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Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in…

Emerged as a biology-inspired method, Spiking Neural Networks (SNNs) mimic the spiking nature of brain neurons and have received lots of research attention. SNNs deal with binary spikes as their activation and therefore derive extreme…

Algorithm unrolling has emerged as a learning-based optimization paradigm that unfolds truncated iterative algorithms in trainable neural-network optimizers. We introduce Stochastic UnRolled Federated learning (SURF), a method that expands…

Inspired by our previous work on mitigating the Kolmogorov barrier using a quadratic approximation manifold, we propose in this paper a computationally tractable approach for combining a projection-based reduced-order model (PROM) and an…

The following work presents a generalized (extended) finite element formulation for the advection-diffusion equation. Using enrichment functions that represent the exponential nature of the exact solution, smooth numerical solutions are…

This paper deals with the following important research questions. Is it possible to solve challenging advection-dominated diffusion problems in one and two dimensions using Physics Informed Neural Networks (PINN) and Variational Physics…

Adder Neural Networks (ANNs) which only contain additions bring us a new way of developing deep neural networks with low energy consumption. Unfortunately, there is an accuracy drop when replacing all convolution filters by adder filters.…

A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…

We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…

We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…

Supervised classification is the most active and emerging research trends in today's scenario. In this view, Artificial Neural Network (ANN) techniques have been widely employed and growing interest to the researchers day by day. ANN…

Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network…

The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…

We develop the Randomized Neural Networks with Petrov-Galerkin Methods (RNN-PG methods) to solve linear elasticity problems. RNN-PG methods use Petrov-Galerkin variational framework, where the solution is approximated by randomized neural…

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements,…

Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…

Sign Gradient Descent (SignGD) is a simple yet robust optimization method, widely used in machine learning for its resilience to gradient noise and compatibility with low-precision computations. While its empirical performance is well…

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…