We show how to break the sequential bottleneck in evaluating stable nonlinear dynamical systems. Parallel hardware such as GPUs has fueled rapid advances in artificial intelligence (AI) by accelerating primitive computations such as matrix multiplications. Yet many systems of interest across STEM are both nonlinear and dynamic, making their evaluation inherently sequential and limiting the extent to which they can benefit from GPU acceleration.
In this talk, I will present a framework that reformulates the evaluation of nonlinear dynamics as a parallelizable optimization problem. We show that this optimization problem satisfies a Polyak–Łojasiewicz (gradient dominance) condition, with conditioning governed by the predictability of the underlying dynamical system: the degree to which small perturbations to the state affect future trajectories. Predictable systems give rise to well-conditioned optimization problems, enabling dramatic reductions in evaluation time relative to sequential methods. In contrast, chaotic or unpredictable systems lead to poorly conditioned problems, making parallel evaluation impractical.
Our analysis provides a precise characterization of when GPU acceleration can be effectively leveraged to evaluate nonlinear dynamical systems. It also yields concrete design principles for training neural network architectures that are stable and parallelizable by construction. We will illustrate these results through examples from computational biology and statistics, including the parallelization of Markov Chain Monte Carlo across time.
Leo is an Assistant Professor in the School of Engineering at Brown University, as well as the Carney Institute for Brain Science, where he directs the Dynamic Intelligence Lab. His research centers on fundamental questions in simulating, modeling, and learning nonlinear dynamical systems, with a particular focus on systems that can learn, adapt, and act intelligently. Previously, he was the 2024–2025 Goldstine Postdoctoral Fellow in the Mathematics of Computation Department at IBM Research. He received his PhD from MIT in the Department of Brain and Cognitive Sciences in 2023. Before that he majored in physics and minored in mathematics at Rutgers University in his homeland of New Jersey.
