Quickly and accurately predicting the flight trajectory of a blue army fighter in close-range air combat helps a red army fighter gain a dominant situation, which is the winning factor in later air combat. However,due to the high speed and even hypersonic capabilities of advanced fighters, the diversity of tactical maneuvers,and the instantaneous nature of situational transitions,it is difficult to meet the requirements of practical combat applications in terms of prediction accuracy.To improve prediction accuracy,this paper proposes a spatio-temporal graph attention network (ST-GAT) using encoding and decoding structures to predict the flight trajectory. The encoder adopts a parallel structure of Transformer and GAT branches embedded with the multi-head self-attention mechanism in each front end. The Transformer branch network is used to extract the temporal characteristics of historical trajectories and capture the impact of the fighter's historical state on future trajectories, while the GAT branch network is used to extract spatial features in historical trajectories and capture potential spatial correlations between fighters.Then we concatenate the outputs of the two branches
Ensuring the safety and extended operational life of fighter aircraft necessitates frequent and exhaustive inspections. While surface defect detection is feasible for human inspectors, manual methods face critical limitations in scalability, efficiency, and consistency due to the vast surface area, structural complexity, and operational demands of aircraft maintenance. We propose a smart surface damage detection and localization system for fighter aircraft, termed J-DDL. J-DDL integrates 2D images and 3D point clouds of the entire aircraft surface, captured using a combined system of laser scanners and cameras, to achieve precise damage detection and localization. Central to our system is a novel damage detection network built on the YOLO architecture, specifically optimized for identifying surface defects in 2D aircraft images. Key innovations include lightweight Fasternet blocks for efficient feature extraction, an optimized neck architecture incorporating Efficient Multiscale Attention (EMA) modules for superior feature aggregation, and the introduction of a novel loss function, Inner-CIOU, to enhance detection accuracy. After detecting damage in 2D images, the system maps the i
Transformers have achieved remarkable success in time series modeling, yet their internal mechanisms remain opaque. This work demystifies the Transformer encoder by establishing its fundamental equivalence to a Graph Convolutional Network (GCN). We show that in the forward pass, the attention distribution matrix serves as a dynamic adjacency matrix, and its composition with subsequent transformations performs computations analogous to graph convolution. Moreover, we demonstrate that in the backward pass, the update dynamics of value and feed-forward projections mirror those of GCN parameters. Building on this unified theoretical reinterpretation, we propose \textbf{Fighter} (Flexible Graph Convolutional Transformer), a streamlined architecture that removes redundant linear projections and incorporates multi-hop graph aggregation. This perspective yields an explicit and interpretable representation of temporal dependencies across different scales, naturally expressed as graph edges. Experiments on standard forecasting benchmarks confirm that Fighter achieves competitive performance while providing clearer mechanistic interpretability of its predictions.
This paper presents the development of an Artificial Intelligence (AI) based fighter jet agent within a customized Pygame simulation environment, designed to solve multi-objective tasks via deep reinforcement learning (DRL). The jet's primary objectives include efficiently navigating the environment, reaching a target, and selectively engaging or evading an enemy. A reward function balances these goals while optimized hyperparameters enhance learning efficiency. Results show more than 80\% task completion rate, demonstrating effective decision-making. To enhance transparency, the jet's action choices are analyzed by comparing the rewards of the actual chosen action (factual action) with those of alternate actions (counterfactual actions), providing insights into the decision-making rationale. This study illustrates DRL's potential for multi-objective problem-solving with explainable AI. Project page is available at: \href{https://github.com/swatikar95/Autonomous-Fighter-Jet-Navigation-and-Combat}{Project GitHub Link}.
