10 citations · 11 across the 7 of their papers we have counts for
10 papers
Volumetric Harmonic Field Navigation for Quadrotors
Shuxiu Jia, Amartya Mukherjee, Yating Yuan +1
Quadrotor navigation in cluttered 3-D environments requires global guidance while local motion remains subject to collision and motion limits. Harmonic potentials provide dense gui…
Almost Sure Convergence Analysis of Stochastic Gradient Methods with Clipping and Additive Noise
Amartya Mukherjee, Jun Liu
Stochastic gradient descent (SGD) with gradient clipping and additive noise has become a standard technique for training machine learning models, particularly in applications requi…
Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative
Amartya Mukherjee, Tristan Milne, Kry Yik-Chau Lui +2
Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions. Despite being commonly described as low-likelihood events, existing g…
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physi…
Almost Sure Convergence Analysis of Differentially Private Stochastic Gradient Methods
Amartya Mukherjee, Jun Liu
Differentially private stochastic gradient descent (DP-SGD) has become the standard algorithm for training machine learning models with rigorous privacy guarantees. Despite its wid…
ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes
Amartya Mukherjee, Ruizhi Deng, He Zhao +3
This work introduces a novel approach to modeling temporal point processes using diffusion models with an asynchronous noise schedule. At each step of the diffusion process, the no…
Manifold-Guided Lyapunov Control with Diffusion Models
Amartya Mukherjee, Thanin Quartz, Jun Liu
This paper presents a novel approach to generating stabilizing controllers for a large class of dynamical systems using diffusion models. The core objective is to develop stabilizi…
Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification
Yiming Meng, Ruikun Zhou, Amartya Mukherjee +3
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonli…
Denoising Diffusion Restoration Tackles Forward and Inverse Problems for the Laplace Operator
Amartya Mukherjee, Melissa M. Stadt, Lena Podina +2
Diffusion models have emerged as a promising class of generative models that map noisy inputs to realistic images. More recently, they have been employed to generate solutions to p…
Harmonic Control Lyapunov Barrier Functions for Constrained Optimal Control with Reach-Avoid Specifications
Amartya Mukherjee, Ruikun Zhou, Haocheng Chang +1
This paper introduces harmonic control Lyapunov barrier functions (harmonic CLBF) that aid in constrained control problems such as reach-avoid problems. Harmonic CLBFs exploit the…