Related papers: Merging automatic differentiation and the adjoint …
Neural ordinary differential equations (NODEs) have recently attracted increasing attention; however, their empirical performance on benchmark tasks (e.g. image classification) are significantly inferior to discrete-layer models. We…
The inverse design of photonic integrated circuits (PICs) presents distinctive computational challenges, including their large memory requirements. Advancements in the two-photon polymerization (2PP) fabrication process introduce additional…
High-contrast imaging instruments need extreme wavefront control to directly image exoplanets. This requires highly sensitive wavefront sensors which optimally make use of the available photons to sense the wavefront. Here, we propose to…
Image registration has traditionally been done using two distinct approaches: learning based methods, relying on robust deep neural networks, and optimization-based methods, applying complex mathematical transformations to warp images…
Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where…
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…
Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared to finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions…
End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…
In the optimization of turbomachinery components, shape sensitivities for fluid dynamical objective functions have been used for a long time. As peak stress is not a differential func- tional of the shape, such highly efficient procedures…
Adjoint field methods are both elegant and efficient for calculating sensitivity information required across a wide range of physics-based inverse problems. Here we provide a unified approach to the derivation of such methods for problems…
Model Agnostic Meta Learning (MAML) is widely used to find a good initialization for a family of tasks. Despite its success, a critical challenge in MAML is to calculate the gradient w.r.t. the initialization of a long training trajectory…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
The alternating direction method of multipliers (ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable…
Metasurfaces provide the disruptive technology enabling miniaturization of complex cascades of optical elements on a plane. We leverage the benefits of such a surface to develop a planar integrated photonic beam collimator for on-chip…
We derive methods to compute higher order differentials (Hessians and Hessian-vector products) of the rendering operator. Our approach is based on importance sampling of a convolution that represents the differentials of rendering…
Integrated photonics computing has emerged as a promising approach to overcome the limitations of electronic processors in the post-Moore era, capitalizing on the superiority of photonic systems. However, present integrated photonics…
Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…
In this work we propose an efficient stochastic plug-and-play (PnP) algorithm for imaging inverse problems. The PnP stochastic gradient descent methods have been recently proposed and shown improved performance in some imaging applications…
This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are…