Ken Trotti

Andrea Angino, Ken Trotti, Diego Ulisse Pizzagalli et al.

Gaseous microemboli (GME) represent a common complication of cardiac structural interventions across both surgical and transcatheter approaches. Transthoracic cardiac ultrasound imaging represents a convenient methodology to visualize the presence of circulating GME. However, their detection and quantification are far from trivial due to operator-dependent view, high velocity, and objects with similar structure in the background. Here, we propose an approach based on a 2.5D U-Net architecture to segment GME in space-time connected data. Such an approach yields robust detection against the background and high segmentation accuracy while retaining real-time execution speed. These properties facilitated the integration of the proposed pipeline into patient-monitoring surgical protocols, providing the quantification of GME area over time.

Andrea Angino, Bindi Çapriqi, Shega Likaj et al.

Training deep neural networks at scale can benefit from domain decomposition, where the network is split into subdomains trained in parallel and coupled by a global trust-region mechanism. Building on the Additively Preconditioned Trust-Region Strategy (APTS), we propose a non-monotone variant with a nonlinear additive Schwarz preconditioner that combines parallel subdomain corrections with global coarse-space directions. A windowed acceptance criterion allows controlled objective increases, avoiding needless rejection of effective coarse steps. The resulting non-monotone APTS (NAPTS) preserves accuracy while reducing CPU time by 30\% and cutting rejected steps to one third of those in APTS.

Ken Trotti, Samuel A. Cruz Alegría, Alena Kopaničáková et al.

We propose to train neural networks (NNs) using a novel variant of the ``Additively Preconditioned Trust-region Strategy'' (APTS). The proposed method is based on a parallelizable additive domain decomposition approach applied to the neural network's parameters. Built upon the TR framework, the APTS method ensures global convergence towards a minimizer. Moreover, it eliminates the need for computationally expensive hyper-parameter tuning, as the TR algorithm automatically determines the step size in each iteration. We demonstrate the capabilities, strengths, and limitations of the proposed APTS training method by performing a series of numerical experiments. The presented numerical study includes a comparison with widely used training methods such as SGD, Adam, LBFGS, and the standard TR method.

Samuel A. Cruz Alegría, Ken Trotti, Alena Kopaničáková et al.

Parallel training methods are increasingly relevant in machine learning (ML) due to the continuing growth in model and dataset sizes. We propose a variant of the Additively Preconditioned Trust-Region Strategy (APTS) for training deep neural networks (DNNs). The proposed APTS method utilizes a data-parallel approach to construct a nonlinear preconditioner employed in the nonlinear optimization strategy. In contrast to the common employment of Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), which are both variants of gradient descent (GD) algorithms, the APTS method implicitly adjusts the step sizes in each iteration, thereby removing the need for costly hyperparameter tuning. We demonstrate the performance of the proposed APTS variant using the MNIST and CIFAR-10 datasets. The results obtained indicate that the APTS variant proposed here achieves comparable validation accuracy to SGD and Adam, all while allowing for parallel training and obviating the need for expensive hyperparameter tuning.