# Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach

arXiv: https://arxiv.org/abs/2207.05779 · HTML: https://mlsanity.com/paper/2207.05779/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 92 references that are in the map.
- First posted on arXiv 12 Jul 2022.

## Builds on (most cited first, 25 of 25)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Solving and Learning Nonlinear PDEs with Gaussian Processes](https://mlsanity.com/paper/2103.12959/) (2021)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equations](https://mlsanity.com/paper/2012.02895/) (2020)
- [DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)](https://mlsanity.com/paper/1911.09145/) (2019)
- [Deep learning observables in computational fluid dynamics](https://mlsanity.com/paper/1903.03040/) (2019)
- [Coarse-scale PDEs from fine-scale observations via machine learning](https://mlsanity.com/paper/1909.05707/) (2019)
- [Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs](https://mlsanity.com/paper/1911.02109/) (2019)
- [On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements](https://mlsanity.com/paper/2110.14121/) (2021)
- [Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach](https://mlsanity.com/paper/2201.13323/) (2022)
- [Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration](https://mlsanity.com/paper/1801.00203/) (2017)
- [Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learning](https://mlsanity.com/paper/2205.00579/) (2022)
- [Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space](https://mlsanity.com/paper/2204.12536/) (2022)
- [A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics](https://mlsanity.com/paper/1707.06757/) (2017)
- [Partial observations and conservation laws: Grey-box modeling in biotechnology and optogenetics](https://mlsanity.com/paper/1909.04234/) (2019)
- [Autonomics: In Search of a Foundation for Next Generation Autonomous Systems](https://mlsanity.com/paper/1911.07133/) (2019)
- [Time Series Forecasting Using Manifold Learning](https://mlsanity.com/paper/2110.03625/) (2021)
- [Using learning to control artificial avatars in human motor coordination tasks](https://mlsanity.com/paper/1810.04191/) (2018)

## Built on by (most cited first, 15 of 15)

- [Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning](https://mlsanity.com/paper/2309.07946/) (2023)
- [Enabling Local Neural Operators to perform Equation-Free System-Level Analysis](https://mlsanity.com/paper/2505.02308/) (2025)
- [Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.12360/) (2024)
- [GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws](https://mlsanity.com/paper/2410.22193/) (2024)
- [Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operator](https://mlsanity.com/paper/2304.11925/) (2023)
- [Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning](https://mlsanity.com/paper/2303.08884/) (2023)
- [Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points](https://mlsanity.com/paper/2309.14334/) (2023)
- [A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEs](https://mlsanity.com/paper/2403.11591/) (2024)
- [Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning](https://mlsanity.com/paper/2508.03926/) (2025)
- [Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators](https://mlsanity.com/paper/2509.23975/) (2025)
- [The Lost Art of Mathematical Modelling](https://mlsanity.com/paper/2301.08559/) (2023)
- [Cell reprogramming design by transfer learning of functional transcriptional networks](https://mlsanity.com/paper/2403.04837/) (2024)
- [Invariant Manifolds of Discrete-time Dynamical Systems with Nonlinear Exosystems via Hybrid Physics-Informed Neural Networks](https://mlsanity.com/paper/2506.13950/) (2025)
- [RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation](https://mlsanity.com/paper/2601.14794/) (2026)
- [Complex Diffusion Maps with ω-Parameterized Kernels Revealing Inherent Harmonic Representations](https://mlsanity.com/paper/2605.01691/) (2026)

## Abstract (arXiv)

We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modelled via microscopic/agent-based simulators. The approach obviates the need for construction of surrogate, reduced-order models.~The proposed implementation consists of three steps: (A) from high-dimensional agent-based simulations, machine learning (in particular, non-linear manifold learning (Diffusion Maps (DMs)) helps identify a set of coarse-grained variables that parametrize the low-dimensional manifold on which the emergent/collective dynamics evolve. The out-of-sample extension and pre-image problems, i.e. the construction of non-linear mappings from the high-dimensional input space to the low-dimensional manifold and back, are solved by coupling DMs with the Nystrom extension and Geometric Harmonics, respectively; (B) having identified the manifold and its coordinates, we exploit the Equation-free approach to perform numerical bifurcation analysis of the emergent dynamics; then (C) based on the previous steps, we design data-driven embedded wash-out controllers that drive the agent-based simulators to their intrinsic, imprecisely known, emergent open-loop unstable steady-states, thus demonstrating that the scheme is robust against numerical approximation errors and modelling uncertainty.~The efficiency of the framework is illustrated by controlling emergent unstable (i) traveling waves of a deterministic agent-based model of traffic dynamics, and (ii) equilibria of a stochastic financial market agent model with mimesis.