28 citations · 119 across the 17 of their papers we have counts for
19 papers
Diffusion models recover accurate mixture weights despite score function insensitivity
Andrew Dennehy, Ramchandran Muthukumar, Rebecca Willett +1
Score-based generative models exhibit a puzzling behavior: they often appear to cover all modes of a target multimodal distribution and yet may fail to learn the correct relative m…
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan Waniorek
We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time- solution operators of dissipative evolution equations. The analysis build…
On the Robustness of Distribution Support under Diffusion Guidance
Ruijia Cao, Yuchen Wu, Nisha Chandramoorthy
Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by i…
When and how can inexact generative models still sample from the data manifold?
Nisha Chandramoorthy, Adriaan de Clercq
A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples a…
When are dynamical systems learned from time series data statistically accurate?
Jeongjin Park, Nicole Yang, Nisha Chandramoorthy
Conventional notions of generalization often fail to describe the ability of learned models to capture meaningful information from dynamical data. A neural network that learns comp…
Score Operator Newton transport
Nisha Chandramoorthy, Florian Schaefer, Youssef Marzouk
We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the t…
On the generalization of learning algorithms that do not converge
Nisha Chandramoorthy, Andreas Loukas, Khashayar Gatmiry +1
Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural ne…
Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems
Nisha Chandramoorthy, Malo Jézéquel
Ruelle gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations of Ruelle's formula have emerged that potentially enab…
Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds
Nisha Chandramoorthy, Qiqi Wang
This paper presents the space-split sensitivity or the S3 algorithm to transform Ruelle's linear response formula into a well-conditioned ergodic-averaging computation. We prove a…
Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems
Adam A. Sliwiak, Nisha Chandramoorthy, Qiqi Wang
An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and th…
On the probability of finding a nonphysical solution through shadowing
Nisha Chandramoorthy, Qiqi Wang
This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a smal…
Variational optimization and data assimilation in chaotic time-delayed systems with automatic-differentiated shadowing sensitivity
Nisha Chandramoorthy, Luca Magri, Qiqi Wang
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differe…
Ergodic Sensitivity Analysis of One-Dimensional Chaotic Maps
Adam A. Sliwiak, Nisha Chandramoorthy, Qiqi Wang
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach,…
An ergodic averaging method to differentiate covariant Lyapunov vectors
Nisha Chandramoorthy, Qiqi Wang
Covariant Lyapunov vectors or CLVs span the expanding and contracting directions of perturbations along trajectories in a chaotic dynamical system. Due to efficient algorithms to c…
A computable realization of Ruelle's formula for linear response of statistics in chaotic systems
Nisha Chandramoorthy, Qiqi Wang
We present a computable reformulation of Ruelle's linear response formula for chaotic systems. The new formula, called Space-Split Sensitivity or S3, achieves an error convergence…
Sensitivity computation of statistically stationary quantities in turbulent flows
Nisha Chandramoorthy, Qiqi Wang
It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not s…
Toward computing sensitivities of average quantities in turbulent flows
Nisha Chandramoorthy, Zhong-Nan Wang, Qiqi Wang +1
Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoi…
Feasibility analysis of ensemble sensitivity computation in turbulent flows
Nisha Chandramoorthy, Pablo Fernandez, Chaitanya Talnikar +1
In chaotic systems, such as turbulent flows, the solutions to tangent and adjoint equations exhibit an unbounded growth in their norms. This behavior renders the instantaneous tang…
Solving Lubrication Problems at the Nanometer Scale
Nisha Chandramoorthy, Nicolas G. Hadjiconstantinou
Lubrication problems at lengthscales for which the traditional Navier-Stokes description fails can be solved using a modified Reynolds lubrication equation that is based on the fol…