such as demand (Heracleous et al 2017) or the behavioral relationships between traffic and cellular network congestion (Barrett et al 2010).
The first interdependency models were developed by mathematicians and physicists but eventually became an interdisciplinary field (Pederson et al 2006, Satumtira and. Following the seminal definition of interdependencies by Rinaldi et al (2001), the first numerical studies focused on the behavior of non-specific interdependent networks (Eusgeld et al 2011). These initial models used networks with simple node and edge structures. They also had binary interdependency relationships and randomized disturbances that were less realistic (Kalstad and Wolthusen 2007, Holden et al 2013, Ganin et al 2016. These confirmed the theory that interdependencies can often lead to more severe cascades and thus deserve greater attention. Satumtira and Dueñas-Osorio (2010) reviewed studies of interdependency and confirmed at the time that current models were too rudimentary and recommended the development of dynamic models with realistic engineering principles. Models also needed to be developed for practitioners and commercial use to make interdependency study more accessible (Pederson et al 2006, Satumtira and. Subsequently, more studies focused on practical applications, asking questions about how interdependence affects infrastructure. Shen (2013) coupled an IEEE test case power model and a random network to simulate interdependence with SCADA and optimized interconnections by minimizing construction and repair time when disturbances were introduced. They concluded that simplified network interdependency was inadequate for optimizing infrastructure network construction. Nan and Sansavini (2015) focused on interactions between Switzerland's simplified power transmission, associated communication networks, and stochastic human operator decisions during disturbances. They used these interactions to find how interdependence and operator decision-making affected power resilience. Interdependence modeling has recently come from theoretical and practical applications (Sharma and Gardoni 2022). Theoretical models are rooted in physics, seeking broadly applicable virtues of interdependency, while practical models employ engineering design principles to answer specific resilience questions (Buldyrev et al 2010, Mahabadi et al 2021. Practical models have struggled to emerge in the absence of real-world data. Stakeholder participation is needed to improve understanding of real interdependencies to make the models more realistic (Mitsova 2021, Suo et al 2021. Methodologies for interdependency generally revolve around feedback between networks, stochastic factors, topology (i.e. the shape of the network), and node and edge criticality (Abdel-Mottaleb et al 2019, Bachmann et al 2020, Schweikert et al 2021. Graph and network theory are long-time accepted methods for representation and analysis (Satumtira and Dueñas-Osorio 2010). Interdependency studies can model feedback between the networks bilaterally or unilaterally. Bilateral modeling simulates dynamic exchanges between infrastructure networks but is computationally expensive and can be complicated to synchronize temporally. Unilateral representations lose some dynamic realism, but researchers try to balance this loss with stochastic variables. Both feedback methodologies are currently used (Sharma and Gardoni 2022). Additionally, stochastic factors are used in other ways to increase realism. For example, some components may deteriorate over time, affecting the probability of spontaneous and interdependent failures (Bondank et al 2018, Yang et al 2020b. Another example is Zhou et al (2022), who stochastically represented dynamic response prioritization based on node and edge criticality. They found that this prioritization improves long-term network performance. Studies focusing on topology construct usually seek distinctive physical traits of the more resilient networks. The hope is that these unique traits may correlate to real-world resilience (Dueñas-Osorio and Vemuru 2009). Results have been mixed on whether interdependency generally aides or hampers robustness. Wang et al (2018) found that interdependency sometimes caused a decrease in robustness during targeted attacks on crucial nodes. Similarly, Zorn et al (2020) found that sympathetic failures spilled across networks when interdependence was high. But context is important in these conclusions. When networks had asymmetric interdependent connections, the network was more resistant to cascading failure (Liu et al 2019). Also, Korkali et al (2017) compared two models, one with simple feedback between networks and the other with more realistic and complex feedback. They found that in the realistic model, robustness increased as interdependency increased. But the inverse was true for simple networks. So there is no firm conclusion regarding topology construct and robustness. Similar to topology research, other studies have investigated node and edge criticality for network resilience. In these models, highly connected nodes are bottlenecks. Munikoti et al (2021) found that outages involving critical nodes were more destabilizing to multi-network models. Ouyang (2016) had similar results for node criticality but found that edge criticality was not as impactful on resilience. Overall, interdependency research has standards for methodologies, but the interdisciplinary nature of this field implies that there will be variance in how models are constructed.
