Beyond Static Models: Adaptive online learning of effective dynamics for complex systems across scales

Pantelis Vlachas

Keywords: adaptive learning, complex systems, machine learning, dynamical systems

TL;DR: This presentation presents a learning framework that enables fast, accurate, and adaptive predictions of complex dynamical systems.

Abstract:

Predictive simulations are vital in applications like weather forecasting, material design, and understanding complex systems. Their success hinges on accurately modeling their dynamics. Traditional simulation methods have limitations: high-fidelity, large-scale simulations, while precise, are computationally intensive and restrict experimental flexibility. Reduced-order models, though faster, often oversimplify dynamics, sacrificing accuracy through linearization and heuristic closures.
This presentation examines how machine learning (ML) techniques, particularly Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Mixture Density Networks (MDNs), address these challenges. Enhanced with innovative training strategies, these ML models can forecast high-dimensional chaotic dynamics, capture reduced-order dynamics with minimal accuracy loss, and model complex stochastic behaviors in molecular dynamics. We demonstrate the effectiveness of these models using benchmarks like the Kuramoto-Sivashinsky equation (chaotic systems), the Lorenz-96 system (atmospheric dynamics), and Alanine Dipeptide simulations (molecular dynamics), underscoring their potential for accurate prediction.
The presentation also introduces a framework called Adaptive Learning of Effective Dynamics (AdaLED), which builds on the Equation-Free paradigm. AdaLED offers a middle ground between detailed simulations and reduced-order models by adaptively learning and forecasting multiscale systems’ effective dynamics. Using autoencoders for dimensionality reduction and a probabilistic RNN ensemble for time-stepping, AdaLED alternates between simulations and surrogate models, speeding up known dynamic simulations while enabling the exploration of new dynamic regimes through continuous online adaptation.
AdaLED’s capabilities are validated on various systems, including the Van der Pol oscillator, 2D reaction-diffusion equations, and 2D Navier-Stokes flow. It dynamically adapts to new conditions, showing a substantial advantage for complex simulations requiring adaptability. This innovative framework marks a significant advancement in computational dynamics, providing a powerful tool for predictive modeling across various applications.

Submission Number: 52