Related papers: The Adjoint Method Applied to Time-Distance Helios…

The parent paper to this Addendum describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. In that paper, we show that Voigt function derivatives can be calculated…

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is…

Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total…

A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative,…

We propose a strategy for optimizing a sensor trajectory in order to estimate the time dependence of a localized scalar source in turbulent channel flow. The approach leverages the view of the adjoint scalar field as the sensitivity of…

Deconvolving ("unfolding'') detector distortions is a critical step in the comparison of cross section measurements with theoretical predictions in particle and nuclear physics. However, most existing approaches require histogram binning…

We introduce a quasi-geostrophic model of core dynamics, which aims at describing core processes on geomagnetic secular variation timescales. It extends the formalism of Alfv\'en torsional oscillations by incorporating non-zonal motions.…

We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward…

With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications…

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…

In this paper, I will introduce a new form of regression, that can adjust overfitting and underfitting through, "distance-based regression." Overfitting often results in finding false patterns causing inaccurate results, so by having a new…

Many physical systems exhibit limit cycle oscillations induced by Hopf bifurcations. In aerospace engineering, limit cycle oscillations arise from undesirable Hopf bifurcation phenomena such as aeroelastic flutter and transonic buffet. In…

For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…

Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values…

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…

We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, namely the shallow water equations, in an effort to recover the…

The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the…

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

The article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the…