Some studies focus on the role of interdependencies in real-world events. These studies often use case studies investigating the practical dynamics of disturbance-related interdependence in real-world infrastructure. Krishnamurthy et al (2016) did an in-depth case-study on power and communications interdependencies after earthquakes in Japan and Chile. They found that power is dependent on communications for SCADA operation, and coordination of response and repair teams also relies on communication infrastructure, significantly affecting operations and recovery for both systems. These dynamics imply that more continuous exchanges between these two networks may be necessary for interdependent studies modeling continuous cascades (Varga et al 2014). Another study used historical outage data from Hurricane Hermine to train a statistical model, predicting road closures and power outages (Madhavi et al 2019). They used the model for predictions of failure in future storms. Studying real data from past events may help inform how interdependencies should be modeled in the future and is necessary to improve models (Bachmann et al 2020).
There are three primary research gaps for infrastructure interdependence, according to Haggag et al (2020): (i) resilience quantification, (ii) defining interdependence, and (iii) modeling of real-life systems. These issues are rooted in several shortfalls. First, models have computational limitations. They cannot account for all spatial and temporal factors; there is tension between the accuracy of models and the time and cost to produce and run them. Second, researchers have limited access to or cannot collect data to study and mimic real-world infrastructure. Thus, researchers are forced to narrow their questions.
Interdependency research is a broad and interdisciplinary field. The focus is primarily on power, water, communications, and transportation. Other civil infrastructure are not as developed. Non-technological critical infrastructure (e.g. medical, agriculture, logistics) has yet to be included in interdependency research. Physics and mathematics-based methods have successfully unearthed macro-behaviors. Detailed models seek to elucidate more nuanced behaviors, which are slow to emerge.

Infrastructure cascading failure
Cascading failure modeling is a prominent subfield of infrastructure research. Cascading failure models have been applied to many infrastructure, evaluating failure behaviors and recovery strategies. Cascading failure models have two primary approaches. The first is to capture reactions to progressive failure. This method tests robustness by progressively removing nodes and edges and often foregoes detailed engineering functions within the physical and operational model (Mahabadi et al 2021). The other approach, dynamic failure, introduces an initial disturbance and uses engineering operations combined with stochastic variables to simulate responses within the model (Wu et al 2021). These models are often complex and computationally expensive (Valdez et al 2020). Cascading failure models are used for the general purposes of (1) resilience framework development; (2) topology evaluation, (3) identifying component criticality; (4) seeking thresholds for total collapse, and (5) supporting interdependency model development. Some models focus only on cascading failure within these uses, while others expand the model to simulate post-disturbance recovery. Methods and uses are discussed in this section, followed by a brief overview of which infrastructure has been of focus in cascading failure models.
Some research efforts develop models to evaluate the resilience of real-world networks. These studies use theoretical test networks to simulate dynamic failure and observe behaviors to derive evaluation metrics. These metrics form the basis for a framework, which can then be used to evaluate other infrastructure networks for resilience. Often, the studies will use a second test network to validate the framework (Bagchi et al 2010, Guidotti et al 2016, Wu et al 2016, Korkali et al 2017, Nan and Sansavini 2017, Thacker et al 2017, Kong et al 2019, Oughton et al 2019, Yang et al 2019, 2020a, Cardoni et al 2020, Zorn et al 2020, Munikoti et al 2021, Balakrishnan and Cassottana 2022, Cárdenas et al 2022, Sharma and Gardoni 2022. A body of work focuses on the resilience of different network topologies when subjected to disturbances (Dueñas-Osorio and Vemuru 2009, Buldyrev et al 2010, Berardi et al 2014, Korkali et al 2017, Azzolin et al 2018, Liu et al 2019, Wu et al 2021, Wang et al 2022a. For example, cascading failures were used to optimize topology for a coupled power and gas model in Harris County, Texas, by changing the network characteristics (Ouyang and Dueñas-Osorio 2011). Additionally, Dueñas-Osorio and Vemuru (2009) modeled cascading failure in a simple power network and found that a strategic combination of intentional redundancy and islanding via weak links decreased failures.
Cascading failure models are used to identify critical components of single and multi-network models (Dueñas-Osorio and Vemuru 2009, Buldyrev et al 2010, Berardi et al 2014, Ouyang 2016, Wang et al 2018, Abdel-Mottaleb and Zhang 2020, Schweikert et al 2021, Zhou et al 2022. For a single network model, a power grid study might focus only on critical nodes and edges (Dueñas-Osorio and Vemuru 2009). Conversely, a water-road model might consider the water network's service level and how the road network may flood when a water pipe bursts (Abdel-Mottaleb and Zhang 2020). These models typically use dynamic failure simulations.
