Related papers: Adjoint approach to calculating shape gradients fo…
This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes the gradient approximately by solving the corresponding…
A novel 3D shape classification scheme, based on collaborative representation learning, is investigated in this work. A data-driven feature-extraction procedure, taking the form of a simple projection operator, is in the core of our…
We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem…
We present improvements of a recently introduced numerical method [Arrigoni etal, Phys. Rev. Lett. 110, 086403 (2013)] to compute steady state properties of strongly correlated electronic systems out of equilibrium. The method can be…
Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…
Integrated gradients are widely employed to evaluate the contribution of input features in classification models because it satisfies the axioms for attribution of prediction. This method, however, requires an appropriate baseline for…
In this paper we derive aggregate separation bounds, named after Davenport-Mahler-Mignotte (\dmm), on the isolated roots of polynomial systems, specifically on the minimum distance between any two such roots. The bounds exploit the…
We investigate the effect of external magnetic fields on equilibration in the improved holographic QCD theory in the deconfined phase using the AdS/CFT correspondence. In particular we calculate the quasinormal mode spectra in the…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective…
An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…
Directly parameterizing and learning gradients of functions has widespread significance, with specific applications in inverse problems, generative modeling, and optimal transport. This paper introduces gradient networks (GradNets): novel…
We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…
The effect of an external guide field on the turbulence-like properties of magnetic reconnection is studied using five different 2.5D kinetic particle-in-cell (PIC) simulations. The magnetic energy spectrum is found to exhibit a slope of…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
We explain how to compute gradients of functions of the form $G = \frac{1}{2} \sum_{i=1}^{m} (E y_i - C_i)^2$, which often appear in the calibration of stochastic models, using Automatic Adjoint Differentiation and parallelization. We…
We consider the optimization of a neural network previously developed by the authors for the joint inversion of 3D gravitational and magnetic fields in the context of mineral exploration. The distinctive feature of this neural network is…
The purpose of this study is to show some mathematical aspects of the adjoint method that is a numerical method for the Cauchy problem, an inverse boundary value problem. The adjoint method is an iterative method based on the variational…
The intrinsic magnetic fields of exoplanets affect the structure of their atmospheres and plasmaspheres and, therefore, the observational manifestations of transit absorptions. This work proposes a new method for constraining the presence…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…