Hunting for Weaknesses in Cyber-Physical Systems with AI

Author: Denis Avetisyan

A new framework uses neural networks and formal verification techniques to efficiently pinpoint vulnerabilities in complex systems controlling physical processes.

The Ramponn framework establishes a system for navigating the inevitable entropy of neural networks, offering a pathway to gracefully manage decay rather than resist it.

RampoNN leverages DeepBernstein Networks and reachability analysis for efficient cyber-kinetic vulnerability detection.

Detecting vulnerabilities in Cyber-Physical Systems-where software errors can induce hazardous physical consequences-remains a critical but challenging task due to the complexity of coupled software and physical dynamics. This paper introduces RampoNN: A Reachability-Guided System Falsification for Efficient Cyber-Kinetic Vulnerability Detection, a novel framework that accelerates the identification of these vulnerabilities by intelligently pruning the search space. RampoNN leverages Deep Bernstein neural networks and reachability analysis to provide high-precision bounds on system behavior, effectively guiding a falsification engine toward the most promising-and potentially dangerous-traces. Could this approach unlock scalable, reliable verification for increasingly complex and safety-critical cyber-physical applications?

The Evolving Landscape of Cyber-Physical Systems

The proliferation of Cyber-Physical Systems (CPS) marks a significant shift in technological design, moving beyond purely digital computation to encompass the intricate interplay between software and the physical world. These systems, ubiquitous in modern infrastructure – from the automated steering of autonomous vehicles and the precision of robotic surgery to the sophisticated control networks managing power grids and manufacturing plants – tightly integrate computational algorithms with physical processes. This convergence necessitates a holistic approach to system design, acknowledging that failures are no longer confined to the digital realm but can manifest as tangible, real-world consequences. The increasing complexity stems not only from the sheer scale of these integrated systems, but also from the diverse and often unpredictable interactions between the computational and physical components, demanding novel engineering strategies and rigorous validation techniques to ensure safety and reliability.

The increasing prevalence of hybrid systems – those integrating discrete computational logic with continuous physical processes – introduces unprecedented verification challenges. Traditional software testing methods prove inadequate when dealing with the interplay between digital commands and analog world responses; a system might function perfectly in simulation, yet exhibit unexpected behavior when interacting with real-world variables like temperature, friction, or sensor noise. This complexity stems from the infinite number of possible states within the continuous domain, combined with the logical branching inherent in discrete control algorithms. Consequently, ensuring the safety and reliability of these systems demands advanced verification techniques, including formal methods, model checking, and runtime monitoring, capable of exhaustively analyzing the combined state space and guaranteeing desired properties like stability, responsiveness, and freedom from hazards. Without robust assurances, even minor flaws in the interaction between software and physical components can lead to catastrophic consequences, emphasizing the urgent need for innovative validation strategies.

The convergence of computation and physical processes in modern systems introduces a critical vulnerability: failures can manifest as tangible, real-world consequences. Unlike software errors that might result in data loss or inconvenience, malfunctions in cyber-physical systems – such as those controlling autonomous vehicles, power grids, or medical devices – can directly impact physical safety and infrastructure. A flawed algorithm guiding a self-driving car could lead to collisions, while a compromised industrial control system might trigger equipment failures or even environmental disasters. Consequently, rigorous validation methods are no longer simply desirable, but essential for ensuring the reliability and safe operation of these increasingly complex systems; traditional software testing paradigms prove inadequate when dealing with the interplay between digital commands and physical outcomes, demanding innovative approaches to verification and hazard analysis.

This example demonstrates how a cyber-kinetic vulnerability can lead to a physically unsafe trajectory (right) due to the exponential growth of possible control decisions illustrated by the cyber trajectory tree (left).

The Limits of Traditional Analytical Approaches

Reachability analysis, a formal verification technique, systematically explores all possible states of a system to determine if a given property holds. However, the number of reachable states grows exponentially with system complexity, a phenomenon known as the “state explosion” problem. This occurs because each state is determined by the combination of all system variables and their possible values; adding even a single variable or increasing its range significantly expands the state space. Consequently, practical application of reachability analysis is often limited to relatively small and simplified systems, or requires substantial abstraction and approximation techniques to reduce the computational burden.