The possibility of total collapse when key tipping points are reached is another area of focus. These studies typically use progressive failure approaches with simple networks and interdependent relationships. They progressively and randomly fail nodes and edges until the entire network collapses (Mahabadi et al 2021). Networks will often continue to function despite initial outages but reach a transition point where collapse occurs quickly. A single-or multi-network model is considered more robust if the transition point occurs late in the failure process, indicating that the network can withstand more failures before the collapse suddenly accelerates (Barrett et al 2010, Pahwa et al 2015, Liu et al 2018.
In some cases, cascading failure models are often used within other models that focus on the dynamics of infrastructure interdependencies. In these cases, failure is generally not the focus but how failures affect dynamics and exchanges between the modeled networks (Holden et al 2013, Heracleous et al 2017, Wang et al 2022b, Yin et al 2022. Cascading failure models generally focus on infrastructure vulnerabilities (Mahabadi et al 2021, Meyur 2022, but some studies also focus on recovery from disturbances. (Barrett et al 2010, Holden et al 2013, Shen 2013, Guidotti et al 2016, Nan and Sansavini 2017, Yang et al 2019, Munikoti et al 2021, Sharma and Gardoni 2022. For example, Sharma and Gardoni (2022) modeled power-water recovery after an earthquake to estimate recovery times for Tennessee emergency management response plans. Recovery from cascading failure is also modeled to test disturbance response strategies. Kong et al (2019) found that prioritizing path-dependent (i.e. more connected) assets during recovery minimized restoration times for the overall system of interdependent networks. Also, recovery modeling can test how maintenance strategies for components will change how networks fail and recover from outages, helping infrastructure managers seek an optimal return on investment (Wang et al 2022a).
There is a notable absence of research on perfect storms and black swans in cascading failure research. Many cascading failure models simulate failure until total collapse. But the subsequent analysis tends to focus on generalized behaviors, avoiding low-probability-high-impact outcomes. Previous literature has pointed out that cascading failure models and risk assessment tools have historically been inadequate for analyzing black swans (Paté-Cornell 2012, Aven 2013, Hasan and Foliente 2015. The current literature review confirms that this inadequacy is still true. Cascading failure has been studied across many infrastructure, such as electricity, energy, water, stormwater, sewer, and transportation. Power is the most studied infrastructure (Pagani and Aiello 2013). Studies that focused solely on electricity investigated questions around ideal network topologies and sought to understand the dynamics of outages in transmission and distribution. These studies have recommended topology changes to decrease cascading failure (Dueñas-Osorio and Vemuru 2009, Azzolin et al 2018).
Dueñas-Osorio and Vemuru (2009) used dynamic failures to recommend topology changes involving 'weak links' in the transmission network. As a result, service areas would be naturally islanded from specific line failures during outages, protecting the remaining network. Others used progressive failures to estimate total collapse thresholds. They found that larger networks are more at risk of catastrophic blackouts and prescribed methods for intentional islanding during disturbances (Pahwa et al 2015). For water, mechanical component failure is often the cause of cascading failures. Berardi et al (2014) used dynamic failure to determine the criticality of components. They found that prioritizing preventive maintenance by criticality rather than component age reduced cascade severity. For roads,  progressively failed random portions of the road network to estimate the critical point at which Portland's transportation infrastructure transitioned to total collapse. These single-network studies bring critical insight into how cascades occur. But there is also a growing need to study and quantify how failures in one network may also affect other networks (Rinaldi et al 2001).
