Related papers: A deterministic adjoint-based semi-analytical algo…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…
This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves…
Purpose: To demonstrate a proton imaging system based on well-established fast scintillator technology to achieve high performance with low cost and complexity, with the potential of a straightforward translation into clinical use. Methods:…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…
This study aims to assess the composition of scattered particles generated in proton therapy for tumours situated proximal to titanium dental implants. The investigation involves decomposing the mixed field and recording Linear Energy…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) are useful for many practical tasks in machine learning. Synaptic weights, as well as neuron activation functions within the deep network are typically stored with…
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…
Federated learning has emerged in the last decade as a distributed optimization paradigm due to the rapidly increasing number of portable devices able to support the heavy computational needs related to the training of machine learning…
In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. Recent advances using the distributed gradient…
Change-point analysis is thriving in this big data era to address problems arising in many fields where massive data sequences are collected to study complicated phenomena over time. It plays an important role in processing these data by…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
The mean resolvent operator predicts, in the frequency domain, the mean linear response to forcing. As such, it provides the optimal linear time-invariant approximation of the input-output dynamics of time-varying flows in the statistically…
Purpose: Proton therapy provides superior dose conformity compared to photon therapy, but its treatment planning is challenged by sensitivity to anatomical changes, setup/range uncertainties, and computational complexity. This review…
Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many…