Los Alamos Researchers Apply Mori-Zwanzig Formalism to Turbulent Particle Dynamics

Researchers at Los Alamos National Laboratory have introduced a machine learning framework designed to simulate the chaotic motion of particles within turbulent flows. Published in the Proceedings of the National Academies of Science on June 11, 2026, the study addresses one of the most persistent computational hurdles in classical physics by utilizing a data-driven, auto-regressive approach to predict particle trajectories.

Daniel Livescu, a scientist at Los Alamos National Laboratory, identified the modeling of particle motions within turbulence as a primary obstacle in physical system simulation. The research team sought to mitigate the extreme computational costs typically associated with resolving multiscale vortex dynamics by developing a surrogate dynamical system. This surrogate model reproduces particle trajectories and statistical behaviors without requiring the exhaustive computational resources of traditional high-fidelity simulations.

The architecture relies on neural networks enhanced by the Mori-Zwanzig formalism, a mathematical method that decomposes dynamical systems into resolved dynamics based on both current state observations and historical data. By incorporating this memory-dependent structure, the model effectively captures the chaotic nature of Lagrangian turbulence. The framework was specifically trained on short-term predictive tasks to ensure the accurate realization of long-term statistical outcomes.

Turbulence remains a multiscale phenomenon, manifesting in diverse environments ranging from astrophysical systems to inertial confinement fusion. The inability to predict velocity and trajectory at smaller scales has historically limited the accuracy of predictive models in these fields. By applying an auto-regressive framework, the team demonstrated that machine learning can successfully navigate these multiscale complexities where traditional numerical methods often struggle with efficiency.

The team successfully demonstrated that their model could reproduce complex particle trajectories with high fidelity. By training the neural networks on short-term predictions, they achieved a robust realization of the long-term statistical behavior of Lagrangian turbulence. This capability is essential for researchers who need to understand the evolution of turbulent systems without performing full-scale, computationally expensive simulations for every scenario.

Xander de Wit, a researcher at Los Alamos National Laboratory and the lead author of the paper, noted that the inclusion of memory effects distinguishes this approach from standard predictive models. The team anticipates that this methodology will provide a foundation for addressing other complex systems characterized by similar Lagrangian dynamics. The research was supported by the Laboratory Directed Research and Development program at Los Alamos National Laboratory.

The integration of the Mori-Zwanzig formalism into neural network architectures represents a shift toward physics-aware machine learning. By constraining the model with established physical principles, the researchers ensured that the surrogate system respects the underlying dynamics of the turbulent environment. This hybrid approach offers a pathway for researchers to maintain physical consistency while leveraging the pattern-recognition capabilities of deep learning.

Beyond fluid dynamics, the potential applications for this framework extend to various fields involving large-scale particle or agent interactions. De Wit suggested that crowd movement analysis could serve as a logical extension for this research, given the shared Lagrangian aspects between turbulent flows and dense human dynamics. The ability to model these systems with reduced computational overhead could facilitate more rapid iterations in complex system design.

The research group, which included members of the Physics Aware AI/ML division at the laboratory and an international collaborator, has established a new benchmark for surrogate modeling in chaotic systems. As the team continues to refine the framework, the focus will likely shift toward optimizing the memory-retention components for even more expansive datasets. The work underscores the growing importance of embedding physical formalisms directly into the training loops of neural networks to improve generalization and predictive accuracy.

Future investigations will determine the scalability of this framework across different Reynolds numbers and varying degrees of flow complexity. The upcoming transition of De Wit to a Richard Feynman Distinguished Postdoctoral Fellow position suggests a sustained institutional commitment to this line of inquiry. Observers should monitor subsequent publications for evidence of the model’s performance in non-fluid applications, which will serve as a critical test for the framework’s broader utility in complex system modeling.