# Multiscale Simulations of Complex Systems by Learning their Effective Dynamics

arXiv: https://arxiv.org/abs/2006.13431 · HTML: https://mlsanity.com/paper/2006.13431/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 30 of 86)

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- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Learning Controllable Adaptive Simulation for Multi-resolution Physics](https://mlsanity.com/paper/2305.01122/) (2023)
- [Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data](https://mlsanity.com/paper/2205.13545/) (2022)
- [Multi-fidelity reduced-order surrogate modeling](https://mlsanity.com/paper/2309.00325/) (2023)
- [PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems](https://mlsanity.com/paper/2410.01337/) (2024)
- [Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learning](https://mlsanity.com/paper/2205.00579/) (2022)
- [Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations](https://mlsanity.com/paper/2408.00157/) (2024)
- [Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach](https://mlsanity.com/paper/2207.05779/) (2022)
- [When are dynamical systems learned from time series data statistically accurate?](https://mlsanity.com/paper/2411.06311/) (2024)
- [Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics](https://mlsanity.com/paper/2212.07892/) (2022)
- [On latent dynamics learning in nonlinear reduced order modeling](https://mlsanity.com/paper/2408.15183/) (2024)
- [MORPH: PDE Foundation Models with Arbitrary Data Modality](https://mlsanity.com/paper/2509.21670/) (2025)
- [Autoencoders for discovering manifold dimension and coordinates in data from complex dynamical systems](https://mlsanity.com/paper/2305.01090/) (2023)
- [Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecasts](https://mlsanity.com/paper/2302.11101/) (2023)
- [Interpretable learning of effective dynamics for multiscale systems](https://mlsanity.com/paper/2309.05812/) (2023)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning](https://mlsanity.com/paper/2309.07946/) (2023)
- [A scalable generative model for dynamical system reconstruction from neuroimaging data](https://mlsanity.com/paper/2411.02949/) (2024)
- [CD-ROM: Complemented Deep-Reduced Order Model](https://mlsanity.com/paper/2202.10746/) (2022)
- [Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data](https://mlsanity.com/paper/2210.17230/) (2022)
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- [A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators](https://mlsanity.com/paper/2403.13858/) (2024)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)

## Abstract (arXiv)

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the system dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation while their findings may not allow for generalisation. On the other hand reduced order models are fast but limited by the frequently adopted linearization of the system dynamics and/or the utilization of heuristic closures. Here we present a novel systematic framework that bridges large scale simulations and reduced order models to Learn the Effective Dynamics (LED) of diverse complex systems. The framework forms algorithmic alloys between non-linear machine learning algorithms and the Equation-Free approach for modeling complex systems. LED deploys autoencoders to formulate a mapping between fine and coarse-grained representations and evolves the latent space dynamics using recurrent neural networks. The algorithm is validated on benchmark problems and we find that it outperforms state of the art reduced order models in terms of predictability and large scale simulations in terms of cost. LED is applicable to systems ranging from chemistry to fluid mechanics and reduces the computational effort by up to two orders of magnitude while maintaining the prediction accuracy of the full system dynamics. We argue that LED provides a novel potent modality for the accurate prediction of complex systems.