mlsanityData to 7 Oct 2026

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

arXiv 2207.05779 ↗First posted 12 Jul 2022math.DS cs.LG cs.NAcited by 15

Not on the map. Why?

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.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 25 of its 92 references that are in the map. First posted on arXiv 12 Jul 2022.

Builds on

25 of 92 references.

References · 25

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  4. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  5. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  6. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  7. 2018Deep learning to represent sub-grid processes in climate modelscited by 156
  8. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  9. 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 128
  10. 2020Multiscale Simulations of Complex Systems by Learning their Effective Dynamicscited by 86
  11. 2020Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equationscited by 78
  12. 2019DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)cited by 40
13 more
  1. 2019Deep learning observables in computational fluid dynamicscited by 38
  2. 2019Coarse-scale PDEs from fine-scale observations via machine learningcited by 35
  3. 2019Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEscited by 27
  4. 2021On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elementscited by 25
  5. 2022Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approachcited by 25
  6. 2017Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape explorationcited by 24
  7. 2022Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Spacecited by 16
  8. 2022Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learningcited by 16
  9. 2017A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesicscited by 10
  10. 2019Partial observations and conservation laws: Grey-box modeling in biotechnology and optogeneticscited by 9
  11. 2019Autonomics: In Search of a Foundation for Next Generation Autonomous Systemscited by 8
  12. 2021Time Series Forecasting Using Manifold Learningcited by 7
  13. 2018Using learning to control artificial avatars in human motor coordination taskscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 4; 2025: 4; 2026: 2.

15 papers.

Sort:

  1. 2023Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learningcited by 10
  2. 2025Enabling Local Neural Operators to perform Equation-Free System-Level Analysiscited by 10
  3. 2024Nonlinear Discrete-Time Observers with Physics-Informed Neural Networkscited by 8
  4. 2024GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Lawscited by 8
  5. 2023Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operatorcited by 5
  6. 2023Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learningcited by 4
  7. 2023Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Pointscited by 3
  8. 2024A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEscited by 2
  9. 2025Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learningcited by 2
  10. 2025Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operatorscited by 1
  11. 2023The Lost Art of Mathematical Modellingcited by 0
  12. 2024Cell reprogramming design by transfer learning of functional transcriptional networkscited by 0
3 more
  1. 2025Invariant Manifolds of Discrete-time Dynamical Systems with Nonlinear Exosystems via Hybrid Physics-Informed Neural Networkscited by 0
  2. 2026RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservationcited by 0
  3. 2026Complex Diffusion Maps with ω-Parameterized Kernels Revealing Inherent Harmonic Representationscited by 0