Models of cascading failure involving multiple interdependent infrastructure have begun to appear in recent years. Power networks appear most frequently and are often paired with water distribution, communications, and non-electrical energy (e.g. oil and natural gas) infrastructure (Haggag et al 2020). These models frequently elucidate how interdependent relationships affect cascading failure (Zorn et al 2020). Power-water cascading failure is a topic of interest due to their high interdependence in the face of rising global temperatures (Bagchi et al 2010, Bartos and Chester 2014, Clark et al 2019, Balakrishnan and Cassottana 2022. Power and communications network cascading failure is also commonly examined due to the inseparable nature of power and SCADA and the associated risks of catastrophic outages (Krishnamurthy et al 2016, Korkali et al 2017, Liu et al 2019. Power and other energy infrastructure are often paired due to the economic impact of power failures that may affect oil and gas production and distribution (Ouyang and Dueñas-Osorio 2011, Ouyang 2016, Wu et al 2016, Wang et al 2018. Abdel-Mottaleb and Zhang (2020) paired water-road networks to inform water component maintenance priorities based on how water pipe failures degraded road transportation. In an exceptional case, Zorn et al (2020) created cascading failure model for ten interdependent infrastructure networks. But their results were necessarily more granular than models with only two or three infrastructures.

Discussion: a framework for the future of SICFMs
This section fuses the three domains to propose a framework for SICFMs. Synthetic networks are detailed and realistic enough to serve as a modeling foundation. But SICFMs need synthetic networks to reach a viable point of development before deployment. SICFMs will also need expanded interdisciplinary stakeholder support to ensure that the specialized facets of the model are robust and continuously validated. Researchers should balance automated modeling with expert design to maximize deployability and realism. SICFMs should employ dynamic interdependencies for coupled networks, expanding opportunities for cyber and logical interdependencies. With these new developments, SICFMs should incorporate other non-technological factors to tie cascading failures back to human capabilities. These improvements should provide novel opportunities for fine-scale risk analysis to scan the horizon for surprise events (i.e. perfect storms and black swans). These recommendations are summarized and shown in figure 2.
Synthetic network methodologies should strive to meet two requirements before deployment in SICFMs. First, the methodology should be usable across many geographic locations (Mohammadi andSaleh 2021, Mateo et al 2020). Second, the method must withstand rigorous validation (Birchfield et al 2017, Idehen et al 2020, Mohammadi and Saleh 2021, Ali et al 2022. Synthetic power models can currently produce highly detailed transmission and distribution networks in nearly any location in the United States and Europe (Gegner et al 2016, Birchfield et al 2019, Saha et al 2019, Ali et al 2022. Thus, power networks appear mature enough to be deployed for SICFMs. Water models have been developed, and some are applicable in many geographic regions, but further validation of current methodologies is needed (Ahmad et al 2020, Momeni et al 2023. Some synthetic networks exist for other energy, transportation, and communication, but only water and power methodologies have been explicitly developed with multiple research papers. More work is needed to bring other infrastructure to the same level of development as power and water. This need also reveals an ongoing challenge for SICFM development. SICFMs come from interdisciplinary research. But interdisciplinary researchers seeking to develop SICFMs may not have the expertise to engineer synthetic networks for specific infrastructure. In the state of practice, synthetic network development comes from research experts in an infrastructure field, prompting two recommendations. First, stakeholder partnerships should be expanded across research fields to foster synthetic development (Hasan andFoliente 2015, Cantelmi et al 2021). Second, synthetic networks should be designed for easy access by the Figure 2. Realistic network models are necessary to form the foundation for the operation of SICFMs. Without realistic networks, it will remain difficult to model realistic interdependencies and cascading failure. Additionally, continuous validation should be viewed as an enabling process to advance model development rather than simply a step to 'pass muster' for the model. broader research community, and expert designers should structure synthetic models so interdisciplinary researchers can integrate them into SICFMs (Marcos et al 2017, Mohammadi and Saleh 2021).
Notably, research for synthetic power has exemplified how to blend automation with expert design during crucial parts of the modeling process (Li et al 2020, Mohammadi andSaleh 2021). Expert design may not be as fast as automated procedures. However, an expert engineer can specify important details during the modeling process. This nuance is necessary for risk analysis for surprise events (Paté-Cornell 2012), further emphasizing that broad stakeholder participation is vital for developing SICFMs (Hasan and Foliente 2015).