Falsification-based verification operates by systematically searching for inputs that cause a system to violate specified safety properties. This process is computationally expensive due to the need to explore a potentially vast input space and execute the system-or a model thereof-for each input. The incompleteness of falsification stems from the heuristic nature of the search algorithms employed; they may not explore all possible inputs, meaning a violation of a safety property could exist but remain undetected. The efficiency of falsification is highly dependent on the chosen search strategy and the complexity of the system under test, with more complex systems requiring significantly more computational resources to achieve adequate coverage.

Accurate modeling of the cyber trajectory – the complete sequence of control actions and resulting system states over time – is fundamental to both reachability analysis and falsification. However, complex systems, particularly those with numerous interacting components, non-linear dynamics, or external dependencies, present significant challenges to trajectory modeling. Creating a faithful representation requires detailed knowledge of system behavior under all possible operating conditions, including potential sensor noise, actuator limitations, and environmental factors. The combinatorial increase in possible states and transitions, coupled with the difficulty of capturing nuanced system interactions, leads to models that are either overly simplified and inaccurate, or computationally intractable for analysis. Consequently, verification results based on these models may be incomplete or misleading due to inaccuracies in the represented cyber trajectory.

Execution time increases with the number of identified vulnerabilities across both the Water Tank and Automotive Engine models.

RampoNN: A Neural Network-Enhanced Verification Framework

RampoNN addresses limitations in traditional vulnerability detection by integrating reachability analysis and falsification with neural network methodologies. Reachability analysis determines the set of states a system can reach from an initial state, while falsification attempts to disprove safety properties by finding violating trajectories. RampoNN leverages neural networks to approximate these computationally expensive analyses, enabling efficient exploration of the state space. This combined approach allows for the detection of vulnerabilities that may be missed by either technique alone, and offers scalability improvements for complex systems compared to purely formal methods. The framework’s architecture facilitates both over-approximation and under-approximation, providing a balance between completeness and precision in vulnerability identification.

RampoNN’s core reachability analysis is performed using DeepBern-Nets, neural networks that leverage Bernstein polynomials as activation functions. This approach demonstrates a 19.0082% improvement in tightness compared to traditional reachability analysis methods employing ReLU activations. Importantly, the DeepBern-Net implementation achieves this improved precision while simultaneously reducing the volume of reachable sets by a factor exceeding 1000x; a significant reduction in computational overhead and memory requirements for complex system verification. This efficiency is directly attributable to the properties of Bernstein polynomials, allowing for more accurate and compact representation of system state spaces during analysis.

RampoNN employs ‘DynamicsNN’ to model the continuous physical dynamics of the system under verification, representing these dynamics as a neural network to facilitate efficient analysis. Simultaneously, ‘STL2NN’ converts Signal Temporal Logic (STL) specifications – used to express complex safety requirements – into neural networks. This dual neural network representation allows RampoNN to perform verification by analyzing the neural network models of both the system dynamics and the safety specifications, resulting in improved robustness and scalability compared to traditional methods that rely on symbolic or numerical techniques for handling these aspects.

Validation and Benchmarking: Demonstrating RampoNN’s Capabilities

RampoNN’s applicability was validated through implementation on both the ‘Water Tank Model’ and the ‘Automotive Engine Model’. The Water Tank Model served as an initial proof-of-concept, while the Automotive Engine Model-a significantly more complex system-demonstrated RampoNN’s scalability to higher-dimensional state spaces and increased computational demands. Performance metrics on both models indicated a high degree of accuracy in identifying potential vulnerabilities, with results consistently aligning with established ground truth data. This successful application to diverse system complexities confirms RampoNN’s potential for broader deployment across various control systems.

RampoNN utilizes the Abstract Cyber Trajectory Tree (ACTT) to optimize vulnerability analysis by systematically reducing the explored state space. The ACTT represents possible system trajectories in an abstract form, pruning branches that cannot lead to vulnerabilities based on pre-defined safety properties. This abstraction significantly decreases the computational complexity of the search process compared to exhaustive state space exploration. Benchmarking demonstrates that this approach yields a substantial speedup in execution time, allowing RampoNN to analyze complex systems more efficiently and identify vulnerabilities that would be computationally prohibitive for traditional methods to detect within a reasonable timeframe.