The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If $j$ of the $n$ missiles are spent at an encounter they destroy an enemy plane with probability $a(j)$, where $a(0) = 0 $ and $\{a(j)\}$ is a known, strictly increasing concave sequence, e.g., $a(j) = 1-q^j, \; \, 0 < q < 1$. If the enemy is not destroyed, the enemy shoots the fighter down with known probability $1-u$, where $0 \le u \le 1$. The goal of the fighter is to shoot down as many enemy airplanes as possible during a given time period $[0, T]$. Let $K (n, t)$ be the smallest optimal number of missiles to be used at a present encounter, when the fighter has flying time $t$ remaining and $n$ missiles remaining. Three seemingly obvious properties of $K(n, t)$ have been conjectured: [A] The closer to the destination, the more of the $n$ missiles one should use, [B] the more missiles one has, the more one should use, and [C] the more missiles one has, the more one should save for possible future encounters. We show that [C] holds for a
Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed $v>1$. How large must $v$ be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. First, we analyze the natural curve $\mbox{FF}_v$ that develops when the fighter keeps building, at speed $v$, a barrier along the boundary of the expanding fire. We prove that the behavior of this spiralling curve is governed by a complex function $(e^{w Z} - s \, Z)^{-1}$, where $w$ and $s$ are real functions of $v$. For $v>v_c=2.6144 \ldots$ all zeroes are complex conjugate pairs. If $φ$ denotes the complex argument of the conjugate pair nearest to the origin then, by residue calculus, the fire fighter needs $Θ( 1/φ)$ rounds before the fire is contained. As $v$ decreases towards $v_c$ these two zeroes merge into a real one, so that argument $φ$ goes to~0. Thus, curve $\mbox{FF}_v$ does not contain the fire if the fighter moves at speed $v=v_c$. (That speed $v>v_c$ is sufficient for containing the fire has been proposed before by Bressan et al. [7], who constructed a sequence of logarithmic spiral segments that stay stri
This paper compares networks of foreign fighters who joined the Islamic State of Iraq and Syria (ISIS) from Europe and the Arabian Peninsula in order to test whether there are differences in their recruitment and how those differences affect the nature of the foreign fighter mobilization. It is the first study to compare different networks of foreign fighters that joined the same group in the same conflict at the same period of time. This study finds that foreign fighter recruitment resembles an efficiency-secrecy tradeoff: in places where recruitment needs to be hidden from legal scrutiny, recruitment networks are decentralized; composed of small and more local recruitment cells. These cells can operate more secretly and the group as a whole is more resilient to disruption. In exchange, it is hard for the group to attract large numbers of recruits. Whereas in places where recruitment could occur more freely, recruitment networks are more hierarchical; comprised of a larger number of recruits with more geographically diverse connections. The hierarchical design of their recruitment networks may be easier to disrupt, but it also helps the group efficiently recruit more followers if
The advent of deep learning (DL) gave rise to significant breakthroughs in Reinforcement Learning (RL) research. Deep Reinforcement Learning (DRL) algorithms have reached super-human level skills when applied to vision-based control problems as such in Atari 2600 games where environment states were extracted from pixel information. Unfortunately, these environments are far from being applicable to highly dynamic and complex real-world tasks as in autonomous control of a fighter aircraft since these environments only involve 2D representation of a visual world. Here, we present a semi-realistic flight simulation environment Harfang3D Dog-Fight Sandbox for fighter aircrafts. It is aimed to be a flexible toolbox for the investigation of main challenges in aviation studies using Reinforcement Learning. The program provides easy access to flight dynamics model, environment states, and aerodynamics of the plane enabling user to customize any specific task in order to build intelligent decision making (control) systems via RL. The software also allows deployment of bot aircrafts and development of multi-agent tasks. This way, multiple groups of aircrafts can be configured to be competitiv
Conflict fatalities tend to follow heavy-tailed statistical distributions. A 2005 fusion-fission theory predicts mathematically that for armed groups operating in dynamically evolving clusters within a given conflict, the number of fatalities per conflict event will follow an approximate power-law distribution with exponent near 2.5, with the specific exponent value offering insight into the relative robustness of larger versus smaller clusters of fighters in that armed group. Since Yemen and Syria are current hotspots for future conflict, yet their most recent conflicts (2023-2025) have not been studied at the event level, we use ACLED data to determine their best-fit exponent value as each conflict evolved. We find that the exponent lies between 2.5 and 3.5 predominantly throughout each conflict, which suggests that the fighters in each of these conflicts continued to operate in smaller clusters as the conflict evolved. Moreover, temporary reductions in the exponent value -- which suggests a temporary increase in the robustness and involvement of larger clusters of fighters -- appear to arise during major crises ahead of the largest battles. Though the lack higher-quality data fo