Additionally, synthetic models are engineered to react dynamically to changes in supply and demand (Gegner et al 2016), so they should also be engineered with points of connection for interdependencies with other infrastructure. These connections would allow synthetic models to react not only to the direct impacts of hazards but also to unexpected changes in interdependency. For example, a power model can allow a coal-powered generation plant to rely on water cooling to maintain performance. These continuous integrations are necessary to make SICFMs more realistic (Satumtira and Dueñas-Osorio 2010, Shen 2013, Nan and Sansavini 2015. Thus, synthetic models should be constructed for modular interfacing to maximize portability in interdisciplinary research. SICFMs may also open possibilities for more meaningful results in studying interdependencies between technological, social, and ecological infrastructure (e.g. financial, medical, and logistics). Infrastructure as technological and physical assets cannot be divorced from social and environmental contexts. The interactions between social, ecological, and technological infrastructure have yet to be meaningfully captured (Markolf et al 2018, McPhearson et al 2021. Historically, studies that seek to model interactions between civil infrastructure and other domains struggle to include geospatial dimensions or incorporate realistic engineered designs (due to complexity) (Min et al 2007, Zhang and Peeta 2014, Haggag et al 2020. SICFMs may provide a realistic foundation that can be coupled with these other domains to extend the results of SICFMs to human capabilities. This extension may reframe priorities for infrastructure based on the impact on people, which has been done in select studies (Thacker et al 2017, Oughton et al 2019, Zorn et al 2020. But these studies did not delve into social or ecological infrastructure. Yet, they remind us that cascading failure studies should be concerned with human capabilities, not just technological infrastructure systems (Clark et al 2018). SICFMs may create novel opportunities for this type of advanced research.
Infrastructure managers need greater insight regarding surprise events, and SICFMs might be able to elucidate these insights. Generally, interdependency and cascading failure research use simulations to generate distributions of outcomes, critical failure thresholds, or recovery rates. But, in the state of practice, there was no analysis of outliers or 'fat tails' to find low-probability-high-impact vulnerabilities. The concept of emergence demonstrates that infrastructure continues to interact in complex ways that have never been imagined (Taleb 2007, Allenby and Chester 2018, Oughton et al 2018. Thus, infrastructure managers must meet this increasing complexity with requisite organizational complexity (Boisot andMcKelvey 2011, Chester andAllenby 2022). Requisite complexity can take the form of more detailed risk analysis to scan horizons for weak signals of change and vulnerability (Chester and Allenby 2022). Risk analysis for surprise events requires imagination and systematic history study, especially near-miss events, to search for precursor symptoms (Paté-Cornell 2012). Risk analysis using simple networks (i.e. theoretical) has a limited depth of insight (Hasan andFoliente 2015, Mahabadi et al 2021). But synthetic networks' realistic and fine-scale capability may allow for more imaginative and systematic distributions of outcomes for SICFMs (Marcos et al 2017).
Validation of SICFMs should underpin the modeling process and include many stakeholders. Validation of realistic infrastructure models usually requires real-world data, which is paradoxical because the absence of real-world data is the primary motivator to create synthetic networks. Currently, many studies use publicly available meta-data and comparisons of previous test cases for validation (Ahmad et al 2020, Mohammadi and Saleh 2021. But the future research community for SICFMs should include stakeholders from outside organizations in the validation process. Stakeholders with engineering knowledge of the imitated networks can give feedback during modeling (Meyur et al 2020, Ali et al 2022. Also, community stakeholders often possess tacit insight into interdependencies between infrastructure networks and can advise engineers accordingly (Zhou et al 2020, Mitsova 2021. With this iterative feedback, SICFMs can progressively imitate their real-world counterparts. Some research possibilities for SICFMs may enhance the use of interdependent models for identifying vulnerabilities, determining maintenance priorities for infrastructure components, and establishing which infrastructure systems are most critical to humanity during emergencies. First, it may become easier to identify the components that may be critical during cascading failure-and thus require maintenance prioritization. Also, realistic interdependency dynamics combined with highly detailed infrastructure can allow for fine-scale sensitivity analysis during the design phase or when performing failure risk analysis . Additionally, because SICFMs should yield more realistic behavior during failure (Marcos et al 2017), the performance of individual components should be more insightful when including cascades in other critical infrastructure networks (Abdel-Mottaleb and Zhang 2020). Moreover, realistic behaviors and highly detailed networks can allow social infrastructure and human needs to be considered during failure simulations, linking human capabilities to infrastructure services. Thus, modeling these diverse interdependencies can give a new perspective on infrastructure criticality (Clark et al 2018).
SICFMs may also improve how the four different types of interdependencies are studied. Physical and geological interdependencies are most commonly studied, whereas logical and cyber interdependencies remain difficult to capture (Cárdenas et al 2022). Simplistic networks usually only allow for binary (i.e. simple) interdependent relationships between networks (Korkali et al 2017). But this may change as synthetic networks are designed with more accurate engineering principles. As previously discussed, this capability should allow for realistic connections between infrastructure. In the model, interdependent networks should exchange some resource, energy, or 'flow,' as Varga et al (2014) proposed. This type of modeling should allow for a distinct representation of all four interdependency types from Rinaldi et al (2001).
