Agent‐based models (ABMs) are increasing in popularity as tools to simulate and explore many biological systems. Successes in simulation lead to deeper investigations, from designing systems to optimizing performance. The typically stochastic, rule‐based structure of ABMs, however, does not lend itself to analytic and numerical techniques of optimization the way traditional dynamical systems models do. The goal of this work is to illustrate a technique for approximating ABMs with a partial differential equation (PDE) system to design some management strategies on the ABM. We propose a surrogate modeling approach, using differential equations that admit direct means of determining optimal controls, with a particular focus on environmental heterogeneity in the ABM. We implement this program with both PDE and ordinary differential equation (ODE) approximations on the well‐known rabbits and grass ABM, in which a pest population consumes a resource. The control problem addressed is the reduction of this pest population through an optimal control formulation. After fitting the ODE and PDE models to ABM simulation data in the absence of control, we compute optimal controls using the ODE and PDE models, which we them apply to the ABM. The results show promise for approximating ABMs with differential equations in this context.
This content will become publicly available on January 1, 2025
Optimal boundary control of a model thin-film fiber coating model
This paper considers the control of fluid on a solid vertical fiber, where the fiber radius is larger than the film thickness. The fluid dynamics is governed by a fourth-order partial differential equation (PDE) that models this flow regime. Fiber coating is affected by the Rayleigh–Plateau instability that leads to breakup into moving droplets. In this work, we show that control of the film profile can be achieved by dynamically altering the input flux to the fluid system that appears as a boundary condition of the PDE. We use the optimal control methodology to compute the control function. This method entails solving a minimization of a given cost function over a time horizon. We formally derive the optimal control conditions, and numerically verify that subject to the domain length constraint, the thin film equation can be controlled to generate a desired film profile with a single point of actuation. Specifically, we show that the system can be driven to both constant film profiles and traveling waves of certain speeds.
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- Award ID(s):
- 2309774
- NSF-PAR ID:
- 10509722
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Physica D: Nonlinear Phenomena
- Volume:
- 457
- Issue:
- C
- ISSN:
- 0167-2789
- Page Range / eLocation ID:
- 133942
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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