Large-scale outbreaks of epidemics, misinformation, or other harmful contagions pose significant threats to human society, yet the fundamental question of whether an emerging outbreak will escalate into a major epidemic or naturally die out remains largely unaddressed. This problem is challenging, partially due to inadequate data during the early stages of outbreaks and also because established models focus on average behaviors of large epidemics rather than the stochastic nature of small transmission chains. Here, we introduce the first systematic framework for forecasting whether initial transmission events will amplify into major outbreaks or fade into extinction during early stages, when intervention strategies can still be effectively implemented. Using extensive data from stochastic spreading models, we developed a deep learning framework that predicts early-stage spreading outcomes in real-time. Validation across Erdős-Rényi and Barabási-Albert networks with varying infectivity levels shows our method accurately forecasts stochastic spreading events well before potential outbreaks, demonstrating robust performance across different network structures and infectivity scenarios.To address the challenge of sparse data during early outbreak stages, we further propose a pretrain-finetune framework that leverages diverse simulation data for pretraining and adapts to specific scenarios through targeted fine-tuning. The pretrain-finetune framework consistently outperforms baseline models, achieving superior performance even when trained on limited scenario-specific data. To our knowledge, this work presents the first framework for predicting stochastic take-off versus die-out. This framework provides valuable insights for epidemic preparedness and public health decision-making, enabling more informed early intervention strategies.

Large Language Models (LLMs) offer new opportunities to automate complex interdisciplinary research domains. Epidemic modeling, characterized by its complexity and reliance on network science, dynamical systems, epidemiology, and stochastic simulations, represents a prime candidate for leveraging LLM-driven automation. We introduce \textbf{EpidemIQs}, a novel multi-agent LLM framework that integrates user inputs and autonomously conducts literature review, analytical derivation, network modeling, mechanistic modeling, stochastic simulations, data visualization and analysis, and finally documentation of findings in a structured manuscript. We introduced two types of agents: a scientist agent for planning, coordination, reflection, and generation of final results, and a task-expert agent to focus exclusively on one specific duty serving as a tool to the scientist agent. The framework consistently generated complete reports in scientific article format. Specifically, using GPT 4.1 and GPT 4.1 mini as backbone LLMs for scientist and task-expert agents, respectively, the autonomous process completed with average total token usage 870K at a cost of about \$1.57 per study, achieving a 100\% completion success rate through our experiments. We evaluate EpidemIQs across different epidemic scenarios, measuring computational cost, completion success rate, and AI and human expert reviews of generated reports. We compare EpidemIQs to the single-agent LLM, which has the same system prompts and tools, iteratively planning, invoking tools, and revising outputs until task completion. The comparison shows consistently higher performance of the proposed framework across five different scenarios. EpidemIQs represents a step forward in accelerating scientific research by significantly reducing costs and turnaround time of discovery processes, and enhancing accessibility to advanced modeling tools.

This paper describes the comprehensive safety framework th at underpinned the development, release process, and regulatory approval of BMW's first SAE Level 3 Au tomated Driving System. The framework combines established qualitative and quantitative me thods from the fields of Systems Engineering, Engineering Risk Analysis, Bayesian Data Analysis, Design of Experiments, and Statistical Learning in a novel manner. The approach systematically minimizes the r isks associated with hardware and software faults, performance limitations, and insufficient specifica tions to an acceptable level that achieves a Positive Risk Balance. At the core of the framework is the system atic identification and quantification of uncertainties associated with hazard scenarios and the red undantly designed system based on designed experiments, field data, and expert knowledge. The residual risk of the system is then estimated through Stochastic Simulation and evaluated by Sensitivity Analys is. By integrating these advanced analytical techniques into the V-Model, the framework fulfills, unifies, and complements existing automotive safety standards. It therefore provides a comprehensive, rigorou s, and transparent safety assurance process for the development and deployment of Automated Driving System s.

