The foundation of the work rests on a branch of control theory known as discrete event systems, or DES. Unlike continuous models that track variables such as temperature or velocity as smooth functions of time, DES abstract a system’s behavior into a sequence of discrete events: the landing gear deploys, the motor engages, the sensor reports nominal. This abstraction is captured mathematically using deterministic finite automata, which are state machines that move between defined states as events occur. Within this framework, engineers can construct diagnosers, specialized observers that monitor the stream of events and determine, with formal guarantees, whether a fault has occurred and which fault it is. The elegance of this approach is that it is exhaustive and provable; nothing about the event language escapes the diagnoser’s scrutiny.

The problem, as the authors emphasize, is scale. Building a diagnoser requires synthesizing the full behavioral model of the system and then continuously updating it as the system evolves, is reconfigured, or exhibits new operating modes. For small systems this synthesis is tractable, but for large-scale or dynamically evolving platforms the computational cost can become prohibitive. The state space of a realistic engineered system grows explosively with the number of components and interactions, a manifestation of the well-known state explosion problem. Every redesign of the diagnoser means re-enumerating enormous portions of that space, and in safety-critical applications where the model must track the live system in real time, the cost of keeping the diagnoser synchronized can exceed what onboard or even ground-based computing can deliver.

The researchers’ answer is not to abandon formal methods but to delegate the heavy lifting to a recurrent neural network. Their framework proceeds in two stages. First, the system’s behavior is represented as a deterministic finite automaton, preserving the discrete-event abstraction that makes formal diagnosis possible. Second, a recurrent neural network is trained on this automaton to learn and reproduce the event-driven dynamics of the system. Recurrent architectures are naturally suited to this task because they maintain an internal hidden state that is updated as each event arrives, effectively encoding the memory of the event history. Once trained, the network acts as a learned surrogate for the diagnoser, capturing the mapping from event sequences to fault conclusions without requiring the diagnoser to be rebuilt from scratch each time the underlying model changes.

This division of labor is what gives the method its computational advantage. The formal automaton provides a compact, structured description of what the system can do, and the neural network learns to navigate that description efficiently. When the system is redesigned or its behavior evolves, the network can be retrained on the updated automaton rather than forcing a full re-synthesis of the diagnostic machinery. The authors describe this as reducing the complexity associated with redesigning the fault diagnosing system, and it addresses one of the most persistent obstacles to deploying formal diagnosis in practice: the mismatch between the theoretical guarantees of DES methods and the practical budgets of real engineering programs.

To demonstrate that the framework works outside of toy examples, the team validated it on a hybrid aircraft platform, specifically a generic urban air mobility model of an electric vertical take-off and landing aircraft, or eVTOL. These vehicles are among the most demanding imaginable testbeds for fault diagnosis. They transition between hovering, cruising, and landing phases, blending aerodynamic and propulsion dynamics, and they are intended to operate over cities where a failure could be catastrophic. The hybrid nature of the platform, mixing continuous flight dynamics with discrete mode changes, makes it a natural fit for a discrete-event abstraction layered over the underlying physics. The results showed that the proposed framework accurately detects and isolates faults while incurring minimal computational cost, suggesting that the approach could keep pace with the real-time demands of an airborne vehicle.

The word isolation matters as much as detection. A diagnostic system that merely announces that something is wrong is of limited use to an operator or an autonomous safety manager; it must also pinpoint which component or subsystem has failed so that corrective action can be taken, whether that means rerouting power, switching to a backup actuator, or initiating an emergency landing. In the discrete-event formalism, isolation is achieved because different faults produce distinguishable event signatures, and the diagnoser can reason over those signatures to attribute the anomaly to its source. The learned network inherits this capability by reproducing the automaton’s event-driven logic, so the framework retains the diagnostic resolution of the formal method while shedding much of its computational burden.

The research was supported by the NASA University Leadership Initiative Program under Award 80NSSC22M0070, an affiliation that underscores the practical motivation behind the work. NASA’s investment in urban air mobility reflects a broader recognition that the next generation of air vehicles will need onboard intelligence capable of assuring safety without constant human oversight. A diagnoser that is too slow to run in flight, or too expensive to update whenever the vehicle’s software or configuration changes, is of little value in that vision. By demonstrating the framework on an eVTOL model, the authors have positioned it squarely within one of the most consequential application domains for trustworthy autonomy, where certification authorities will demand both performance and explainable reasoning about system health.

More broadly, the study contributes to a growing conversation about how formal methods and machine learning can complement rather than compete with each other. Pure neural approaches to fault diagnosis can be flexible and fast, but they offer no inherent guarantees and can fail unpredictably on event sequences they never saw during training. Pure formal approaches are exhaustive but brittle in the face of scale. The hybrid strategy explored here uses the automaton as a structured curriculum for the network, so the learner is grounded in a complete and well-defined behavioral model rather than in raw, noisy data alone. This grounding is a form of built-in verification: the network’s task is to reproduce a known formal object, which constrains what it can learn and makes its behavior more auditable than that of a network trained end-to-end on sensor streams.

The implications extend well beyond aircraft. Power grids, chemical plants, autonomous driving stacks, and robotic fleets all generate event streams that could be abstracted into automata and diagnosed with this framework, and all of them face the same tension between model fidelity and computational feasibility. If the approach generalizes as the eVTOL case study suggests, engineers may be able to deploy diagnosers that stay synchronized with evolving systems at a fraction of the current cost, bringing formal safety guarantees within reach of systems that today rely on heuristic alarms. The open-access article, received in May 2026 and published on 24 September 2026, offers a concrete template for that future: model the behavior, teach a network to walk the model, and let the learned diagnoser watch the machine. It is a quiet but potentially far-reaching step toward machines that can explain, in the precise language of events, exactly what has gone wrong with them.

Subject of Research: Learning-based fault diagnosis of complex systems using discrete event models and recurrent neural networks

Article Title: Learning-enabled fault diagnosis based on abstract behaviors of the system

Article References: Learning-enabled fault diagnosis based on abstract behaviors of the system. (n.d.). https://doi.org/10.1007/s40747-026-02525-8

Image Credits: AI Generated

DOI: 10.1007/s40747-026-02525-8

Keywords: fault diagnosis, discrete event systems, recurrent neural network, deep learning, deterministic finite automata, eVTOL, urban air mobility, hybrid aircraft, NASA, machine learning, complex systems, safety