It is important to also address security concerns for highly detailed models such as SICFMs. While infrastructure managers may intend to use them for constructive purposes, there are adversaries that may intend to use such models for destructive purposes. Geopolitical strategic competition between adversaries is an essential consideration for critical infrastructure managers and has transformed civil infrastructure systems into military targets (CITE ALLENBY). Additionally, infrastructure are also vulnerable to local threats such as terrorists (Miller and Lachow 2008, DoD 2019, Efron et al 2020, Grant 2021. Thus, as SICFMs become more advanced, researchers must consider security measures during development and use discretion when in how they make the models available. Lastly, there are some practices that SICFMs should incorporate for more realistic results. First, models that seek to create realistic behaviors must be rooted in realistic demand patterns (Meyur et al 2020).
Power and water infrastructure already have repositories for researchers to retrieve realistic demand patterns for the United States (Hill et al 2016, Sharvelle et al 2017, Frick et al 2019, Thorve et al 2019, Wilson et al 2022. Some demand models may even incorporate agent-based behavior, where nodes can have nuanced demands and human elements might be incorporated (Nan and Sansavini 2015. Second, infrastructure systems are not merely physical technological systems. They extend into social and ecological constructs as well (Markolf et al 2018). Model development could eventually extend to consider relationships and dynamics from these other systems. Third, models can use time series calculations that synchronize infrastructure network operations . Time series will likely be necessary to create the 'flows' between networks and may assist in portraying differences in demand (Varga et al 2014). Fourth, the condition-based performance of individual components (i.e. reliability) within SICFMs changes the dynamics of cascading failure models. When reliability is incorporated, models typically use time series to introduce condition changes (Bondank et al 2018, Yang et al 2020a, Zhou et al 2022.
The proposed framework is a roadmap for how researchers could use SICFMs to gain a more meaningful and expedited understanding of how infrastructure responds to disturbances. Novel research efforts are immediately needed to confront the destabilizing conditions of the Anthropocene.

Conclusion
This paper has discussed the intersection of synthetic infrastructure networks, interdependency models, and cascading failure simulations. At the nexus of these domains, there are opportunities for improving how we understand infrastructure vulnerabilities and prepare infrastructure for destabilizing future conditions. The inclusion of synthetic networks will benefit interdependency and cascading failure models. However, synthetic networks still require development, and future work should include the development of synthetic methodologies for other infrastructures besides power and water. Additionally, it may be worthwhile to perform case studies of interdependencies in historical events to aid the development of realistic interdependencies for synthetic infrastructure networks. This real-world data might be used to validate and inform how interdependencies can be integrated into synthetic models. Moreover, future SICFM development should intentionally embed stakeholders for network development, hazard scenario planning for dynamic failures, and interdependent links with continuous flows.
Ultimately, SICFMs seek to create novel insights into interdependent cascading failures. In their basic form, SICFMs are realistic representations of physical assets, relationships, and rules. Synthetic networks are a method to meaningfully organize these attributes. However, if realistic networks representations might be obtained via some other means, then the intent of SICFMs will still be satisfied. Naturally, if utility owners share data regarding their networks more frequently, then synthetic networks may become unnecessary. But currently, synthetic networks may be the best available tool for interdependent cascading failure analysis.
Lastly, it is worth recognizing that SICFMs will undoubtedly tend towards computationally large and complex models. However, 'There is nothing inherently wrong with complex models, just as there is nothing inherently correct with simple models; it is more a question of appropriateness.' (Logan 1994). For infrastructure research, simple models are not providing the necessary insights for adequate horizon scanning (Chester and Allenby 2022). Thus, we suggest that advancing modeling for analysis at fine scales may provide the surgical information needed to intervene (Alderson et al 2022). Infrastructure organizations must be prepared to face the accelerating challenges and hazards of the future (Chester et al 2020). To this end, SICFMs may be rife with insights, which are scarce today (Paté-Cornell 2012, Chester and Allenby 2022).

Data availability statement
The data cannot be made publicly available upon publication because no suitable repository exists for hosting data in this field of study. The data that support the findings of this study are available upon reasonable request from the authors.