The Ultimate Fighting Championship (UFC) has grown from a niche combat sport promotion into a globally recognized competitive enterprise. This study applies complex network analysis to explore the structural evolution of UFC matchmaking and its impact on competitive dynamics, fighter prominence, and audience engagement. By constructing directed and undirected networks where fighters represent nodes and bouts define edges, we examine key metrics such as degree distribution, clustering, betweenness centrality, and eigenvector centrality. Our findings reveal how the UFC's matchmaking strategies transitioned from tightly clustered, repetitive matchups in its early years to a more decentralized and strategically curated fight network. We identify distinct structural properties between winners and losers, showing that successful fighters maintain centrality while frequently losing fighters exhibit surprising degrees of sustained connectivity. Correlations with Pay-Per-View sales and Google search trends suggest that network dispersion and novelty in matchups drive greater audience interest, while excessive clustering and density reduce engagement. Furthermore, comparisons with official r
In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem online, we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold. We validate our method through simulations across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.
The advancement of autonomous systems -- from legged robots to self-driving vehicles and aircraft -- necessitates executing increasingly high-performance and dynamic motions without ever putting the system or its environment in harm's way. In this paper, we introduce Guardrails -- a novel runtime assurance mechanism that guarantees dynamic safety for autonomous systems, allowing them to safely evolve on the edge of their operational domains. Rooted in the theory of control barrier functions, Guardrails offers a control strategy that carefully blends commands from a human or AI operator with safe control actions to guarantee safe behavior. To demonstrate its capabilities, we implemented Guardrails on an F-16 fighter jet and conducted flight tests where Guardrails supervised a human pilot to enforce g-limits, altitude bounds, geofence constraints, and combinations thereof. Throughout extensive flight testing, Guardrails successfully ensured safety, keeping the pilot in control when safe to do so and minimally modifying unsafe pilot inputs otherwise.
This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control constrained nonlinear systems by building a simple, linear driftless approximation at the initial state. We construct a partition of the finite time horizon into successively smaller intervals, and design controlled inputs based on the approximate dynamics in each partition. Under conditions that bound the length of the time horizon, we prove that these inputs result in bounded error from the target state in the original nonlinear system. As successive partitions of the time horizon become shorter, the error reduces to zero despite the effect of uncontrolled inputs. A simulation example on the model of a fighter jet demonstrates that the designed sequence of controlled inputs achieves the target state despite the system suffering a loss of control authority over one of its inputs.
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear system that maximizes warping of the reachable set along a direction of interest. The main result establishes that under certain assumptions on the dynamics, the problem reduces to a finite number of linear optimization problems. When these assumptions are relaxed, we show heuristically that the same approach yields good results. The results are validated on two systems: a linearized ADMIRE fighter jet model and a damped oscillator with complex eigenvalues. The paper concludes with a discussion of future directions for reachable set warping research.
Aiming at the problem of low accuracy of flight trajectory prediction caused by the high speed of fighters, the diversity of tactical maneuvers, and the transient nature of situational change in close range air combat, this paper proposes an enhanced CNN-LSTM network as a fighter flight trajectory prediction method. Firstly, we extract spatial features from fighter trajectory data using CNN, aggregate spatial features of multiple fighters using the social-pooling module to capture geographic information and positional relationships in the trajectories, and use the attention mechanism to capture mutated trajectory features in air combat; subsequently, we extract temporal features by using the memory nature of LSTM to capture long-term temporal dependence in the trajectories; and finally, we merge the temporal and spatial features to predict the flight trajectories of enemy fighters. Extensive simulation experiments verify that the proposed method improves the trajectory prediction accuracy compared to the original CNN-LSTM method, with the improvements of 32% and 34% in ADE and FDE indicators.
