Related papers: Adjoint approach to calculating shape gradients fo…
To increase the predictive power of a model, one needs to estimate its unknown parameters. Almost all parameter estimation techniques in ordinary differential equation models suffer from either a small convergence region or enormous…
Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyze this dependence using multiple machine learning methods and a dataset of > 200,000 nonlinear simulations of…
A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We show that in-plane-magnetic-field assisted spectroscopy allows extraction of the in-plane orientation and full 3D shape of the quantum mechanical orbitals of a single electron GaAs lateral quantum dot with sub-nm precision. The method is…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable…
A full three-dimensional model for the calculation of the electronic structure of semiconductor quantum dots (QD) and molecules (QDM) grown on high index surfaces and/or in the presence of an external magnetic field is presented. The strain…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
Strong Alfv\'enic turbulence develops eddy-like motions perpendicular to the local direction of magnetic fields. This local alignment induces velocity gradients perpendicular to the local direction of the magnetic field. We use this fact to…
Differentiable rendering aims to compute the derivative of the image rendering function with respect to the rendering parameters. This paper presents a novel algorithm for 6-DoF pose estimation through gradient-based optimization using a…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has…
This paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a…
Vertical excursion fixed-field alternating gradient accelerators can be designed with tunes that are invariant with respect to momentum and trajectories that are scaled images of each other displaced only in the vertical direction. This is…
We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic…
This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…
Correlation between orbital structure and magnetic ordering in bilayered manganites is examined. A level separation between the $3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$ orbitals in a Mn ion is calculated in the ionic model for a large number of…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…