Stochastic simulations such as large-scale, spatiotemporal, age-structured epidemic models are computationally expensive at fine-grained resolution. We propose Interactive Neural Process (INP), an interactive framework to continuously learn a deep learning surrogate model and accelerate simulation. Our framework is based on the novel integration of Bayesian active learning, stochastic simulation and deep sequence modeling. In particular, we develop a novel spatiotemporal neural process model to mimic the underlying process dynamics. Our model automatically infers the latent process which describes the intrinsic uncertainty of the simulator. This also gives rise to a new acquisition function that can quantify the uncertainty of deep learning predictions. We design Bayesian active learning algorithms to iteratively query the simulator, gather more data, and continuously improve the model. We perform theoretical analysis and demonstrate that our approach reduces sample complexity compared with random sampling in high dimension. Empirically, we demonstrate our framework can faithfully imitate the behavior of a complex infectious disease simulator with a small number of examples, enabling rapid simulation and scenario exploration.

Fighting Fantasy is a popular recreational fantasy gaming system worldwide. Combat in this system progresses through a stochastic game involving a series of rounds, each of which may be won or lost. Each round, a limited resource (`luck') may be spent on a gamble to amplify the benefit from a win or mitigate the deficit from a loss. However, the success of this gamble depends on the amount of remaining resource, and if the gamble is unsuccessful, benefits are reduced and deficits increased. Players thus dynamically choose to expend resource to attempt to influence the stochastic dynamics of the game, with diminishing probability of positive return. The identification of the optimal strategy for victory is a Markov decision problem that has not yet been solved. Here, we combine stochastic analysis and simulation with dynamic programming to characterise the dynamical behaviour of the system in the absence and presence of gambling policy. We derive a simple expression for the victory probability without luck-based strategy. We use a backward induction approach to solve the Bellman equation for the system and identify the optimal strategy for any given state during the game. The optimal control strategies can dramatically enhance success probabilities, but take detailed forms; we use stochastic simulation to approximate these optimal strategies with simple heuristics that can be practically employed. Our findings provide a roadmap to improving success in the games that millions of people play worldwide, and inform a class of resource allocation problems with diminishing returns in stochastic games.

The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a given system, it is not known beforehand which closure approximation is optimal, i.e. which higher order terms are relevant in the current regime. Further, the generalization of such approximations is typically poor, as higher order corrections may become relevant over long timescales. We have developed a method to learn moment closure approximations directly from data using dynamic Boltzmann distributions (DBDs). The dynamics of the distribution are parameterized using basis functions from finite element methods, such that the approach can be applied without knowing the true dynamics of the system under consideration. We use the hierarchical architecture of deep Boltzmann machines (DBMs) with multinomial latent variables to learn closure approximations for progressively higher order spatial correlations. The learning algorithm uses a centering transformation, allowing the dynamic DBM to be trained without the need for pre-training. We demonstrate the method for a Lotka-Volterra system on a lattice, a typical example in spatial chemical reaction networks. The approach can be applied broadly to learn deep generative models in applications where infinite systems of differential equations arise.

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

In recent years, researchers in decision analysis and artificial intelligence (Al) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in the field have shown that the problem of probabilistic inference in belief networks is difficult and almost certainly intractable. K N ET, a software environment for constructing knowledge-based systems within the axiomatic framework of decision theory, contains a randomized approximation scheme for probabilistic inference. The algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models of medical diagnosis. Unlike previously described stochastic algorithms for probabilistic inference, the randomized approximation scheme computes a priori bounds on running time by analyzing the structure and contents of the belief network. In this article, we describe a randomized algorithm for probabilistic inference and analyze its performance mathematically. Then, we devote the major portion of the paper to a discussion of the algorithm's empirical behavior. The results indicate that the generation of good trials (that is, trials whose distribution closely matches the true distribution), rather than the computation of numerous mediocre trials, dominates the performance of stochastic simulation. Key words: probabilistic inference, belief networks, stochastic simulation, computational complexity theory, randomized algorithms.

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling, and a method described by Pearl, called stochastic simulation. We first review the conditions under which logic sampling is computationally infeasible. Such cases motivated the development of the Pearl's stochastic simulation algorithm. We have found that this stochastic simulation algorithm, when applied to certain networks, leads to much slower than expected convergence to the true posterior probabilities. This behavior is a result of the tendency for local areas in the network to become fixed through many simulation cycles. The time required to obtain significant convergence can be made arbitrarily long by strengthening the probabilistic dependency between nodes. We propose the use of several forms of graph modification, such as graph pruning, arc reversal, and node reduction, in order to convert some networks into formats that are computationally more efficient for simulation.

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