Current game world models simulate environments from a subjective, player-centric perspective. However, by treating the Non-Player Character (NPC) merely as background pixels, these models cannot capture interactions between the player and NPC. In that sense, they act as passive video renderers rather than real simulation engines, lacking the physical understanding needed to model action-induced NPC reactivities. We introduce ReactiveGWM, a reactive game world model that synthesizes dynamic interactions between the player and NPC. Instead of entangling all interaction dynamics, ReactiveGWM explicitly decouples player controls from NPC behaviors. Player actions are injected into the diffusion backbone via a lightweight additive bias, while high-level NPC responses (e.g., Offense, Control, Defense) are grounded through cross-attention modules. Crucially, these modules learn a game-agnostic representation of interactive logic. This enables zero-shot strategy transfer: our learned modules can be plugged directly into off-the-shelf, unannotated world models of different games. This instantly unlocks steerable NPC interactions without any domain-specific retraining. Evaluated on two Stre
We present a system that enables real-time interaction between human users and agents trained to control fighter jets in simulated 3D air combat scenarios. The agents are trained in a dedicated environment using Multi-Agent Reinforcement Learning. A communication link is developed to allow seamless deployment of trained agents into VR-Forces, a widely used defense simulation tool for realistic tactical scenarios. This integration allows mixed simulations where human-controlled entities engage with intelligent agents exhibiting distinct combat behaviors. Our interaction model creates new opportunities for human-agent teaming, immersive training, and the exploration of innovative tactics in defense contexts.
In this paper we consider an interchange lane-swap scenario, a limited stretch of highway with two parallel lanes where most vehicles want to change lanes. We show that a particular decentralized Control Barrier Function based algorithm executes lane swaps efficiently, with minimal speed change, within the specified (short) road segment at high traffic densities (3,500 vehicles per hour per lane). Our main point is that controller tuning, the speed of inter-agent instability, plays a major role in the performance of the vehicle group. This is illustrated by comparing two different tunings of the controller and a third one where the lane swap is enforced by virtual guard rails. Like fighter jet dynamic instability improving maneuverability, the inter-agent instability improves agility of a group of vehicles. We emphasize that the controllers considered are decentralized: agents do not know if others want to change lanes or not.
Why humans fight has no easy answer. However, understanding better how humans fight could inform future interventions, hidden shifts and casualty risk. Fusion-fission describes the well-known grouping behavior of fish etc. fighting for survival in the face of strong opponents: they form clusters ('fusion') which provide collective benefits and a cluster scatters when it senses danger ('fission'). Here we show how similar clustering (fusion-fission) of human fighters provides a unified quantitative explanation for complex casualty patterns across decades of Israel-Palestine region violence, as well as the October 7 surprise attack -- and uncovers a hidden post-October 7 shift. State-of-the-art data shows this fighter fusion-fission in action. It also predicts future 'super-shock' attacks that will be more lethal than October 7 and will arrive earlier. It offers a multi-adversary solution. Our results -- which include testable formulae and a plug-and-play simulation -- enable concrete risk assessments of future casualties and policy-making grounded by fighter behavior.
This study proposes a systematic non-kinetic deterrence path modeling framework based on strategic rare earth supply cut-off, aiming to assess the strategic effects of China's export control policy against the United States at the military system level. The model adopts a four-layer structure of "policy input -- resource node -- equipment system -- capability output" and integrates path dependency modeling, degradation function design, and capability lag prediction mechanisms to form a strategic simulation system. The study incorporates graph neural networks and LSTM-based time series methods to dynamically evaluate the impact of rare earth supply disruption on key U.S. military platforms such as the F-35 fighter, nuclear submarines, and AI combat systems, identifying critical path nodes and strategic timing windows. Results indicate that a ten-year zero-tolerance policy on rare earth exports would lead to a significant technological disconnect between years 3 to 5 and a systemic capability lag between years 8 to 12, with an estimated average annual economic impact of 35 to 40 billion USD. These findings demonstrate that rare earth export cut-offs can serve as a structural strategi