arXiv subjects

Nicholas Zolman

Publications and source records attributed to Nicholas Zolman.

7 recordsLinked to original sources

arXiv2026

Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections

Extreme events -- such as earthquakes and coronal mass ejections -- are common in many chaotic dynamical systems, yet are difficult to characterize and predict due to the subtle instability mechanisms that drive them. In this work, we develop an interpretable technique that reveals the underlying mechanisms behind extreme events and uses them to build data-driven forecasts and intuitive event suppression controllers. In particular, we utilize the covariance balancing reduction using adjoint snapshots (CoBRAS) method to identify linear oblique projections that best capture the sensitivity of a quantity of interest and reconstruct the original state. Importantly, we bypass the need for cumbersome adjoint calculations, instead using backpropagation via modern automatically differentiable numerical frameworks. To accommodate spatially localized events, we also introduce a new variant of CoBRAS to obtain local sensitivity-balanced projections. We demonstrate the utility of this approach to characterize extreme events across a diverse set of challenging systems, including turbulent bursts of energy dissipation in the 2D Kolmogorov Flow, spontaneous synchronization in networks of coupled FitzHugh-Nagumo oscillators, and the localized formation of ocean rogue waves from a modified nonlinear Schr\"odinger equation. For each example, we show that our simple forecast models accurately predict extreme events and that the underlying mechanisms may be used to design control laws to prevent these events. Finally, we demonstrate that by learning a neural network surrogate model of the dynamics directly from data, we may extend this approach to experimental systems and systems that are not natively written in an automatically differentiable programming language.

nlin.CD↗

arXiv2026

SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse identification of nonlinear dynamics (SINDy) is a complementary approach that allows for learning sparse equations for dynamical systems from data; however, learned equations are limited by the library. In this work, we present SINDy-KANs, which simultaneously train a KAN and a SINDy-like representation to increase interpretability of KAN representations with SINDy applied at the level of each activation function, while maintaining the function compositions possible through deep KANs. We apply our method to a number of symbolic regression tasks, including dynamical systems, to show accurate equation discovery across a range of systems.

cs.LG↗

arXiv2025

The HydroGym Reinforcement Learning Platform for Fluid Dynamics

Modeling and controlling fluids is critical across science and engineering. Effective flow control can increase lift, reduce drag, enhance mixing, and attenuate noise, potentially unlocking new technologies. Yet controlling fluids is hard: the dynamics are high-dimensional, nonlinear, and multiscale. While reinforcement learning (RL) has recently succeeded in robotics and protein folding through shared benchmarks, fluid dynamics has resisted such progress: each controller is typically tuned to a single geometry and operating point, making results hard to accumulate, transfer, and compare. We introduce HydroGym, a solver-independent RL platform for flow control, and show that standardized infrastructure unlocks transferable control intelligence across flow regimes. HydroGym provides 61+ validated environments spanning laminar to turbulent flows, with systematic Reynolds number progressions up to Re=400,000 and Mach number variations in 2D and 3D. It supports diverse backends, including finite-volume, spectral-element, finite-element, lattice-Boltzmann, and fully differentiable solvers for gradient-enhanced optimization. Across environments, RL agents consistently discover robust control principles, such as boundary-layer manipulation, acoustic-feedback disruption, and wake reorganization, yielding drag reductions exceeding 90% in canonical configurations. Critically, we demonstrate zero-shot transfer: agents trained only on a simplified channel flow achieve 38% friction-drag reduction on an unseen 3D wing section at chord Reynolds number Re=200,000 reducing exploration costs by four orders of magnitude versus direct on-wing optimization. This suggests RL agents uncover essential physics rather than configuration-specific patterns, pointing toward generalizable control. HydroGym offers extensible, scalable community infrastructure for fluid dynamics, machine learning, and control research.

physics.flu-dyn↗

arXiv2024

SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in complex environments, such as stabilizing a tokamak fusion reactor or minimizing the drag force on an object in a fluid flow. However, DRL requires an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and flow control problems, including gust mitigation on a 3D NACA 0012 airfoil at $Re=1000$. SINDy-RL achieves comparable performance to modern DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a DRL policy.

cs.LG↗

arXiv2023

A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning

Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be extrapolated to the farthest reaches of the universe. Symmetry is essential to achieving this extrapolatory power in machine learning applications. For example, translation invariance in image classification allows models with fewer parameters, such as convolutional neural networks, to be trained on smaller data sets and achieve state-of-the-art performance. In this paper, we provide a unifying theoretical and methodological framework for incorporating symmetry into machine learning models in three ways: 1. enforcing known symmetry when training a model; 2. discovering unknown symmetries of a given model or data set; and 3. promoting symmetry during training by learning a model that breaks symmetries within a user-specified group of candidates when there is sufficient evidence in the data. We show that these tasks can be cast within a common mathematical framework whose central object is the Lie derivative associated with fiber-linear Lie group actions on vector bundles. We extend and unify several existing results by showing that enforcing and discovering symmetry are linear-algebraic tasks that are dual with respect to the bilinear structure of the Lie derivative. We also propose a novel way to promote symmetry by introducing a class of convex regularization functions based on the Lie derivative and nuclear norm relaxation to penalize symmetry breaking during training of machine learning models. We explain how these ideas can be applied to a wide range of machine learning models including basis function regression, dynamical systems discovery, neural networks, and neural operators acting on fields.

cs.LG↗

arXiv2023

Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution

In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics. The usefulness of standard deep learning methods is also limited, because an image of a rigid body reveals nothing about the distribution of mass inside the body, which, together with initial angular velocity, is what determines how the body will rotate. We present a physics-based neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to $\mathbf{SO}(3)$, computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion. We demonstrate the efficacy of our approach on new rotating rigid-body datasets of sequences of synthetic images of rotating objects, including cubes, prisms and satellites, with unknown uniform and non-uniform mass distributions. Our model outperforms competing baselines on our datasets, producing better qualitative predictions and reducing the error observed for the state-of-the-art Hamiltonian Generative Network by a factor of 2.

cs.CV↗

arXiv2022

Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body

In many real-world settings, image observations of freely rotating 3D rigid bodies, such as satellites, may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics and a lack of interpretability reduces the usefulness of standard deep learning methods. In this work, we present a physics-informed neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to $\mathbf{SO}(3)$, computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion with a learned representation of the Hamiltonian. We demonstrate the efficacy of our approach on a new rotating rigid-body dataset with sequences of rotating cubes and rectangular prisms with uniform and non-uniform density.

cs.CV↗