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Learning Individual Interactions from Population Dynamics with Discrete-Event Simulation Model

Yan Shen, Fan Yang, Mingchen Gao, Wen Dong

TL;DR

The paper addresses learning complex system dynamics from population-level observations by proposing a discrete-event simulation (DES) representation in which system evolution is driven by a sparse set of local stochastic events. It casts the learning problem as estimating event rates and stoichiometric mixing, using a time-discretized Langevin approximation with $\mathbf h(\mathbf x)$ and a matrix $S$, and shows that gradient-based learning is equivalent to a generalized EM algorithm. The authors develop an EKF-based latent-state inference framework to handle noisy observations and derive a scalable training procedure with regularization to promote sparsity. Across predator-prey, prokaryotic auto-regulation, and traffic networks, the DES approach achieves data-efficient dynamics recovery, provides interpretable event structures, and outperforms or matches model-free baselines in terms of KL-divergence and training efficiency. This work offers a principled, interpretable alternative to black-box deep models for learning population-level dynamics with broad applicability in biology, engineering, and social systems.

Abstract

The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture complex system dynamics either with dynamic Bayesian networks and state space models, which is hard to scale because it is non-trivial to prescribe the dynamics with a sparse graph or a system of differential equations; or a deep neural networks, where the distributed representation of the learned dynamics is hard to interpret. In this paper, we will explore the possibility of learning a discrete-event simulation representation of complex system dynamics assuming multivariate normal distribution of the state variables, based on the observation that many complex system dynamics can be decomposed into a sequence of local interactions, which individually change the system state only minimally but in sequence generate complex and diverse dynamics. Our results show that the algorithm can data-efficiently capture complex network dynamics in several fields with meaningful events.

Learning Individual Interactions from Population Dynamics with Discrete-Event Simulation Model

TL;DR

The paper addresses learning complex system dynamics from population-level observations by proposing a discrete-event simulation (DES) representation in which system evolution is driven by a sparse set of local stochastic events. It casts the learning problem as estimating event rates and stoichiometric mixing, using a time-discretized Langevin approximation with and a matrix , and shows that gradient-based learning is equivalent to a generalized EM algorithm. The authors develop an EKF-based latent-state inference framework to handle noisy observations and derive a scalable training procedure with regularization to promote sparsity. Across predator-prey, prokaryotic auto-regulation, and traffic networks, the DES approach achieves data-efficient dynamics recovery, provides interpretable event structures, and outperforms or matches model-free baselines in terms of KL-divergence and training efficiency. This work offers a principled, interpretable alternative to black-box deep models for learning population-level dynamics with broad applicability in biology, engineering, and social systems.

Abstract

The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture complex system dynamics either with dynamic Bayesian networks and state space models, which is hard to scale because it is non-trivial to prescribe the dynamics with a sparse graph or a system of differential equations; or a deep neural networks, where the distributed representation of the learned dynamics is hard to interpret. In this paper, we will explore the possibility of learning a discrete-event simulation representation of complex system dynamics assuming multivariate normal distribution of the state variables, based on the observation that many complex system dynamics can be decomposed into a sequence of local interactions, which individually change the system state only minimally but in sequence generate complex and diverse dynamics. Our results show that the algorithm can data-efficiently capture complex network dynamics in several fields with meaningful events.
Paper Structure (9 sections, 4 theorems, 10 equations, 2 figures, 1 table)

This paper contains 9 sections, 4 theorems, 10 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Discrete Event Representation of Dynamical Systems
  3. Methodology
  4. Problem Definition
  5. Learning Discrete-Event Simulation Dynamics from Discrete-Time Observations
  6. Experiments
  7. Configuration for performance evaluation
  8. Evaluating discrete-event structural learning
  9. Conclusions

Key Result

Theorem 1

Let $d \mathbf x_{t}=\mathbf \mu(\mathbf x_t) dt + \sqrt{\Sigma(\mathbf x_t)} d \mathbf B_t$, where $B_t$ is a Brownian motion process, $\mu(\mathbf x_t)$ is a drift term and $\Sigma(\mathbf x_t)$ is a covariance matrix. Let $\max_{\mathbf x}\|\operatorname{diag}(\sqrt{|\mu(\mathbf x)|})\|_2\le C_1$

Figures (2)

  • Figure 1: Several representations of a discrete event process. (a) Production rule system, (b) Petri net. (c) System of partial differential equations. (d) Stock and flow diagram.
  • Figure 2: Comparing learned vs ground truth prokaryotic auto-regulation dynamics.

Theorems & Definitions (9)

  • Theorem 1
  • proof : Proof sketch
  • Theorem 2
  • proof
  • Corollary 1
  • Lemma 1
  • proof : Proof of Lemma \ref{['thm:gradient-recursion']}
  • proof : Proof of Corollary \ref{['cor:gradient']}
  • proof : Proof of Theorem \ref{['thm:existence']}