6 papers
VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification
Paolo Conti, Jonas Kneifl, Andrea Manzoni +4
The simulation of many complex phenomena in engineering and science requires solving expensive, high-dimensional systems of partial differential equations (PDEs). To circumvent thi…
SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning
Nicholas Zolman, Christian Lagemann, Urban Fasel +2
Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in complex environments, such as stabilizing a tokamak f…
A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning
Samuel E. Otto, Nicholas Zolman, J. Nathan Kutz +1
Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincaré invariance, allo…
Advanced Differential Equations: Asymptotics & Perturbations
J. Nathan Kutz
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numeric…
Separation of periodic orbits in the delay embedded space of chaotic attractors
Prerna Patil, Eurika Kaiser, J Nathan Kutz +1
This work explores the intersection of time-delay embeddings, periodic orbit theory, and symbolic dynamics. Time-delay embeddings have been effectively applied to chaotic time seri…
Data-Driven Discovery of a New Ginzburg-Landau Reduced-Order Model for Vortex Shedding
Joseph J. Williams, Zachary G. Nicolaou, J. Nathan Kutz +1
Vortex shedding is an important physical phenomenon observed across many spatial and temporal scales in fluids. Previous experimental and theoretical studies have established a hie…