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Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic…
Field inversion and machine learning are implemented in this study to describe three-dimensional separation flow around an axisymmetric hill and augment the Spart-Allmaras model. The discrete adjoint method is used to solve the field…
Sinusoidal parameter estimation is a fundamental task in applications from spectral analysis to time-series forecasting. Estimating the sinusoidal frequency parameter by gradient descent is, however, often impossible as the error function…
The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a…
It is of crucial importance to be able to identify the location of atmospheric pollution sources in our planet. Global models of atmospheric transport in combination with diverse Earth observing systems are a natural choice to achieve this…
Quantitative imaging of sub-surface Earth's properties in elastic media is performed from Distributed Acoustic Sensing data. A new misfit functional based upon the reciprocity-gap is designed, taking cross-correlations of displacement and…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice,…
We study the conjugate gradient method for solving s system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
Using recently developed adjoint methods for computing the shape derivatives of functions that depend on MHD equilibria (Antonsen et al. 2019; Paul et al. 2020), we present the first example of analytic gradient-based optimization of…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Metabolic flux analysis using 13C labeled substrates is an important tool for metabolic engineering. Although it has now been evolving for more than ten years, metabolic flux analysis has still not reached the limits of its application.…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…
The goal of this paper is to give a comprehensive and short review on how to compute the first and second order topological derivative and potentially higher order topological derivatives for PDE constrained shape functionals. We employ the…
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a…
We present an optimization framework for photo-acoustic tomography of brain based on a system of coupled equations that describe the propagation of sound waves in linear isotropic inhomogeneous and lossy elastic media with the absorption…
It is well known that we need to choose the hyper-parameters in Momentum, AdaGrad, AdaDelta, and other alternative stochastic optimizers. While in many cases, the hyper-parameters are tuned tediously based on experience becoming more of an…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…