no code implementations • 20 Mar 2024 • Yifan Chen, Mark Goldstein, Mengjian Hua, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden
We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling.
1 code implementation • 16 Jan 2024 • Nanye Ma, Mark Goldstein, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden, Saining Xie
We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT).
no code implementations • 5 Oct 2023 • Michael S. Albergo, Mark Goldstein, Nicholas M. Boffi, Rajesh Ranganath, Eric Vanden-Eijnden
In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings.
no code implementations • 5 Oct 2023 • Michael S. Albergo, Nicholas M. Boffi, Michael Lindsey, Eric Vanden-Eijnden
Given a set of $K$ probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals.
no code implementations • 22 Sep 2023 • Nicholas M. Boffi, Eric Vanden-Eijnden
We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles.
1 code implementation • 15 Mar 2023 • Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden
The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient.
no code implementations • 9 Jun 2022 • Nicholas M. Boffi, Eric Vanden-Eijnden
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation.
no code implementations • 20 Dec 2021 • Thomas T. C. K. Zhang, Stephen Tu, Nicholas M. Boffi, Jean-Jacques E. Slotine, Nikolai Matni
Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems.
no code implementations • 7 Jun 2021 • Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions.
no code implementations • 26 Nov 2020 • Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine
We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances.
no code implementations • 13 Aug 2020 • Nicholas M. Boffi, Stephen Tu, Nikolai Matni, Jean-Jacques E. Slotine, Vikas Sindhwani
Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property.
no code implementations • 15 Jun 2020 • Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine
Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks.
no code implementations • 31 Dec 2019 • Nicholas M. Boffi, Jean-Jacques E. Slotine
Stable concurrent learning and control of dynamical systems is the subject of adaptive control.
no code implementations • 28 Dec 2018 • Nicholas M. Boffi, Jean-Jacques E. Slotine
We analyze the effect of synchronization on distributed stochastic gradient algorithms.