RampoNN incorporates Neural Network Verification (NNV) techniques to rigorously assess the reliability of its neural network components, mitigating potential false positives and ensuring dependable vulnerability detection. During benchmarking with the Automotive Engine model, RampoNN successfully identified deep-nested vulnerabilities at a horizon of H=10, a level of complexity that existing formal methods and symbolic execution techniques were unable to reach. This demonstrates RampoNN’s capacity to uncover vulnerabilities obscured by the increased computational challenges associated with deeper analysis horizons and more complex systems.

Implications and Future Trajectories: Towards Resilient Systems

The RampoNN framework presents a significant advancement in the verification of cyber-physical systems, which integrate computation with physical processes. Traditional methods often struggle with the complexity of these systems, requiring exhaustive testing or simplified models that may miss critical errors. RampoNN, however, leverages the power of neural networks to learn the system’s behavior and efficiently identify potential violations of safety-critical properties. This approach dramatically reduces the computational burden associated with formal verification, enabling more thorough analysis of intricate designs. By providing a scalable and reliable method for ensuring system correctness, RampoNN holds the potential to accelerate the development and deployment of safe and secure autonomous systems across diverse applications, from self-driving cars to critical infrastructure.

The escalating complexity of modern infrastructure – from self-driving cars navigating dynamic environments to smart grids balancing energy distribution and automated systems controlling industrial processes – demands rigorous safety and security validation. These ‘Cyber-Physical Systems’ increasingly rely on software controlling physical components, creating vulnerabilities exploitable through both digital attacks and unforeseen operational scenarios. Ensuring their reliable function isn’t merely a matter of convenience, but a critical imperative for public safety and economic stability. Consequently, technologies capable of formally verifying these systems – guaranteeing their behavior under all possible conditions – are no longer a research aspiration but a practical necessity, directly impacting the dependability of technologies woven into the fabric of daily life and essential services.

Ongoing development of the RampoNN framework prioritizes scalability to address the increasing complexity of modern cyber-physical systems. Researchers aim to move beyond current limitations by incorporating techniques for managing systems with a vastly larger number of states and interactions. A key component of this expansion involves seamless integration with existing verification tools – such as model checkers and formal analysis suites – to forge a robust and comprehensive safety assurance pipeline. This synergistic approach promises to leverage the strengths of each tool, providing more thorough and reliable verification results, and ultimately accelerating the deployment of safe and secure autonomous technologies across critical infrastructure and beyond.

The pursuit of system robustness, as detailed in this work concerning RampoNN and cyber-kinetic vulnerability detection, echoes a fundamental truth about all complex systems: their eventual confrontation with limitations. The framework’s innovative use of reachability analysis and DeepBernstein Networks to prune the search space, effectively guiding falsification, is akin to carefully charting a system’s decay-identifying potential failure points before they manifest. As Andrey Kolmogorov observed, “The most important things are the ones you don’t know.” This sentiment perfectly encapsulates the core of vulnerability research; it’s not merely about verifying what a system can do, but proactively discovering what it cannot-the hidden weaknesses that define its boundaries and, ultimately, its lifespan. The efficiency gained by RampoNN allows for a more comprehensive exploration of these unknown territories.

What Lies Ahead?

The pursuit of formal verification in cyber-physical systems inevitably encounters the limitations of scale. RampoNN offers a temporary reprieve, a localized slowing of entropy through guided falsification. However, the fundamental challenge remains: complexity accrues far faster than verification techniques can adapt. The framework’s reliance on DeepBernstein Networks, while effective for pruning search spaces, introduces a new layer of approximation. Each abstraction is a controlled loss of fidelity, a deliberate simplification of reality. Technical debt, in this context, is akin to erosion – seemingly minor concessions accumulate, eventually compromising the integrity of the system.

Future work must address the inherent tension between precision and tractability. Exploration of hybrid approaches – combining the rigor of formal methods with the adaptability of machine learning – is crucial. The development of verification techniques capable of operating on increasingly abstract representations of system behavior, without sacrificing critical safety properties, represents a significant, though distant, goal. Uptime, after all, is a rare phase of temporal harmony, not a permanent state.

Ultimately, the field must acknowledge that absolute certainty is an illusion. The focus should shift toward building resilient systems capable of gracefully degrading in the face of inevitable imperfections. Rather than striving for flawless verification, perhaps the more pragmatic path lies in developing robust anomaly detection and recovery mechanisms – accepting the inevitability of failure and preparing for it.

Original article: https://arxiv.org/pdf/2511.16765.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/